problem solving of scientific method

What is the Scientific Method: How does it work and why is it important?

The scientific method is a systematic process involving steps like defining questions, forming hypotheses, conducting experiments, and analyzing data. It minimizes biases and enables replicable research, leading to groundbreaking discoveries like Einstein's theory of relativity, penicillin, and the structure of DNA. This ongoing approach promotes reason, evidence, and the pursuit of truth in science.

Updated on November 18, 2023

Beginning in elementary school, we are exposed to the scientific method and taught how to put it into practice. As a tool for learning, it prepares children to think logically and use reasoning when seeking answers to questions.

Rather than jumping to conclusions, the scientific method gives us a recipe for exploring the world through observation and trial and error. We use it regularly, sometimes knowingly in academics or research, and sometimes subconsciously in our daily lives.

In this article we will refresh our memories on the particulars of the scientific method, discussing where it comes from, which elements comprise it, and how it is put into practice. Then, we will consider the importance of the scientific method, who uses it and under what circumstances.

What is the scientific method?

The scientific method is a dynamic process that involves objectively investigating questions through observation and experimentation . Applicable to all scientific disciplines, this systematic approach to answering questions is more accurately described as a flexible set of principles than as a fixed series of steps.

The following representations of the scientific method illustrate how it can be both condensed into broad categories and also expanded to reveal more and more details of the process. These graphics capture the adaptability that makes this concept universally valuable as it is relevant and accessible not only across age groups and educational levels but also within various contexts.

Steps in the scientific method

While the scientific method is versatile in form and function, it encompasses a collection of principles that create a logical progression to the process of problem solving:

• Define a question : Constructing a clear and precise problem statement that identifies the main question or goal of the investigation is the first step. The wording must lend itself to experimentation by posing a question that is both testable and measurable.
• Gather information and resources : Researching the topic in question to find out what is already known and what types of related questions others are asking is the next step in this process. This background information is vital to gaining a full understanding of the subject and in determining the best design for experiments. 
• Form a hypothesis : Composing a concise statement that identifies specific variables and potential results, which can then be tested, is a crucial step that must be completed before any experimentation. An imperfection in the composition of a hypothesis can result in weaknesses to the entire design of an experiment.
• Perform the experiments : Testing the hypothesis by performing replicable experiments and collecting resultant data is another fundamental step of the scientific method. By controlling some elements of an experiment while purposely manipulating others, cause and effect relationships are established.
• Analyze the data : Interpreting the experimental process and results by recognizing trends in the data is a necessary step for comprehending its meaning and supporting the conclusions. Drawing inferences through this systematic process lends substantive evidence for either supporting or rejecting the hypothesis.
• Report the results : Sharing the outcomes of an experiment, through an essay, presentation, graphic, or journal article, is often regarded as a final step in this process. Detailing the project's design, methods, and results not only promotes transparency and replicability but also adds to the body of knowledge for future research.
• Retest the hypothesis : Repeating experiments to see if a hypothesis holds up in all cases is a step that is manifested through varying scenarios. Sometimes a researcher immediately checks their own work or replicates it at a future time, or another researcher will repeat the experiments to further test the hypothesis.

Where did the scientific method come from?

Oftentimes, ancient peoples attempted to answer questions about the unknown by:

• Making simple observations
• Discussing the possibilities with others deemed worthy of a debate
• Drawing conclusions based on dominant opinions and preexisting beliefs

For example, take Greek and Roman mythology. Myths were used to explain everything from the seasons and stars to the sun and death itself.

However, as societies began to grow through advancements in agriculture and language, ancient civilizations like Egypt and Babylonia shifted to a more rational analysis for understanding the natural world. They increasingly employed empirical methods of observation and experimentation that would one day evolve into the scientific method . 

In the 4th century, Aristotle, considered the Father of Science by many, suggested these elements , which closely resemble the contemporary scientific method, as part of his approach for conducting science:

• Study what others have written about the subject.
• Look for the general consensus about the subject.
• Perform a systematic study of everything even partially related to the topic.

By continuing to emphasize systematic observation and controlled experiments, scholars such as Al-Kindi and Ibn al-Haytham helped expand this concept throughout the Islamic Golden Age . 

In his 1620 treatise, Novum Organum , Sir Francis Bacon codified the scientific method, arguing not only that hypotheses must be tested through experiments but also that the results must be replicated to establish a truth. Coming at the height of the Scientific Revolution, this text made the scientific method accessible to European thinkers like Galileo and Isaac Newton who then put the method into practice.

As science modernized in the 19th century, the scientific method became more formalized, leading to significant breakthroughs in fields such as evolution and germ theory. Today, it continues to evolve, underpinning scientific progress in diverse areas like quantum mechanics, genetics, and artificial intelligence.

Why is the scientific method important?

The history of the scientific method illustrates how the concept developed out of a need to find objective answers to scientific questions by overcoming biases based on fear, religion, power, and cultural norms. This still holds true today.

By implementing this standardized approach to conducting experiments, the impacts of researchers’ personal opinions and preconceived notions are minimized. The organized manner of the scientific method prevents these and other mistakes while promoting the replicability and transparency necessary for solid scientific research.

The importance of the scientific method is best observed through its successes, for example: 

• “ Albert Einstein stands out among modern physicists as the scientist who not only formulated a theory of revolutionary significance but also had the genius to reflect in a conscious and technical way on the scientific method he was using.” Devising a hypothesis based on the prevailing understanding of Newtonian physics eventually led Einstein to devise the theory of general relativity .
• Howard Florey “Perhaps the most useful lesson which has come out of the work on penicillin has been the demonstration that success in this field depends on the development and coordinated use of technical methods.” After discovering a mold that prevented the growth of Staphylococcus bacteria, Dr. Alexander Flemimg designed experiments to identify and reproduce it in the lab, thus leading to the development of penicillin .
• James D. Watson “Every time you understand something, religion becomes less likely. Only with the discovery of the double helix and the ensuing genetic revolution have we had grounds for thinking that the powers held traditionally to be the exclusive property of the gods might one day be ours. . . .” By using wire models to conceive a structure for DNA, Watson and Crick crafted a hypothesis for testing combinations of amino acids, X-ray diffraction images, and the current research in atomic physics, resulting in the discovery of DNA’s double helix structure .

Final thoughts

As the cases exemplify, the scientific method is never truly completed, but rather started and restarted. It gave these researchers a structured process that was easily replicated, modified, and built upon. 

While the scientific method may “end” in one context, it never literally ends. When a hypothesis, design, methods, and experiments are revisited, the scientific method simply picks up where it left off. Each time a researcher builds upon previous knowledge, the scientific method is restored with the pieces of past efforts.

By guiding researchers towards objective results based on transparency and reproducibility, the scientific method acts as a defense against bias, superstition, and preconceived notions. As we embrace the scientific method's enduring principles, we ensure that our quest for knowledge remains firmly rooted in reason, evidence, and the pursuit of truth.

The AJE Team

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What Is the Scientific Method?

The scientific method is a systematic way of conducting experiments or studies so that you can explore the things you observe in the world and answer questions about them. The scientific method, also known as the hypothetico-deductive method, is a series of steps that can help you accurately describe the things you observe or improve your understanding of them.

Ultimately, your goal when you use the scientific method is to:

• Find a cause-and-effect relationship by asking a question about something you observed
• Collect as much evidence as you can about what you observed, as this can help you explore the connection between your evidence and what you observed
• Determine if all your evidence can be combined to answer your question in a way that makes sense

Francis Bacon and René Descartes are usually credited with formalizing the process in the 16th and 17th centuries. The two philosophers argued that research shouldn’t be guided by preset metaphysical ideas of how reality works. They supported the use of inductive reasoning to come up with hypotheses and understand new things about reality.

Scientific Method Steps

The scientific method is a step-by-step problem-solving process. These steps include:

Observe the world around you. This will help you come up with a topic you are interested in and want to learn more about. In many cases, you already have a topic in mind because you have a related question for which you couldn't find an immediate answer.

Either way, you'll start the process by finding out what people before you already know about the topic, as well as any questions that people are still asking about. You may need to look up and read books and articles from academic journals or talk to other people so that you understand as much as you possibly can about your topic. This will help you with your next step.

Ask questions. Asking questions about what you observed and learned from reading and talking to others can help you figure out what the "problem" is. Scientists try to ask questions that are both interesting and specific and can be answered with the help of a fairly easy experiment or series of experiments. Your question should have one part (called a variable) that you can change in your experiment and another variable that you can measure. Your goal is to design an experiment that is a "fair test," which is when all the conditions in the experiment are kept the same except for the one you change (called the experimental or independent variable).

Form a hypothesis and make predictions based on it.  A hypothesis is an educated guess about the relationship between two or more variables in your question. A good hypothesis lets you predict what will happen when you test it in an experiment. Another important feature of a good hypothesis is that, if the hypothesis is wrong, you should be able to show that it's wrong. This is called falsifiability. If your experiment shows that your prediction is true, then your hypothesis is supported by your data.

Test your prediction by doing an experiment or making more observations.  The way you test your prediction depends on what you are studying. The best support comes from an experiment, but in some cases, it's too hard or impossible to change the variables in an experiment. Sometimes, you may need to do descriptive research where you gather more observations instead of doing an experiment. You will carefully gather notes and measurements during your experiments or studies, and you can share them with other people interested in the same question as you. Ideally, you will also repeat your experiment a couple more times because it's possible to get a result by chance, but it's less possible to get the same result more than once by chance.

Draw a conclusion. You will analyze what you already know about your topic from your literature research and the data gathered during your experiment. This will help you decide if the conclusion you draw from your data supports or contradicts your hypothesis. If your results contradict your hypothesis, you can use this observation to form a new hypothesis and make a new prediction. This is why scientific research is ongoing and scientific knowledge is changing all the time. It's very common for scientists to get results that don't support their hypotheses. In fact, you sometimes learn more about the world when your experiments don't support your hypotheses because it leads you to ask more questions. And this time around, you already know that one possible explanation is likely wrong.

Use your results to guide your next steps (iterate). For instance, if your hypothesis is supported, you may do more experiments to confirm it. Or you could come up with a hypothesis about why it works this way and design an experiment to test that. If your hypothesis is not supported, you can come up with another hypothesis and do experiments to test it. You'll rarely get the right hypothesis in one go. Most of the time, you'll have to go back to the hypothesis stage and try again. Every attempt offers you important information that helps you improve your next round of questions, hypotheses, and predictions.

Share your results. Scientific research isn't something you can do on your own; you must work with other people to do it.   You may be able to do an experiment or a series of experiments on your own, but you can't come up with all the ideas or do all the experiments by yourself .

Scientists and researchers usually share information by publishing it in a scientific journal or by presenting it to their colleagues during meetings and scientific conferences. These journals are read and the conferences are attended by other researchers who are interested in the same questions. If there's anything wrong with your hypothesis, prediction, experiment design, or conclusion, other researchers will likely find it and point it out to you.

It can be scary, but it's a critical part of doing scientific research. You must let your research be examined by other researchers who are as interested and knowledgeable about your question as you. This process helps other researchers by pointing out hypotheses that have been proved wrong and why they are wrong. It helps you by identifying flaws in your thinking or experiment design. And if you don't share what you've learned and let other people ask questions about it, it's not helpful to your or anyone else's understanding of what happens in the world.

Scientific Method Example

Here's an everyday example of how you can apply the scientific method to understand more about your world so you can solve your problems in a helpful way.

Let's say you put slices of bread in your toaster and press the button, but nothing happens. Your toaster isn't working, but you can't afford to buy a new one right now. You might be able to rescue it from the trash can if you can figure out what's wrong with it. So, let's figure out what's wrong with your toaster.

Observation. Your toaster isn't working to toast your bread.

Ask a question. In this case, you're asking, "Why isn't my toaster working?" You could even do a bit of preliminary research by looking in the owner's manual for your toaster. The manufacturer has likely tested your toaster model under many conditions, and they may have some ideas for where to start with your hypothesis.

Form a hypothesis and make predictions based on it. Your hypothesis should be a potential explanation or answer to the question that you can test to see if it's correct. One possible explanation that we could test is that the power outlet is broken. Our prediction is that if the outlet is broken, then plugging it into a different outlet should make the toaster work again.

Test your prediction by doing an experiment or making more observations. You plug the toaster into a different outlet and try to toast your bread.

If that works, then your hypothesis is supported by your experimental data. Results that support your hypothesis don't prove it right; they simply suggest that it's a likely explanation. This uncertainty arises because, in the real world, we can't rule out the possibility of mistakes, wrong assumptions, or weird coincidences affecting the results. If the toaster doesn’t work even after plugging it into a different outlet, then your hypothesis is not supported and it's likely the wrong explanation.

Use your results to guide your next steps (iteration). If your toaster worked, you may decide to do further tests to confirm it or revise it. For example, you could plug something else that you know is working into the first outlet to see if that stops working too. That would be further confirmation that your hypothesis is correct.

If your toaster failed to toast when plugged into the second outlet, you need a new hypothesis. For example, your next hypothesis might be that the toaster has a shorted wire. You could test this hypothesis directly if you have the right equipment and training, or you could take it to a repair shop where they could test that hypothesis for you.

Share your results. For this everyday example, you probably wouldn't want to write a paper, but you could share your problem-solving efforts with your housemates or anyone you hire to repair your outlet or help you test if the toaster has a short circuit.

What the Scientific Method Is Used For

The scientific method is useful whenever you need to reason logically about your questions and gather evidence to support your problem-solving efforts. So, you can use it in everyday life to answer many of your questions; however, when most people think of the scientific method, they likely think of using it to:

Describe how nature works . It can be hard to accurately describe how nature works because it's almost impossible to account for every variable that's involved in a natural process. Researchers may not even know about many of the variables that are involved. In some cases, all you can do is make assumptions. But you can use the scientific method to logically disprove wrong assumptions by identifying flaws in the reasoning.

Do scientific research in a laboratory to develop things such as new medicines.

Develop critical thinking skills.  Using the scientific method may help you develop critical thinking in your daily life because you learn to systematically ask questions and gather evidence to find answers. Without logical reasoning, you might be more likely to have a distorted perspective or bias. Bias is the inclination we all have to favor one perspective (usually our own) over another.

The scientific method doesn't perfectly solve the problem of bias, but it does make it harder for an entire field to be biased in the same direction. That's because it's unlikely that all the people working in a field have the same biases. It also helps make the biases of individuals more obvious because if you repeatedly misinterpret information in the same way in multiple experiments or over a period, the other people working on the same question will notice. If you don't correct your bias when others point it out to you, you'll lose your credibility. Other people might then stop believing what you have to say.

Why Is the Scientific Method Important?

When you use the scientific method, your goal is to do research in a fair, unbiased, and repeatable way. The scientific method helps meet these goals because:

It's a systematic approach to problem-solving. It can help you figure out where you're going wrong in your thinking and research if you're not getting helpful answers to your questions. Helpful answers solve problems and keep you moving forward. So, a systematic approach helps you improve your problem-solving abilities if you get stuck.

It can help you solve your problems.  The scientific method helps you isolate problems by focusing on what's important. In addition, it can help you make your solutions better every time you go through the process.

It helps you eliminate (or become aware of) your personal biases.  It can help you limit the influence of your own personal, preconceived notions . A big part of the process is considering what other people already know and think about your question. It also involves sharing what you've learned and letting other people ask about your methods and conclusions. At the end of the process, even if you still think your answer is best, you have considered what other people know and think about the question.

The scientific method is a systematic way of conducting experiments or studies so that you can explore the world around you and answer questions using reason and evidence. It's a step-by-step problem-solving process that involves: (1) observation, (2) asking questions, (3) forming hypotheses and making predictions, (4) testing your hypotheses through experiments or more observations, (5) using what you learned through experiment or observation to guide further investigation, and (6) sharing your results.

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scientific method

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• University of Nevada, Reno - College of Agriculture, Biotechnology and Natural Resources Extension - The Scientific Method
• World History Encyclopedia - Scientific Method
• LiveScience - What Is Science?
• Verywell Mind - Scientific Method Steps in Psychology Research
• WebMD - What is the Scientific Method?
• Chemistry LibreTexts - The Scientific Method
• National Center for Biotechnology Information - PubMed Central - Redefining the scientific method: as the use of sophisticated scientific methods that extend our mind
• Khan Academy - The scientific method
• Simply Psychology - What are the steps in the Scientific Method?
• Stanford Encyclopedia of Philosophy - Scientific Method

scientific method , mathematical and experimental technique employed in the sciences . More specifically, it is the technique used in the construction and testing of a scientific hypothesis .

The process of observing, asking questions, and seeking answers through tests and experiments is not unique to any one field of science. In fact, the scientific method is applied broadly in science, across many different fields. Many empirical sciences, especially the social sciences , use mathematical tools borrowed from probability theory and statistics , together with outgrowths of these, such as decision theory , game theory , utility theory, and operations research . Philosophers of science have addressed general methodological problems, such as the nature of scientific explanation and the justification of induction .

The scientific method is critical to the development of scientific theories , which explain empirical (experiential) laws in a scientifically rational manner. In a typical application of the scientific method, a researcher develops a hypothesis , tests it through various means, and then modifies the hypothesis on the basis of the outcome of the tests and experiments. The modified hypothesis is then retested, further modified, and tested again, until it becomes consistent with observed phenomena and testing outcomes. In this way, hypotheses serve as tools by which scientists gather data. From that data and the many different scientific investigations undertaken to explore hypotheses, scientists are able to develop broad general explanations, or scientific theories.

See also Mill’s methods ; hypothetico-deductive method .

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The 6 Scientific Method Steps and How to Use Them

General Education

When you’re faced with a scientific problem, solving it can seem like an impossible prospect. There are so many possible explanations for everything we see and experience—how can you possibly make sense of them all? Science has a simple answer: the scientific method.

The scientific method is a method of asking and answering questions about the world. These guiding principles give scientists a model to work through when trying to understand the world, but where did that model come from, and how does it work?

In this article, we’ll define the scientific method, discuss its long history, and cover each of the scientific method steps in detail.

What Is the Scientific Method?

At its most basic, the scientific method is a procedure for conducting scientific experiments. It’s a set model that scientists in a variety of fields can follow, going from initial observation to conclusion in a loose but concrete format.

The number of steps varies, but the process begins with an observation, progresses through an experiment, and concludes with analysis and sharing data. One of the most important pieces to the scientific method is skepticism —the goal is to find truth, not to confirm a particular thought. That requires reevaluation and repeated experimentation, as well as examining your thinking through rigorous study.

There are in fact multiple scientific methods, as the basic structure can be easily modified.  The one we typically learn about in school is the basic method, based in logic and problem solving, typically used in “hard” science fields like biology, chemistry, and physics. It may vary in other fields, such as psychology, but the basic premise of making observations, testing, and continuing to improve a theory from the results remain the same.

The History of the Scientific Method

The scientific method as we know it today is based on thousands of years of scientific study. Its development goes all the way back to ancient Mesopotamia, Greece, and India.

The Ancient World

In ancient Greece, Aristotle devised an inductive-deductive process , which weighs broad generalizations from data against conclusions reached by narrowing down possibilities from a general statement. However, he favored deductive reasoning, as it identifies causes, which he saw as more important.

Aristotle wrote a great deal about logic and many of his ideas about reasoning echo those found in the modern scientific method, such as ignoring circular evidence and limiting the number of middle terms between the beginning of an experiment and the end. Though his model isn’t the one that we use today, the reliance on logic and thorough testing are still key parts of science today.

The Middle Ages

The next big step toward the development of the modern scientific method came in the Middle Ages, particularly in the Islamic world. Ibn al-Haytham, a physicist from what we now know as Iraq, developed a method of testing, observing, and deducing for his research on vision. al-Haytham was critical of Aristotle’s lack of inductive reasoning, which played an important role in his own research.

Other scientists, including Abū Rayhān al-Bīrūnī, Ibn Sina, and Robert Grosseteste also developed models of scientific reasoning to test their own theories. Though they frequently disagreed with one another and Aristotle, those disagreements and refinements of their methods led to the scientific method we have today.

Following those major developments, particularly Grosseteste’s work, Roger Bacon developed his own cycle of observation (seeing that something occurs), hypothesis (making a guess about why that thing occurs), experimentation (testing that the thing occurs), and verification (an outside person ensuring that the result of the experiment is consistent).

After joining the Franciscan Order, Bacon was granted a special commission to write about science; typically, Friars were not allowed to write books or pamphlets. With this commission, Bacon outlined important tenets of the scientific method, including causes of error, methods of knowledge, and the differences between speculative and experimental science. He also used his own principles to investigate the causes of a rainbow, demonstrating the method’s effectiveness.

Scientific Revolution

Throughout the Renaissance, more great thinkers became involved in devising a thorough, rigorous method of scientific study. Francis Bacon brought inductive reasoning further into the method, whereas Descartes argued that the laws of the universe meant that deductive reasoning was sufficient. Galileo’s research was also inductive reasoning-heavy, as he believed that researchers could not account for every possible variable; therefore, repetition was necessary to eliminate faulty hypotheses and experiments.

All of this led to the birth of the Scientific Revolution , which took place during the sixteenth and seventeenth centuries. In 1660, a group of philosophers and physicians joined together to work on scientific advancement. After approval from England’s crown , the group became known as the Royal Society, which helped create a thriving scientific community and an early academic journal to help introduce rigorous study and peer review.

Previous generations of scientists had touched on the importance of induction and deduction, but Sir Isaac Newton proposed that both were equally important. This contribution helped establish the importance of multiple kinds of reasoning, leading to more rigorous study.

As science began to splinter into separate areas of study, it became necessary to define different methods for different fields. Karl Popper was a leader in this area—he established that science could be subject to error, sometimes intentionally. This was particularly tricky for “soft” sciences like psychology and social sciences, which require different methods. Popper’s theories furthered the divide between sciences like psychology and “hard” sciences like chemistry or physics.

Paul Feyerabend argued that Popper’s methods were too restrictive for certain fields, and followed a less restrictive method hinged on “anything goes,” as great scientists had made discoveries without the Scientific Method. Feyerabend suggested that throughout history scientists had adapted their methods as necessary, and that sometimes it would be necessary to break the rules. This approach suited social and behavioral scientists particularly well, leading to a more diverse range of models for scientists in multiple fields to use.

The Scientific Method Steps

Though different fields may have variations on the model, the basic scientific method is as follows:

#1: Make Observations 

Notice something, such as the air temperature during the winter, what happens when ice cream melts, or how your plants behave when you forget to water them.

#2: Ask a Question

Turn your observation into a question. Why is the temperature lower during the winter? Why does my ice cream melt? Why does my toast always fall butter-side down?

This step can also include doing some research. You may be able to find answers to these questions already, but you can still test them!

#3: Make a Hypothesis

A hypothesis is an educated guess of the answer to your question. Why does your toast always fall butter-side down? Maybe it’s because the butter makes that side of the bread heavier.

A good hypothesis leads to a prediction that you can test, phrased as an if/then statement. In this case, we can pick something like, “If toast is buttered, then it will hit the ground butter-first.”

#4: Experiment

Your experiment is designed to test whether your predication about what will happen is true. A good experiment will test one variable at a time —for example, we’re trying to test whether butter weighs down one side of toast, making it more likely to hit the ground first.

The unbuttered toast is our control variable. If we determine the chance that a slice of unbuttered toast, marked with a dot, will hit the ground on a particular side, we can compare those results to our buttered toast to see if there’s a correlation between the presence of butter and which way the toast falls.

If we decided not to toast the bread, that would be introducing a new question—whether or not toasting the bread has any impact on how it falls. Since that’s not part of our test, we’ll stick with determining whether the presence of butter has any impact on which side hits the ground first.

#5: Analyze Data

After our experiment, we discover that both buttered toast and unbuttered toast have a 50/50 chance of hitting the ground on the buttered or marked side when dropped from a consistent height, straight down. It looks like our hypothesis was incorrect—it’s not the butter that makes the toast hit the ground in a particular way, so it must be something else.

Since we didn’t get the desired result, it’s back to the drawing board. Our hypothesis wasn’t correct, so we’ll need to start fresh. Now that you think about it, your toast seems to hit the ground butter-first when it slides off your plate, not when you drop it from a consistent height. That can be the basis for your new experiment.

#6: Communicate Your Results

Good science needs verification. Your experiment should be replicable by other people, so you can put together a report about how you ran your experiment to see if other peoples’ findings are consistent with yours.

This may be useful for class or a science fair. Professional scientists may publish their findings in scientific journals, where other scientists can read and attempt their own versions of the same experiments. Being part of a scientific community helps your experiments be stronger because other people can see if there are flaws in your approach—such as if you tested with different kinds of bread, or sometimes used peanut butter instead of butter—that can lead you closer to a good answer.

A Scientific Method Example: Falling Toast

We’ve run through a quick recap of the scientific method steps, but let’s look a little deeper by trying again to figure out why toast so often falls butter side down.

#1: Make Observations

At the end of our last experiment, where we learned that butter doesn’t actually make toast more likely to hit the ground on that side, we remembered that the times when our toast hits the ground butter side first are usually when it’s falling off a plate.

The easiest question we can ask is, “Why is that?”

We can actually search this online and find a pretty detailed answer as to why this is true. But we’re budding scientists—we want to see it in action and verify it for ourselves! After all, good science should be replicable, and we have all the tools we need to test out what’s really going on.

Why do we think that buttered toast hits the ground butter-first? We know it’s not because it’s heavier, so we can strike that out. Maybe it’s because of the shape of our plate?

That’s something we can test. We’ll phrase our hypothesis as, “If my toast slides off my plate, then it will fall butter-side down.”

Just seeing that toast falls off a plate butter-side down isn’t enough for us. We want to know why, so we’re going to take things a step further—we’ll set up a slow-motion camera to capture what happens as the toast slides off the plate.

We’ll run the test ten times, each time tilting the same plate until the toast slides off. We’ll make note of each time the butter side lands first and see what’s happening on the video so we can see what’s going on.

When we review the footage, we’ll likely notice that the bread starts to flip when it slides off the edge, changing how it falls in a way that didn’t happen when we dropped it ourselves.

That answers our question, but it’s not the complete picture —how do other plates affect how often toast hits the ground butter-first? What if the toast is already butter-side down when it falls? These are things we can test in further experiments with new hypotheses!

Now that we have results, we can share them with others who can verify our results. As mentioned above, being part of the scientific community can lead to better results. If your results were wildly different from the established thinking about buttered toast, that might be cause for reevaluation. If they’re the same, they might lead others to make new discoveries about buttered toast. At the very least, you have a cool experiment you can share with your friends!

Key Scientific Method Tips

Though science can be complex, the benefit of the scientific method is that it gives you an easy-to-follow means of thinking about why and how things happen. To use it effectively, keep these things in mind!

Don’t Worry About Proving Your Hypothesis

One of the important things to remember about the scientific method is that it’s not necessarily meant to prove your hypothesis right. It’s great if you do manage to guess the reason for something right the first time, but the ultimate goal of an experiment is to find the true reason for your observation to occur, not to prove your hypothesis right.

Good science sometimes means that you’re wrong. That’s not a bad thing—a well-designed experiment with an unanticipated result can be just as revealing, if not more, than an experiment that confirms your hypothesis.

Be Prepared to Try Again

If the data from your experiment doesn’t match your hypothesis, that’s not a bad thing. You’ve eliminated one possible explanation, which brings you one step closer to discovering the truth.

The scientific method isn’t something you’re meant to do exactly once to prove a point. It’s meant to be repeated and adapted to bring you closer to a solution. Even if you can demonstrate truth in your hypothesis, a good scientist will run an experiment again to be sure that the results are replicable. You can even tweak a successful hypothesis to test another factor, such as if we redid our buttered toast experiment to find out whether different kinds of plates affect whether or not the toast falls butter-first. The more we test our hypothesis, the stronger it becomes!

What’s Next?

Want to learn more about the scientific method? These important high school science classes will no doubt cover it in a variety of different contexts.

Test your ability to follow the scientific method using these at-home science experiments for kids !

Need some proof that science is fun? Try making slime

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Chapter 6: Scientific Problem Solving

If you prefer a video, click this button:

Scientific Problem Solving Video

Science is a method to discover empirical truths and patterns. Roughly speaking, the scientific method consists of

1) Observing

2) Forming a hypothesis

3) Testing the hypothesis and

4) Interpreting the data to confirm or disconfirm the hypothesis.

The beauty of science is that any scientific claim can be tested if you have the proper knowledge and equipment.

You can also use the scientific method to solve everyday problems: 1) Observe and clearly define the problem, 2) Form a hypothesis, 3) Test it, and 4) Confirm the hypothesis... or disconfirm it and start over.

So, the next time you are cursing in traffic or emotionally reacting to a problem, take a few deep breaths and then use this rational and scientific approach. Slow down, observe, hypothesize, and test.

Explain how you would solve these problems using the four steps of the scientific process.

Example: The fire alarm is not working.

1) Observe/Define the problem: it does not beep when I push the button.

2) Hypothesis: it is caused by a dead battery.

3) Test: try a new battery.

4) Confirm/Disconfirm: the alarm now works. If it does not work, start over by testing another hypothesis like “it has a loose wire.”  

• My car will not start.
• My child is having problems reading.
• I owe $20,000, but only make $10 an hour.
• My boss is mean. I want him/her to stop using rude language towards me.
• My significant other is lazy. I want him/her to help out more.

6-8. Identify three problems where you can apply the scientific method.

*Answers will vary.

Application and Value

Science is more of a process than a body of knowledge. In our daily lives, we often emotionally react and jump to quick solutions when faced with problems, but following the four steps of the scientific process can help us slow down and discover more intelligent solutions.

In your study of philosophy, you will explore deeper questions about science. For example, are there any forms of knowledge that are nonscientific? Can science tell us what we ought to do? Can logical and mathematical truths be proven in a scientific way? Does introspection give knowledge even though I cannot scientifically observe your introspective thoughts? Is science truly objective?  These are challenging questions that should help you discover the scope of science without diminishing its awesome power.

But the first step in answering these questions is knowing what science is, and this chapter clarifies its essence. Again, Science is not so much a body of knowledge as it is a method of observing, hypothesizing, and testing. This method is what all the sciences have in common.

Perhaps too science should involve falsifiability, which is a concept explored in the next chapter.

Return to Logic Home                            Next (Chapter 7, Falsifiability)

Click on my affiliate link above (Logic Book Image) to explore the most popular introduction to logic. If you purchase it, I recommend buying a less expensive older edition.

Microbe Notes

Scientific Method: Definition, Steps, Examples, Uses

Sir Francis Bacon, an English philosopher, developed modern scientific research and scientific methods. He is also known as “the Father of modern science.”

He was influenced by Galileo Galilei and Nicholas Copernicus’ writings throughout his study.

The scientific method is a powerful analytical or problem-solving method of learning more about the natural world.  

The scientific method is a combined method, which consists of theoretical knowledge and practical experimentation by using scientific instruments, analysis and comparisons of results, and then peer reviews.

• The scientific method is a procedure that the scientists use to conduct research.
• Scientific investigators play a crucial role in following a series of steps such as asking questions, setting hypothesis to answer questions, performing multiple experiments to confirm the reliability of data/ results, data collection and interpretation, and developing conclusions based on the hypothesis.

Table of Contents

Interesting Science Videos

Steps of Scientific Method

There are seven steps of the scientific method such as:

• Make an observation
• Ask a question
• Background research/ Research the topic
• Formulate a hypothesis
• Conduct an experiment to test the hypothesis
• Data record and analysis
• Draw a conclusion

1. Make an observation

• Before asking a question, you need a proper observation to get information about some topic, which may help to identify the question. 
• Proper observation in the area of investigation or about something you are interested in is required, whether you recognize it or not. 

2. Ask a question

• The scientific method follows a step by asking a question. Based on what you observe, Asking questions starts with Wh- such as What, When, Who, Which, Why, How, Does or Where? 
• A question helps to identify a core problem and form a hypothesis . The question should be relatable and specific as much as possible. 
• Why is this thing happening?
• What is the reason behind this?
• How does this happen?
• Does it need to happen?

3. Background research/ Research the topic

• Background research on the experiment/ topic is necessary to analyze and answer the questions. 
• Many scientists are employing various techniques and equipment, such as libraries and Internet research (research papers, articles, journals, etc.), that push how to investigate, design, and understand the experiment. 
• In addition, you can learn from other experiences, research, or experiments, which helps you not repeat the same mistakes and be aware of doing things further. 
• It helps to predict what will happen in the future. It also helps to understand the theory and background history of the experiment.

4. Formulate a hypothesis

• A Hypothesis is an idea or a guess to explain a specific occurrence, natural event, or particular experience based on prior observation.
• It is another step in the scientific method. A hypothesis allows you to make a prediction. Scientists predict what will be the outcome. 
• It outlines the objectives of the experiment, the variables used, and the expected outcome of the experiment. The hypothesis must be either falsifiable or testable. It also answers the previous question. 
• A hypothesis needs to be testable by gathering evidence. A hypothesis needs to be testable to perform an experiment, whether the evidence supports the hypothesis or not. 

5. Conduct an experiment to test a hypothesis

• After formulating a hypothesis, you must design and conduct an experiment. Experiments are the process of investigations to prove or disprove the hypothesis.
• Two variables play a crucial role in conducting experiments to test the hypothesis. 
• They are Independent variables (Can be manipulated or controlled by the person, or you can change while experimenting) and dependent variables (one you measure, which may be affected by the independent variable).
• They both are the cause and effect. The dependent variable is dependent on the independent variable. 
• All the variables must be under control to ensure that they have no impact on the result.
• You can also set another type of hypothesis, such as a “null hypothesis” or “no difference” hypothesis. 

There is no difference in the intense rain and crop destruction.

6. Data Record and Analysis

• During the experiment, data needs to be recorded and collected. Data is a set of values. It should be represented quantitatively (measured in numbers) or qualitatively (an explanation of outcomes).
• After the data collection, you can interpret the data by drawing a chart or constructing a table or graph to show the result. 
• After the data representation, you can analyze or interpret the data to understand the meaning of the data. 
• You can compare the results with other experiments visually or in graphics form. 

7. Draw a Conclusion

• Your Conclusion always showcases whether the experiments support the prediction and hypothesis or contradict.
• Scientists will analyze the experiment’s results and develop a new hypothesis based on the data they collect if they discover that their experiment did not support their hypothesis or that their prediction is not supported.
• While we conclude the experiment, all the collected results will be analyzed, which helps to interpret the hypothesis.
• Did your experiments support or reject your hypothesis? 
• Does your hypothesis prove or disprove your study? 
• Did your results show a strong correlation? 
• Was there any way to change the thing to make a better experiment?
• Are there things that need to be studied further? 
• If your hypothesis is supported, then that is fine. You can carry on. 
• But If not, do not try to manipulate the result or try to change the result. 
• Keep the result to its original form, or you can further repeat the experiment to get better results.

Application of Scientific Method

• It is essential in many sectors, such as social sciences, empirical sciences, statistics, biology, chemistry, and physics. It can be used in the laboratory.
• Scientific methods lead to discoveries, innovations, and improvements in various disciplines.
• The scientific method can be used to solve problems, explain the phenomena of the study, and find and test solutions.
• Scientific methods guarantee that the findings are based on evidence, making the study reliable and replicable and allowing research to occur objectively and systematically.
• The Editors of Encyclopaedia Britannica. (2024, March 14). Scientific method | Definition, Steps, & Application. Retrieved from https://www.britannica.com/science/scientific-method
• Biology Dictionary. (2020, November 6). Scientific method. Retrieved from https://biologydictionary.net/scientific-method/
• Bailey, R. (2019, August 21). Scientific method. Retrieved from https://www.thoughtco.com/scientific-method-p2-373335
• Buddies, S., & Buddies, S. (2023, August 17). Writing a Science Fair Project research plan. Retrieved from https://www.sciencebuddies.org/science-fair-projects/science-fair/writing-a-science-fair-project-research-plan
• Buddies, S., & Buddies, S. (2024, January 25). Steps of the scientific method. Retrieved from https://www.sciencebuddies.org/science-fair-projects/science-fair/steps-of-the-scientific-method
• Helmenstine, A. (2023, January 1). Steps of the scientific method. Retrieved from https://sciencenotes.org/steps-scientific-method/
• Cartwright, M., & Greer, R. (2023). Scientific method. World History Encyclopedia . Retrieved from https://www.worldhistory.org/Scientific_Method/
• https://www.extension.purdue.edu/extmedia/ID/ID-507-w.pdf
• GeeksforGeeks. (2024, April 18). Applications of scientific methods. Retrieved from https://www.geeksforgeeks.org/applications-of-scientific-methods/

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Biology archive

Course: biology archive   >   unit 1, the scientific method.

• Controlled experiments
• The scientific method and experimental design

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation., 2. ask a question., 3. propose a hypothesis., 4. make predictions., 5. test the predictions..

• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

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Solving Everyday Problems with the Scientific Method

• By (author): 
• Don K Mak , 
• Angela T Mak , and 
• Anthony B Mak
• Add to favorites
• Download Citations
• Track Citations
• Recommend to Library
• Description
• Supplementary

This book describes how one can use The Scientific Method to solve everyday problems including medical ailments, health issues, money management, traveling, shopping, cooking, household chores, etc. It illustrates how to exploit the information collected from our five senses, how to solve problems when no information is available for the present problem situation, how to increase our chances of success by redefining a problem, and how to extrapolate our capabilities by seeing a relationship among heretofore unrelated concepts.

One should formulate a hypothesis as early as possible in order to have a sense of direction regarding which path to follow. Occasionally, by making wild conjectures, creative solutions can transpire. However, hypotheses need to be well-tested. Through this way, The Scientific Method can help readers solve problems in both familiar and unfamiliar situations. Containing real-life examples of how various problems are solved — for instance, how some observant patients cure their own illnesses when medical experts have failed — this book will train readers to observe what others may have missed and conceive what others may not have contemplated. With practice, they will be able to solve more problems than they could previously imagine.

In this second edition, the authors have added some more theories which they hope can help in solving everyday problems. At the same time, they have updated the book by including quite a few examples which they think are interesting.

Sample Chapter(s) Chapter 1: Prelude (63 KB)

• Preface to the Second Edition
• Preface to the First Edition
• The Scientific Method
• Observation
• Recognition
• Problem Situation and Problem Definition
• Induction and Deduction
• Alternative Solutions
• Mathematics
• Probable Value
• Bibliography

FRONT MATTER

• Pages: i–xvi

https://doi.org/10.1142/9789813145313_fmatter

• Claimers and Disclaimers

Chapter 1: Prelude

https://doi.org/10.1142/9789813145313_0001

The father put down the newspaper. It had been raining for the last two hours. The rain finally stopped, and the sky looked clear. After all this raining, the negative ions in the atmosphere would have increased, and the air would feel fresh. The father suggested the family of four should go for a stroll. There was a park just about fifteen minutes walk from their house.

Chapter 2: The Scientific Method

• Pages: 3–18

https://doi.org/10.1142/9789813145313_0002

In the history of philosophical ideation, scientific discoveries, and engineering inventions, it has almost never happened that a single person (or a single group of people) has come up with an idea or a similar idea that no one has ever dreamed of earlier, or at the same time. This person may not be aware of the previous findings, nor someone else in another part of the world has comparable ideas, and thus – his idea may be very original, as far as he is concerned. However, history tells us that it is highly unlikely that no one has already come up with some related concepts.

Chapter 3: Observation

• Pages: 19–56

https://doi.org/10.1142/9789813145313_0003

Observation is the first step of the Scientific Method. However, it can infiltrate the whole scientific process – from the initial perception of a phenomenon, to proposing a solution, and right down to experimentation, where observation of the results is significant.

Chapter 4: Hypothesis

• Pages: 57–95

https://doi.org/10.1142/9789813145313_0004

In scientific discipline, a hypothesis is a set of propositions set forth to explain the occurrence of certain phenomena. In daily language, a hypothesis can be interpreted as an assumption or guess. In this book, we employ both these definitions. Within the context of the first definition, we search for an explanation of why the problem occurs to begin with. Within the context of the second definition, we look for a plausible solution to the problem.

Chapter 5: Experiment

• Pages: 96–121

https://doi.org/10.1142/9789813145313_0005

In scientific discipline, an experiment is a test under controlled conditions to investigate the validity of a hypothesis. In everyday language, experiment can be interpreted as a testing of an idea. In this book, we employ both these definitions. Within the context of the first definition, we attempt to confirm whether an explanation of an observation is correct. Within the context of the second definition, we check whether a proposed idea for a solution is valid.

Chapter 6: Recognition

• Pages: 122–144

https://doi.org/10.1142/9789813145313_0006

Before we can solve any problem, we need to recognize that a problem exists in the first place. That may seem obvious, but while some problems stick out like thorns in a bush, others are hidden like plants in a forest. As such, not only do we need to tune up our observational skills to see that a problem does exist; we should also sharpen our thinking to anticipate that a problem may arise. Thus, recognition can be considered to be a combination of observing and hypothesizing.

Chapter 7: Problem Situation and Problem Definition

• Pages: 145–152

https://doi.org/10.1142/9789813145313_0007

For just about any situation, we can look at it from different perspectives. Take the example of a piece of rock, it will look different from the eyes of a landscaper, an architect, a geologist and an artist.

Chapter 8: Induction and Deduction

• Pages: 153–164

https://doi.org/10.1142/9789813145313_0008

Once a problem has been defined, we need to find a solution. To determine which route we can take, we will have to take a look at the knowledge that we already have in hand, and we may want to search for more information when necessary. It is therefore, much more convenient if we already have an arsenal of tools that have been stored neatly and categorized in our mind. That simply means, that we should have been observing our surroundings, and preferably have come up with some general principles that can guide us in the present problem.

Chapter 9: Alternative Solutions

• Pages: 165–193

https://doi.org/10.1142/9789813145313_0009

While there are various ways to view a problem situation, and thus define a problem differently, there are also different ways to solve a problem once it is defined. Some of the solutions may be better than others. If we have the option of not requiring to make a snap judgement, we should wait till we have come up with several plausible solutions, and then decide which one would be the best. How do we know which solution is the best? We will discuss that in the chapter on Probable Value. Generally speaking, we should train ourselves to come up with a few suggestions, and weigh the pros and cons of each resolution. This would be equivalent to coming up with different hypotheses, and judging which one would provide an optimal result.

Chapter 10: Relation

• Pages: 194–225

https://doi.org/10.1142/9789813145313_0010

Relation is the connection and association among different objects, events, and ideas. Problem solving, quite often, is connected with the ability to see the various relations among diversified concepts. Understanding the affiliation of a mixture of notions can be considered as hypothesizing the existence of certain correlation.

Chapter 11: Mathematics

• Pages: 226–306

https://doi.org/10.1142/9789813145313_0011

Mathematics, even some simple arithmetic, is so important in solving some of the everyday problems, that we think a whole chapter should be written on it.

Chapter 12: Probable Value

• Pages: 307–318

https://doi.org/10.1142/9789813145313_0012

For a certain problem, we may come up with several plausible solutions. Which path should we take? Each path would only have certain chance or probability of success in resolving the problem. If each path or solution has a different reward, we can define the probable value of each path to be the multiplication of the reward by the probability. We should, most likely, choose the path that has the highest probable value. (The term “probable value” is coined by us. The idea is appropriated from the term “expected value” in Statistics. In this sense, expected value can be considered as the sum of all probable values.).

Chapter 13: Epilogue

• Pages: 319–322

https://doi.org/10.1142/9789813145313_0013

We run into problems every day. Even when we do not encounter any problems, it does not mean that they do not exist. Sometimes, we wish we could be able to recognize them earlier. The scientific method of observation, hypothesis, and experiment can help us recognize, define, and solve our problems.

BACK MATTER

• Pages: 323–332

https://doi.org/10.1142/9789813145313_bmatter

Praise for the First Edition:

“The book was fun: a clever and entertaining introduction to basic logical thinking and maths.”

“This ingenious and entertaining volume should be useful to anyone in the general public interested in self-help books; undergraduate students majoring in education or behavioral psychology; and graduates and researchers interested in problem-solving, creativity, and scientific research methodology.”

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Scientific Methods

What is scientific method.

The Scientific method is a process with the help of which scientists try to investigate, verify, or construct an accurate and reliable version of any natural phenomena. They are done by creating an objective framework for the purpose of scientific inquiry and analysing the results scientifically to come to a conclusion that either supports or contradicts the observation made at the beginning.

Scientific Method Steps

The aim of all scientific methods is the same, that is, to analyse the observation made at the beginning. Still, various steps are adopted per the requirement of any given observation. However, there is a generally accepted sequence of steps in scientific methods.

• Observation and formulation of a question:  This is the first step of a scientific method. To start one, an observation has to be made into any observable aspect or phenomena of the universe, and a question needs to be asked about that aspect. For example, you can ask, “Why is the sky black at night? or “Why is air invisible?”
• Data Collection and Hypothesis:  The next step involved in the scientific method is to collect all related data and formulate a hypothesis based on the observation. The hypothesis could be the cause of the phenomena, its effect, or its relation to any other phenomena.
• Testing the hypothesis:  After the hypothesis is made, it needs to be tested scientifically. Scientists do this by conducting experiments. The aim of these experiments is to determine whether the hypothesis agrees with or contradicts the observations made in the real world. The confidence in the hypothesis increases or decreases based on the result of the experiments.
• Analysis and Conclusion:  This step involves the use of proper mathematical and other scientific procedures to determine the results of the experiment. Based on the analysis, the future course of action can be determined. If the data found in the analysis is consistent with the hypothesis, it is accepted. If not, then it is rejected or modified and analysed again.

It must be remembered that a hypothesis cannot be proved or disproved by doing one experiment. It needs to be done repeatedly until there are no discrepancies in the data and the result. When there are no discrepancies and the hypothesis is proved, it is accepted as a ‘theory’.

Scientific Method Examples

Following is an example of the scientific method:

Growing bean plants:

• What is the purpose: The main purpose of this experiment is to know where the bean plant should be kept inside or outside to check the growth rate and also set the time frame as four weeks.
• Construction of hypothesis: The hypothesis used is that the bean plant can grow anywhere if the scientific methods are used.
• Executing the hypothesis and collecting the data: Four bean plants are planted in identical pots using the same soil. Two are placed inside, and the other two are placed outside. Parameters like the amount of exposure to sunlight, and amount of water all are the same. After the completion of four weeks, all four plant sizes are measured.
• Analyse the data:  While analysing the data, the average height of plants should be taken into account from both places to determine which environment is more suitable for growing the bean plants.
• Conclusion:  The conclusion is drawn after analyzing the data.
• Results:  Results can be reported in the form of a tabular form.

Frequently Asked Questions – FAQs

What is scientific method, what is hypothesis, give an example of a simple hypothesis., define complex hypothesis., what are the steps of the scientific method, what is the aim of scientific methods, state true or false: observation and formulation of a question is the third step of scientific method, explain the step: analysis and conclusion..

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Scientific Method: Step 1: QUESTION

Step 1: question.

• Step 2: RESEARCH
• Step 3: HYPOTHESIS
• Step 4: EXPERIMENT
• Step 5: DATA
• Step 6: CONCLUSION

The first step of the scientific method is the " Q uestion ." This step may also be referred to as the " P roblem ." 

Your question should be worded so that it can be answered through experimentation. Keep your question concise and clear so that everyone knows what you are trying to solve. The question should have a purpose ...why do you want to know?  how does this matter?  who wants to know? 

This first step should also have a goal . What purpose will the answer to this question serve?

Need help picking a question/topic?

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Understanding Science

How science REALLY works...

• Understanding Science 101
• Misconceptions
• Science aims to build knowledge about the natural world.
• This knowledge is open to question and revision as we come up with new ideas and discover new evidence.
• Because it has been tested, scientific knowledge is reliable.

Misconception:  Scientific ideas are absolute and unchanging.

Misconception:  Because scientific ideas are tentative and subject to change, they can’t be trusted.

Correction:  Accepted scientific ideas are well-supported and reliable, but could be revised if warranted by the evidence.  Read more about it.

Science aims to explain and understand

The knowledge that is built by science is always open to question and revision. No scientific idea is ever once-and-for-all “proven” Why not? Well, science is constantly seeking new  evidence , which could reveal problems with our current understandings. Ideas that we fully  accept  today may be rejected or modified in light of new evidence discovered tomorrow. For example, up until 1938, paleontologists accepted the idea that coelacanths (an ancient fish) went extinct at the time that they last appear in the fossil record — about 80 million years ago. But that year, a live coelacanth was discovered off the coast of South Africa, causing scientists to revise their ideas and to investigate how this animal survives in the deep sea.

Despite the fact that they are subject to change, scientific ideas are reliable. The ideas that have gained scientific acceptance have done so because they are supported by many lines of evidence and have generated many expectations that hold true. Such scientific ideas allow us to figure out how entities in the natural world are likely to behave (e.g., how likely it is that a child will inherit a particular genetic disease) and how we can harness that understanding to solve problems (e.g., how electricity, wire, glass, and various compounds can be fashioned into a working light bulb). For example, scientific understandings of motion and gases allow us to build airplanes that reliably get us from one airport to the next. Though the knowledge used to design airplanes could be modified and built upon, it is also reliable. Time and time again, that knowledge has allowed us to produce airplanes that fly. We have good reason to trust accepted scientific ideas: they work!

A SCIENCE PROTOTYPE: RUTHERFORD AND THE ATOM

Ernest Rutherford’s investigations were aimed at understanding a small, but illuminating, corner of the natural world: the atom. He investigated this world using alpha particles, which are helium atoms stripped of their electrons. Rutherford had found that when a beam of these tiny, positively-charged alpha particles is fired through gold foil, the particles don’t stay on their beeline course, but change direction when passing through the foil. Rutherford wanted to figure out what this might tell him about the layout of an atom.

Rutherford’s story continues as we examine each item on the Science Checklist. To find out how this investigation measures up against the rest of the checklist, read on.

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Science builds reliable knowledge, but does it seek the truth? Learn more in our side trip on  The many meanings of truth .

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How the Miyawaki method of creating tiny forests could be the solution to Perth's tree canopy issues

Pocket forests are popping up around the country in spaces as small as a car parking spot, a tennis court or a street verge.

Ecologist Dr Grey Coupland sees huge potential in the rise of 'tiny forests' and is championing their development in Perth.

The pocket forests are grown using the Miyawaki method, created by Japanese botanist Akira Miyawaki in the 1970s.

Tiny forests are sprouting up around Australia in spaces as small as just a few square metres.

Because of the way they're created, these forests can mature in 10 to 20 years — instead of 100 — potentially bringing big benefits to our suburbs where tree canopy is dwindling.

Perth ecologist Dr Grey Coupland has been researching the concept, and sees huge potential.

"I thought this is actually a really, really useful method for rapid urban greening," she said.

"We have low canopy cover and we have an urban heat sink problem."

So how do they work?

The tiny forests follow three main principles.

"Soil preparation is really important because in urban areas we don't have much life in the soil and it's often low in nutrients as well," Dr Coupland said.

Before planting, each site is prepared by digging in massive amounts of hydrated coconut coir for moisture retention, compost and a specially prepared 'tea' that is brewed with soil bacteria collected from nearby natural bushland that helps the native species thrive.

Dr Coupland collects the soil while she's conducting biological surveys of local remnant bushland to determine what species to plant — which is the second part of the method.

"Basically you're planting what would have been on the site before the site was cleared for urbanisation and that's critical because those plants are specifically adapted to the area in which you're planting them."

The third part is planting close together.

"That high density creates competition between the plants, so instead of growing outwards they grow upwards and that helps with the rapid growth of the forest."

Size doesn't matter

Miyawaki forests can be grown in a spaces as small as a car parking spot, a tennis court or a street verge.

Dr Coupland has been busy planting them in schools and community areas in Perth and the results are remarkable.

In a two-year old forest at Eddystone Primary School in Perth's northern suburbs, the 'control' plants which were planted outside the specially prepared area are straggly and stand about 30cm tall.

The same species, planted at the same time, inside the Miyawaki forest are healthy and already more than 3m tall.

"These forests are really good for cooling as well," she said.

"We've taken some temperature readings outside the forest and inside the forest on a 43-degree day, it was 69 degrees on the local basketball court, 42 degrees in the forest, and then even 48 degrees on the grass, so the potential for cooling the landscape is pretty significant."

Bush classroom

Dr Coupland has integrated the tiny forests into the national school curriculum and students use it in myriad ways.

"We want to re-engage children with nature, we've got children on one end of the spectrum who are really worried about the climate crisis and feel they can't do anything about it, and at the other end of the spectrum we've got kids who are just on their iPads and their screens and totally disengaged," she said.

"For the children who participate in this program, some have never played in the dirt before, some had never planted a plant before, so this is their first foray into nature.

"To see them actually engage with nature and getting enjoyment out of it and then maybe becoming spokespeople for nature, the next eco warriors, the next scientists, I think that's really critical.

"Because it's only if children are invested in something and care for something, that they'll fight for it and we really need that now."

Ashdale Primary School year three teacher Cymbie Burgoyne learnt about the project while attending a talk Dr Coupland was giving and brought the idea back to her school.

"What I really like about this is that it's a bit like citizen science, they're working with real life scientists and they're working in academically rigorous ways," she said.

The prefect spot for a Miyawaki forest opened up at her school when a demountable classroom was removed.

"It's an outdoor classroom — they're being immersed in nature and the more they are immersed in nature, the more they care about it," Ms Burgoyne said.

Each month a team from Murdoch University goes to the schools to instruct students on how to monitor their forest, collecting data on plant growth, animal diversity, soil and air temperature, as well as birds.

"They're seeing a real purpose for what they're learning and its application and that always makes a difference," Ms Burgoyne said.

The students at Ashdale Primary School who planted their forest in July were already excited by its possibilities, some saying they hoped to convince their parents to plant a pocket forest at their homes.

As part of the wider project, PhD candidates at the Harry Butler Institute will measure the health and wellbeing of the students who interact with the forest against those who aren't involved, as well as the effect of the forest on autism and ADHD diagnoses of students.

Beyond the schoolyard

Dr Coupland has designed and planted 15 Miyawake forests across Perth, mostly in schools, but she is keen to see them grown on street verges, in corners of parks as well as forgotten and neglected bits of vacant land.

"I'd love to see them spread all across Perth, there are so many patches of ground that are vacant it becomes a little bit of an obsession — when you see a vacant patch, you think, Oh, that could be a forest site, let's put one in there."

"It would make our suburbs much more livable because people need nature around them," she said.

The program was nominated for the Australian Museum Eureka Awards — Innovation in Citizen Science prize and has been recognised as a UNESCO 'Green Citizens' program, but Dr Copeland said getting funding to keep the project going beyond 2024 will be crucial to getting more tiny forests into WA schools.

"To actually walk out your door and find a little forest on your doorstep, I think that's quite a magical thing and of course, all the benefits — we're bringing biodiversity back in, the cooling effects, the benefits are enormous."

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How to assess a general-purpose AI model’s reliability before it’s deployed

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Foundation models are massive deep-learning models that have been pretrained on an enormous amount of general-purpose, unlabeled data. They can be applied to a variety of tasks, like generating images or answering customer questions.

But these models, which serve as the backbone for powerful artificial intelligence tools like ChatGPT and DALL-E, can offer up incorrect or misleading information. In a safety-critical situation, such as a pedestrian approaching a self-driving car, these mistakes could have serious consequences.

To help prevent such mistakes, researchers from MIT and the MIT-IBM Watson AI Lab developed a technique to estimate the reliability of foundation models before they are deployed to a specific task.

They do this by considering a set of foundation models that are slightly different from one another. Then they use their algorithm to assess the consistency of the representations each model learns about the same test data point. If the representations are consistent, it means the model is reliable.

When they compared their technique to state-of-the-art baseline methods, it was better at capturing the reliability of foundation models on a variety of downstream classification tasks.

Someone could use this technique to decide if a model should be applied in a certain setting, without the need to test it on a real-world dataset. This could be especially useful when datasets may not be accessible due to privacy concerns, like in health care settings. In addition, the technique could be used to rank models based on reliability scores, enabling a user to select the best one for their task.

“All models can be wrong, but models that know when they are wrong are more useful. The problem of quantifying uncertainty or reliability is more challenging for these foundation models because their abstract representations are difficult to compare. Our method allows one to quantify how reliable a representation model is for any given input data,” says senior author Navid Azizan, the Esther and Harold E. Edgerton Assistant Professor in the MIT Department of Mechanical Engineering and the Institute for Data, Systems, and Society (IDSS), and a member of the Laboratory for Information and Decision Systems (LIDS).

He is joined on a paper about the work by lead author Young-Jin Park, a LIDS graduate student; Hao Wang, a research scientist at the MIT-IBM Watson AI Lab; and Shervin Ardeshir, a senior research scientist at Netflix. The paper will be presented at the Conference on Uncertainty in Artificial Intelligence.

Measuring consensus

Traditional machine-learning models are trained to perform a specific task. These models typically make a concrete prediction based on an input. For instance, the model might tell you whether a certain image contains a cat or a dog. In this case, assessing reliability could be a matter of looking at the final prediction to see if the model is right.

But foundation models are different. The model is pretrained using general data, in a setting where its creators don’t know all downstream tasks it will be applied to. Users adapt it to their specific tasks after it has already been trained.

Unlike traditional machine-learning models, foundation models don’t give concrete outputs like “cat” or “dog” labels. Instead, they generate an abstract representation based on an input data point.

To assess the reliability of a foundation model, the researchers used an ensemble approach by training several models which share many properties but are slightly different from one another.

“Our idea is like measuring the consensus. If all those foundation models are giving consistent representations for any data in our dataset, then we can say this model is reliable,” Park says.

But they ran into a problem: How could they compare abstract representations?

“These models just output a vector, comprised of some numbers, so we can’t compare them easily,” he adds.

They solved this problem using an idea called neighborhood consistency.

For their approach, the researchers prepare a set of reliable reference points to test on the ensemble of models. Then, for each model, they investigate the reference points located near that model’s representation of the test point.

By looking at the consistency of neighboring points, they can estimate the reliability of the models.

Aligning the representations

Foundation models map data points to what is known as a representation space. One way to think about this space is as a sphere. Each model maps similar data points to the same part of its sphere, so images of cats go in one place and images of dogs go in another.

But each model would map animals differently in its own sphere, so while cats may be grouped near the South Pole of one sphere, another model could map cats somewhere in the Northern Hemisphere.

The researchers use the neighboring points like anchors to align those spheres so they can make the representations comparable. If a data point’s neighbors are consistent across multiple representations, then one should be confident about the reliability of the model’s output for that point.

When they tested this approach on a wide range of classification tasks, they found that it was much more consistent than baselines. Plus, it wasn’t tripped up by challenging test points that caused other methods to fail.

Moreover, their approach can be used to assess reliability for any input data, so one could evaluate how well a model works for a particular type of individual, such as a patient with certain characteristics.

“Even if the models all have average performance overall, from an individual point of view, you’d prefer the one that works best for that individual,” Wang says.

However, one limitation comes from the fact that they must train an ensemble of foundation models, which is computationally expensive. In the future, they plan to find more efficient ways to build multiple models, perhaps by using small perturbations of a single model.

“With the current trend of using foundational models for their embeddings to support various downstream tasks — from fine-tuning to retrieval augmented generation — the topic of quantifying uncertainty at the representation level is increasingly important, but challenging, as embeddings on their own have no grounding. What matters instead is how embeddings of different inputs are related to one another, an idea that this work neatly captures through the proposed neighborhood consistency score,” says Marco Pavone, an associate professor in the Department of Aeronautics and Astronautics at Stanford University, who was not involved with this work. “This is a promising step towards high quality uncertainty quantifications for embedding models, and I’m excited to see future extensions which can operate without requiring model-ensembling to really enable this approach to scale to foundation-size models.”

This work is funded, in part, by the MIT-IBM Watson AI Lab, MathWorks, and Amazon.

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Label-free detection methods in medicine using biosensors

Press release, early disease detection in body fluids with photonic biosensors.

Press Release / August 02, 2024

Standard medical procedures are often time-consuming and generally do not take into account the individual characteristics of patients. This can have a negative impact on the success of treatment and impair quality of life. To solve this problem, a Fraunhofer research team from Fraunhofer IPMS, Fraunhofer IZI and Fraunhofer IOF is developing disposable biosensors that deliver rapid results and have extensive multiplexing capabilities. These biosensors enable the early detection of diseases and have the potential to significantly improve healthcare.

The detection method is based on special bioassays developed by Fraunhofer IZI, in which antigen molecules bind specifically to sensor surfaces that have been functionalized with capture molecules. The binding of the molecules to the sensor surface leads to a resonance wavelength shift in the transmission spectra of the biosensor chip. "Thanks to their high sensitivity, these biosensors can precisely detect biological molecules in liquids so that they can be used for the early detection of diseases using body fluids," explains Dr. Florenta Costache, project manager at Fraunhofer IPMS.

The biosensors consist of specially developed, scalable on-chip multichannel micro-ring resonator architectures with currently up to 7 sensors designed for a wavelength of 1550 nm. They are manufactured on a silicon nitride waveguide platform on 200 mm silicon wafers in the CMOS-compatible process line in one of Fraunhofer IPMS's state-of-the-art clean room facilities. To further increase sensitivity, additional sensor designs are currently being developed that operate in the visible range and are based on micro-ring resonators and Mach-Zehnder interferometers in various unique combinations. This results in cost-efficient, scalable sensors with customized design, high precision and reliability.

Costache adds: "We have also developed and successfully implemented a regeneration process to restore the functional surface of the sensor. This allows the sensor to be recycled and used several times. This saves costs and facilitates mobile use under field conditions."

Demonstrator for the detection of biomarkers in neurodegenerative and oncological diseases

The research team has already successfully developed a portable demonstrator based on a multi-channel silicon nitride micro-ring resonator biosensor system that allows for easy chip exchange by implementing special solutions for light coupling and detection. This system enables the multiplex detection of specific miRNA biomarkers associated with neurodegenerative and oncological diseases. The capture molecules immobilized on the sensor surface for the detection of these biomarkers are DNA-based. The developed sensors and the integrated system are versatile and can be adapted for the detection of nucleic acids, various disease-associated biomarkers and pathogens in different fluids.

The biosensors show great potential for use in rapid, minimally invasive diagnostics, particularly for the early detection of diseases, therapy monitoring and drug development. Collaboration with diagnostics companies and clinics is planned for the near future in order to further advance the development of biosensors for relevant biomedical applications. The aim is to demonstrate the practical use of these biosensors in the healthcare sector in the near future.

Presentation at the Pacific Rim Conference on Lasers and Electro-Optics

Dr. Florenta Costache will present the development in an invited talk entitled "Silicon Photonic Biosensors for Label-Free Detection of Small Biomolecules" on August 5, 2024 at the CLEO-PR (Pacific Rim Conference on Lasers and Electro-Optics) in Incheon, South Korea - lecture Mo3G-1.

Information on the research work on photonic biosensors is available on the website .

About Fraunhofer IPMS

Fraunhofer IPMS is one of the leading international research and development service providers for electronic and photonic microsystems in the application fields of intelligent industrial solutions and manufacturing, medical technology and health, and mobility. In two state-of-the-art clean rooms and with a total of four development sites in Dresden, Cottbus and Erfurt, the institute develops innovative MEMS components and microelectronic devices on 200 mm and 300 mm wafers. Services range from consulting and process development to pilot production.

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• Published: 01 August 2024

Study on the key parameters of ice particle air jet ejector structure

• Wang Man 1 ,
• Niu Zehua 1 &
• Yong Liu 2  

Scientific Reports volume  14 , Article number:  17831 ( 2024 ) Cite this article

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Metrics details

• Coarse-grained models
• Engineering
• Mechanical engineering

Existing ice particle jet surface treatment technology is prone to ice particle adhesion during application, significantly affecting surface treatment efficiency. Based on the basic structure of the jet pump, the ice particle air jet surface treatment technology is proposed for the instant preparation and utilization of ice particles, solving the problem of ice particle adhesion and clogging. To achieve efficient utilization of ice particles and high-speed jetting, an integrated jet structure for ice particle ejection and acceleration was developed. The influence of the working nozzle position ( L d ), expansion ratio ( n ), and acceleration nozzle diameter ratio ( D n ) length-to-diameter ratio ( L n ) on the ice particle ejection and acceleration was systematically studied. The structural parameters of the ejector were determined using the impact kinetic energy of ice particles as the comprehensive evaluation index, and the surface treatment test was conducted to verify the results. The study shows that under 2 MPa air pressure, the ejector nozzle parameters of n  = 1.5, D n  = 4.0, L d  = 4, and L n  = 0 mm can effectively eject and accelerate the ice particles. The aluminum alloy plate depainting test obtained a larger paint removal radius and resulted in a smoother aluminum alloy plate surface, reducing the surface roughness from 3.194 ± 0.489 μm to 1.156 ± 0.136 μm. The immediate preparation and utilization of ice particles solved the problems of adhesion and storage in the engineering application of ice particle air jet technology, providing a feasible technical method in the field of material surface treatment.

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Introduction.

Material surface treatment plays a crucial role in anticorrosion and prolonging the service life of materials 1 , 2 , 3 . Traditional methods, such as sandblasting, electroplating brush treatment, and chemical treatment 4 , 5 . are limited by environmental pollution, high energy consumption, and health hazards 6 , 7 , 8 , 9 , 10 , which constrain their widespread adoption.

Consequently, the development of clean and environmentally friendly surface treatment technologies is essential. ARASH et al. 11 investigated atmospheric pressure plasma metal surface treatment technology, which employs microwave-assisted atmospheric plasma for the quantitative removal of pollutants, thereby avoiding environmental pollution and achieving high cleaning speed. However, this technology’s high environmental requirements hinder its broader application. Nuo Jin et al. 12 proposed micro-nanometer bubble surface treatment technology, which is environmentally friendly and minimally damaging to substrate materials. Nevertheless, its industrial application is limited by the high precision required for equipment and low processing efficiency. In response to the need for reducing energy consumption in green cleaning technologies and improving engineering applicability, researchers have proposed ice particle jet surface treatment technology. This method, which uses air jets of ice particles, offers numerous advantages, most notably that the ice abrasive melts into water and is immediately discharged after operation, eliminating the need for abrasive recycling and dust generation 13 . The first ice abrasive jet technology patent involved using ice abrasives for surface formation, akin to sandblasting and paint removal 14 . This method utilizes the strength and hardness of ice particles to create a high-speed abrasive stream driven by a high-speed fluid to clean, strip paint, and remove rust.

The ice-making method is crucial for this technology. Initially, the ice-breaking method was used to prepare ice particles, which were then accelerated by jets of different media for surface treatment. For instance, Liu et al. 15 crushed ice and used high-speed air negative pressure to suction and accelerate ice particles, effectively removing surface paint from workpieces. Geskin et al. 16 from the New Jersey Institute of Technology prepared ice particles using the ice-breaking method, transported them to the nozzle with low-temperature airflow, and mixed them with a high-speed water stream to form an ice-particle water jet for cutting metals and soft materials. However, this method produces varying ice particle sizes and struggles to create particles smaller than millimeters.

To overcome the limitations of the ice-breaking method, Shin. et al. 17 used liquid droplets in a vacuum environment to continuously produce spherical ice particles with a diameter of 50 μm and a temperature of 0 °C. However, this method is equipment-intensive, complex, has high energy consumption, and low production efficiency, and cannot control the ice particle size and temperature. Li Deyu 18 prepared ice pellets by cooling liquid droplets with liquid nitrogen spray, achieving a high preparation efficiency and an average particle size of 100 μm. However, these ice particles easily bonded at temperatures above − 40 °C, blocking the ice particle outlet 19 .

Despite the advantages of ice particle jet technology in surface treatment, it has not seen widespread engineering application due to unresolved issues in ice particle preparation and storage technology. To address these challenges, the authors proposed a technology for preparing ice particles with controllable size and hardness, based on instant preparation and utilization 20 . They used a jet pump ejector to instantly eject and accelerate ice particles, integrating preparation and utilization, thus solving issues of uncontrollable particle size and avoiding adhesion and high energy consumption during storage. Efficient ejector performance is key to the immediate utilization of ice particles and effective jet surface treatment.

Ejector technology is widely used for abrasive jets, effectively mixing fluid–solid mixtures 21 , 22 . Bohnet et al. 23 conducted conveying tests with various powder materials, analyzing the variation of gas velocity, solid particle velocity, and hydrostatic pressure along the axial direction for a given feed. They found that the nozzle location significantly affects the ejector’s operating characteristics. Chellappan 24 studied a moment-type ejector using wheat as the experimental material and found that the ejector’s performance is influenced by nozzle positioning. Similarly, Dawson 25 and Davies et al. 26 conducted studies on parameters affecting ejector performance, with their conclusions aligning with existing literature.

Xiong et al. 27 used simulation to obtain the static pressure distribution inside the ejector, discovering that the working nozzle’s position impacts the static pressure magnitude, which in turn affects the abrasive’s priming rate. Feng et al. 28 designed a liquid nitrogen-ice particle jet working nozzle structure based on jet pump technology and verified its ability to eject ice particles timely and achieve good processing results through testing. Zhang et al. 29 examined the impact of the working nozzle dispersal section length on ejector performance, concluding that a well-designed dispersal section length can significantly enhance processing efficiency. Overall, existing research focuses on the ejection capacity of the ejector but lacks studies on the fluid–solid acceleration performance.

Therefore, this paper examines the impact of injector structural parameters on the ejection and acceleration of ice particles, aiming to improve surface treatment efficiency based on the principle of instant preparation and utilization of ice particles in air jet technology. The injector mainly comprises working nozzles, a mixing chamber, and accelerating nozzles. Instantly prepared ice particles are sucked into the mixing chamber by gravity and the high-speed airflow’s negative pressure from the working nozzle. The high-speed airflow then introduces the ice particles into the accelerating nozzle for thorough mixing and acceleration before ejection. Previous studies 30 , 31 , 32 , 33 , 34 show that the working nozzle’s ejection capacity depends on the nozzle’s expansion ratio and position, while the accelerating nozzle’s acceleration capacity depends on its diameter ratio and aspect ratio. This study analyzes the ejection and acceleration of ice particles under different ejector nozzle structures using the ANSYS-FLUENT gas–solid two-phase flow model. A paint stripping test is conducted on the designed ejector to verify its surface treatment capability, providing theoretical support for the application of ice particle air jets in material surface treatment.

Principle of ice air jet

The principle of ice particle air jet technology, based on the instant preparation and utilization of ice particles, is illustrated in Fig.  1 . Using the principle of heterogeneous nucleation, water is injected into the syringe after being pressurized by the pump. Ice particle size is controlled by changing the needle model and adjusting the injection pressure, resulting in particles ranging from 0.1 mm to 2.52 mm. The temperature of the cold wall is regulated by adjusting the amount of liquid nitrogen added, which controls both the preparation efficiency and the temperature of the ice particles. Once the ice particles condense on the cold wall, a scraper moves from top to bottom to remove them, then resets. The speed of the scraper’s reciprocating movement and the number of needles determine the mass flow rate of ice particle preparation 17 , 18 .

Principle of ice particle air jet injection.

In the ice pellet utilization system, 2 MPa of gas is passed through the ejector working nozzle to form a high-speed jet, creating a negative pressure area at the nozzle outlet. Instantly prepared ice particles are transported to this negative pressure area by low-pressure gas, ejected into the mixing chamber, mixed with the high-speed air jet, and initially accelerated. They then enter the accelerating nozzle for full acceleration before being ejected to form a high-speed ice particle air jet. The working efficiency of the ice particle air jet is determined by the kinetic energy of the impacting ice particles, which is a function of the mass and acceleration of the ejected ice particles. Therefore, the ejection and acceleration capabilities of the ejector are crucial for determining the efficiency of surface treatment.

Numerical simulation

Physical modeling and meshing.

The ejection capacity of the injector is determined by the position of the working nozzle ( L n ) and the expansion ratio ( n ), which is the ratio of the static pressure at the working nozzle outlet cross-section to the ambient pressure. The acceleration capacity is determined by the diameter ratio ( D n = D 3 / D *) and the length-to-diameter ratio ( L d = L 3 / D 3 ) of the accelerating nozzle, as shown in Fig. 2 .

Physical modeling of ice particle air jets.

The meshing of the model is illustrated in Fig. 3 . Using unstructured grids, quadrilateral elements were chosen as the dominant method to generate the computational domain. To improve computational accuracy, the working nozzle, accelerating nozzle, and the flow field and wall zones were regionally refined and validated for mesh independence 35 . According to research needs, the outer basin’s length along the flow direction is 100 mm, and its radius is 30 mm. This was accomplished using the ANSYS Mesh module in Workbench, resulting in approximately 176,000 meshes, with the minimum mesh volume of 6.29 × 10 −11 m 3 , and an average mesh mass of 0.85.

Grid division.

Numerical simulation of control equations

Particle phase control equation.

In the Fluent-EDEM coupled calculations, the motion of a single ice particle follows Newton’s second law. The law of motion for an arbitrary ice particle i is expressed as follows 36 :

where \(\ddot{v}_{i}\) and \(\ddot{\theta }_{i}\) are the gravitational and angular acceleration of ice particle i , respectively, m i and I i are the mass and moment of inertia of particle i , respectively, and F i and M i are the combined force and torque, respectively.

Inside the nozzle and in the jet flow field, solid particles are subjected to various forces, some of which are small and can be neglected, such as virtual mass forces. This study considers trailing forces, particle interaction forces, pressure gradient forces, Magnus forces, and others. The forces on the particles are expressed as 36 :

where f p , i is the trailing force of particle i , f c , ij is the collision force of particle i and particle j , f d , ij is the damping force of particle i and j , fmag ,i is the Magnus force of particle i , and fsaff, i is the Saffman lift force of particle i .

Heat transfer calculation equation

The ice particle air jets are calculated using the Hertz-Mindlin with Heat Conduction contact model, with the governing equations as follows 37 :

Hertz-mindlin(No Slip)

The normal force F n is expressed as:

where \(E^{*}\) is the Young’s modulus, \(R^{*}\) is radius of the contact sphere, δ n is normal overlap function, respectively.

w Rolling friction is considered by applying a moment to the contact surface:

where μ r is the coefficient of rolling friction, R i is the distance from the contact point to the center of mass, and ω i is the unit angular velocity vector of the object at the contact point.

Hertz-mindlin with heat conduction

In this study, the significant contact between particles necessitates considering heat transfer. The heat flow between particles is defined by:

where the contact area is added to the heat transfer coefficient h c , expressed as:

where F N is the normal force, r * is the geometrically averaged radius of the particles calculated from the Hertz elastic contact theory, and E * is the effective Young’s modulus.

Temperature Update Model

The heat transfer algorithm is activated once the heat fluxes are calculated. The temperature change over time for each particle is updated by:

where m p , C p and T are mass, specific heat capacity and temperature, respectively. The right-hand side represents the sum of convective and conductive heat fluxes.

Initial and boundary conditions

The initial and boundary conditions set in EDEM and FLUENT software are shown in Table 1 . Ice particles start moving from the injector inlet, with the initial kinetic energy of the ice particles being zero.

Numerical simulation scheme

The numerical simulation considers the influence of the working and accelerating nozzles on the acceleration effect of ice particles. The test scheme is shown in Table 2 .

To better investigate the acceleration law and process of the ice particle jet, an ice particle capture domain was established on the injector. The width of the capture domain was set to 1.5 times the particle diameter. The optimal structural parameters of the injector nozzle were determined by analyzing the gas velocity, negative gas pressure, and kinetic energy data of each capture domain. The location of the capture domain is illustrated in Fig.  4 .

Schematic diagram of ice particle capture area of ejector.

Numerical simulation results and analysis

Effect of l n 、n on the kinetic energy of ice particle impacts, influence on the amount of ice particles elicited.

Taking n  = 1.5, D n  = 4.5, L d  = 4.0 as an example to illustrate the influence of the position of the working nozzle’s position on the gas’s negative pressure, the calculation results are shown in Fig.  5 . It can be seen that different L n injectors exhibit similar pressure distribution patterns. The gas pressure at the exit of the working nozzle drops significantly, reaching maximum negative pressure in the acceleration nozzle. After the acceleration nozzle, the gas pressure fluctuates and gradually converges to atmospheric pressure. However, L n has a greater impact on the pressure in the mixing chamber. The different positions of the working nozzle affect the spatial pattern in the mixing chamber, which significantly influences the negative gas pressure. As L n increases, the negative gas pressure inside the mixing chamber decreases, then increases, reaching its lowest at L n  = 0 mm. Therefore, it can be concluded that L n  = 0 mm is more favorable for the ejection of ice particles.

Effection of different Ln on the negative pressure of the mixing chamber.

Taking L n  = 0 mm, D n  = 4.5, L d  = 4.0 as examples to illustrate the influence of the working nozzle expansion ratio on the negative pressure of the gas, the calculation results are shown in Fig.  6 . It can be seen that the pressure distribution patterns formed by different working nozzle expansion ratios are basically the same. The gas pressure decreases significantly at the exit of the working nozzle, reaching a minimum at the entrance of the acceleration nozzle. The gas pressure then fluctuates within the acceleration nozzle and gradually stabilizes in the free jet section as the jet develops. Different working nozzle expansion ratios affect the jet morphology in the mixing chamber, which significantly impacts the negative gas pressure. As n increases, the gas pressure gradually decreases, and the negative pressure generated in the mixing chamber is the highest at n  = 1.5. Therefore, it can be assumed that n  = 1.5 is more favorable for the ejection of ice particles.

Effect of different n on the negative pressure of mixing chamber.

Effects on the initial acceleration of ice particles

Ice particles are initially accelerated by the high-speed airflow after elicitation, and the acceleration effect is characterized by the kinetic energy possessed by the ice particles. The effect of the working nozzle position on the impact kinetic energy of ice particles is illustrated with n  = 1.5, D n  = 4.5, L d  = 4.0 as examples, and the calculated results are shown in Fig.  7 . The kinetic energy of ice particles continues to increase after entering the accelerating nozzle, but decreases in the second half of the jet at L n  = − 5 mm and L n  = 5 mm. The kinetic energy of ice particles increases consistently at L n  = 0 mm reaching a maximum of 1.28 × 10 −3  J . The different positions of the working nozzles affect the spatial morphology in the mixing chamber, which greatly impacts the acceleration of ice particles. As shown in the airflow velocity cloud plots at different L n in Fig.  8 , he airflow fluctuation is minimal at L n  = 0 mm, and the gas expands completely inside the accelerating nozzle, resulting in the best acceleration effect. In contrast, at L n  = -5 mm and L n  = 5 mm, the gas flow enters the free flow field with alternating expansion and compression waves, causing intense energy exchange with the surrounding environment, which reduces the jet flow velocity. Therefore, it can be concluded that L n  = 0 mm is more favorable for the initial acceleration of ice particles.

Variation of kinetic energy of ice particles at different Ln.

Airflow velocity clouds at different Ln.

The effect of the working nozzle expansion ratio on the acceleration of ice particles is illustrated with L n  = 0 mm, D n  = 4.5, L d  = 4.0 as examples. The calculation results are shown in Fig.  9 . The kinetic energy of ice particles under different n values continues to increase after entering the accelerating nozzle. At the end of the jet flow field, the velocity of ice particles decreases at n  = 0.8 and n  = 1.5, but the kinetic energy of ice particles is always the highest at n  = 1.5, reaching a peak value of 1.56 × 10 −3  J at a target distance of 75 mm. Combined with the air velocity cloud diagrams under different n values in Fig.  10 , it can be seen that the jet iso-velocity core is the longest and the jet velocity is the highest with a nozzle expansion ratio of n  = 1.5, Although some fluctuations are generated in the free jet stage, the overall jet energy is higher, effectively accelerating the ice particles. The working nozzles with n  = 0.8 and n  = 1 have a limited acceleration effect on ice particles due to their lower jet velocities. Therefore, the nozzle with n  = 1.5 provides the best initial acceleration effect on ice particles.

Variation of kinetic energy of ice particles with different n.

Airflow velocity clouds at different n.

Effect of Dn、Ld on the kinetic energy of ice particle impacts

Effects on the gas velocity field.

The effect of D n on the gas velocity is illustrated with L n  = 0 mm, n  = 1.5 and L d  = 4.0 The calculation results are shown in Fig.  11 . After entering the working nozzle, the gas velocity accelerates, but it starts to decrease gradually when entering the mixing chamber. It accelerates again after entering the accelerating nozzle, although the increase in velocity is not significant. In the free jet section, the gas velocity continues to decrease as the jet develops. Inside the accelerating nozzle, D n significantly affects the gas velocity, which initially increases and then decreases as D n . increases. There is little difference between the gas velocities at D n  = 3.5 and D n  = 4.0, but the gas velocity at D n  = 4.5 is always the smallest. As shown in the gas velocity cloud diagram under different D n values in Fig.  12 , when D n  = 4.0, the gas flow fluctuation is minimal, resulting in lower energy loss. However, when D n  = 3.5, the gas fluctuation is large, and the energy exchange with the environment is intense, reducing the jet’s energy. Therefore, D n  = 4.0 is more conducive to stabilizing the gas flow field.

Axial velocity distribution of acceleration nozzle at different Dn.

Airflow velocity clouds at different Dn.

The effect of the accelerating nozzle L d ratio on the gas velocity is illustrated with L n  = 0 mm, n  = 1.5 and D n  = 4.0, and the calculation results are shown in Fig.  13 . The gas velocity starts to accelerate at the inlet of the working nozzle and reaches its maximum at the outlet of the working nozzle. After the supersonic gas enters the mixing chamber, the velocity begins to decrease gradually. It accelerates again after entering the accelerating nozzle, but the increase in velocity is not significant. In the free jet section, the gas velocity continues to decrease. The gas velocity is always highest at L d  = 4.0. As shown in the gas velocity cloud diagram at different L d values in Fig.  14 , at L d  = 4.0, the gas flow fluctuation is minimal, resulting in lower energy loss and a longer isovelocity core in the free jet stage. In contrast, at L d  = 3.0, the gas fluctuates significantly as it enters the free-flow field, resulting in lower jet energy. The gas velocity is always minimized at L d  = 5.0. Therefore, the gas flow field is more stable at L d  = 4.0.

Axial velocity distribution of acceleration nozzle at different Ld.

Airflow velocity clouds at different Ld.

Effects on ice particle acceleration

The effect of the accelerating nozzle diameter ratio on the kinetic energy of ice particle impact is illustrated with L n  = 0 mm, n  = 1.5 and L d  = 4.0, and the calculated results are shown in Fig.  15 . The kinetic energy of ice particles starts to increase after entering the accelerating nozzle, but decreases at D n  = 3.5. In the free jet stage, different D n values have different effects on the kinetic energy of ice particles. The kinetic energy decreases at D n  = 3.5 and D n  = 4.5 at a larger target distance, but the velocity of ice particles consistently increases at D n  = 4.0, reaching a maximum impact kinetic energy of 1.28 × 10 -3  J at a target distance of 100 mm. Combined with the analytical results in Section  2.5.1, it can be seen that different D n values affect the spatial structure inside the accelerating nozzle, which in turn affects the airflow’s acceleration effect on the ice particles. At D n  = 4.0, the airflow fluctuation is minimal, and the kinetic energy of ice particles increases continuously, providing the best acceleration effect on ice particles.

Variation of kinetic energy of ice particles with different Dn.

The effect of the length-to-diameter ratio of the accelerating nozzle on the kinetic energy of ice particle impact is illustrated with L n  = 0 mm, n  = 1.5, D n  = 4.5 as an example, and the calculated results are shown in Fig.  16 . After entering the accelerating nozzle, the kinetic energy of ice particles keeps increasing at L d  = 4.0, while the velocity of ice particles decreases and then increases at L d  = 3.0 and L d  = 5.0. In the free jet stage, the ice particle velocity changes significantly at different L d values, and the ice particle kinetic energy fluctuates greatly at L d  = 3.0 and L d  = 5.0, but continues to increase at L d  = 4.0 reaching a maximum impact kinetic energy of 1.28 × 10 -3  J at a target distance of 100 mm. Combined with the analytical results in Section  2.5.1, it can be seen that different accelerating nozzle L d ratios affect the spatial morphology inside the accelerating nozzle and thus the acceleration of ice particles. At L d  = 4.0, the airflow fluctuation is minimal, achieving maximum impact kinetic energy, which provides the best effect on the acceleration of ice particles.

Variation of kinetic energy of ice particles with different Ld.

The results show that the optimal ejector structure is a working nozzle with L d  = 4.0, D n  = 4.0 and a pressure ratio of 1.5. At this configuration, the maximum impact kinetic energy achieved by the ice particles is 1.56 × 10 −3  J.

Ice pellet air jet paint stripping test

Experimental system.

The experimental system is shown in Fig.  17 . It mainly consists of a gas supply system, an ice grain preparation system, an ice grain ejector system, and an experimental platform. The gas supply system provides compressed gas at a pressure of 2 MPa, regulated through a pressure-reducing valve. The test platform is used to fix the aluminum alloy specimen, which is a 10 cm × 10 cm aluminum alloy plate. Before the test, the aluminum alloy plate was uniformly sprayed with a paint thickness of 0.1 mm.

Ice Pellet Air Jet Paint Removal Test System.

To further analyze the effect of different ejector nozzle structures on the surface treatment of materials, the Attension Theta Optical Contact Angle Meter was used to test the roughness of the specimens treated with the ice-particle air jet. The device is shown in Fig.  18 . The data from the measured area of the specimen were extracted, and three indicators were used to evaluate the surface treatment effect of the ice-particle air jet on aluminum alloys: Ra , which represents the arithmetic mean of the absolute value of the contour deviation within the sampling length; Rp , which represents the maximum peak of the contour, arithmetically, relative to the mean line within a sampling length; and Sdr , which represents the ratio of the interfacial area to the projected area.

Test instrument for sample morphology.

Experimental program

To obtain the optimal nozzle structure parameters for the ejector, an ice air jet paint removal test was conducted. The test program is shown in Table 3 . The paint removal effect is characterized by the actual paint removal radius and the morphology and roughness of the metal surface after paint removal. A larger paint removal radius indicates a larger paint removal area per unit time, resulting in higher paint removal efficiency. Surface roughness is related to the impact kinetic energy of the ice particles; the smaller the surface roughness, the larger the impact kinetic energy of the ice particles, and the better the effect of ice air jet metal surface treatment. Because the spray paint thickness on the aluminum alloy surface was thin for this test and aimed mainly to verify the jet’s surface treatment ability, a small amount of damage to the surface material is considered normal.

Test results and analysis

To compare the effects of the test, the morphology test results before erosion are shown in Fig.  19 , and the roughness test results before erosion are shown in Table 4 .

Morphology test results of aluminum alloy plate without erosion.

Influence of L n 、n on paint stripping effect

The paint removal effect on aluminum alloy specimens at different L n and nnn values is shown in Fig.  20 , and the data are presented in Fig.  21 . The main purpose of this experiment is to verify that the designed jet structure can effectively remove paint. According to previous studies, the addition of obstacles has been used to improve the effective removal capability of the gas abrasive jet 38 , 39 . However, this requires specific conditions for the obstacles, such as their location and size not affecting the gas jet flow field, which is difficult to achieve in practice. Park et al. 40 conducted experiments to describe the good performance of MAJM in glass micro-cutting grooves. Wakuda et al. 41 , 42 performed MAJM on different engineering ceramics using three different abrasives to identify the material response of alumina ceramics to the impact of micro-abrasive grains and revealed the effect of workpiece properties on the machinability of engineering ceramics during the MAJM process. Compared to previous studies, this paper aims to verify that the designed structure provides better paint removal effects. The paint removal results achieved under the experimental conditions of this study are shown in Fig.  20 . From Fig.  20 , it can be seen that the radius of paint removal increases and then decreases with the increase of L n . The radius of the erosion area produced at L n  = 0 mm is the largest at 21 mm, and the erosion effect is also the best.

Paint removal effect under different Ln、n.

Paint removal radius under different Ln、n.

Taking L n  = 0 mm, L d  = 4.0、 D n  =  4.0 as examples to illustrate the effect of n on the paint removal effect, the paint removal effect of the ice air jet under different n values increases with the increase of n . The surface treatment effect of the ice air jet is best when the pressure ratio n  = 1.5, resulting in more thorough paint removal in the eroded area. The surface morphology and roughness of the specimens were tested, with the results of the surface morphology test shown in Fig.  22 and the results of the roughness test shown in Table 5 .

Morphological test results of aluminum alloy plate under different Ln、n.

From the test results, it can be seen that the roughness of the aluminum alloy plate decreases and then increases as L n  = 0 mm increases, with the surface roughness being the minimum at L n  = 0 mm, measured at 1.437 ± 0.365 μm. From the morphology and roughness test results of the aluminum alloy specimens at different nnn values, it can be seen that the surface roughness decreases consistently with the increase of n . At n  = 1.5, the surface roughness is minimized at 1.156 ± 0.136 μm.

Influence of Dn、Ld on paint stripping effect

The paint removal effect of the specimens under different D n and L d values is shown in Figs. 23 and 24 . From Fig.  24 , it can be seen that the radius of paint stripping increases and then decreases with the increase of D n , with the maximum radius of paint stripping being 20 mm when D n  = 4.0.

Paint removal effect with different Dn、Ld.

Paint removal radius with different Dn、Ld.

Taking L n  = 0 mm, D n  = 4.0 and n = 1.5 as examples to illustrate the effect of L d on the paint removal effect, Fig.  24 shows that at a given target distance, the paint stripping radius first increases and then stabilizes with the increase of L d , When the accelerated nozzle aspect ratio L d  = 4.0 , the paint stripping radius can reach 23 mm.

The specimens were then tested for surface morphology and roughness. The results of the surface morphology test are shown in Fig.  25 , and the results of the roughness test are shown in Table 6 . It can be seen that as D n increases, the roughness of the aluminum alloy plate decreases and then increases, with the surface roughness being the smallest at D n  = 4.0 mm, measured at 1.437 ± 0.365 μm; As L d increases, the roughness of the aluminum alloy plate first decreases and then increases, with the surface roughness being the minimum at L d  = 4.0, measured at 1.437 ± 0.365 μm.

Morphological test results of aluminum alloy plate under different Dn、Ld.

(1) An instantly prepared and instantly utilized ice pellet jet surface treatment technology is proposed to solve the problems of ice pellet bonding and clogging in traditional ice pellet jet paint removal technology.

(2) Numerical simulation studies were carried out using a coupled Fluent-EDEM method to derive the optimal ejector structure parameters that can sufficiently eject accelerated ice particles at 2 MPa.

(3) Through the aluminum alloy paint stripping test, it was verified that the designed ejector structure can change the surface roughness of the aluminum alloy plate from 3.194 ± 0.489 μm to 1.156 ± 0.136 μm, demonstrating a superior surface treatment effect.

(4) Jet structures for instant preparation and utilization of ice particles can provide theoretical and technological support in the field of ice particle air jet surface treatment.

Data availability

All data included in this study are available upon request from the corresponding author.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (52174170, 52374192, 52374193), Henan Provincial Key R&D Programme (231111322000), and New Materials and Highly Efficient Processes for In-situ Degradation of Coal Seam Gas (2023YFC3009002).

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Man, W., Zehua, N. & Liu, Y. Study on the key parameters of ice particle air jet ejector structure. Sci Rep 14 , 17831 (2024). https://doi.org/10.1038/s41598-024-68869-8

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DOI : https://doi.org/10.1038/s41598-024-68869-8

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• Jian Cheng   ORCID: orcid.org/0009-0009-1067-0765 1  

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In this work, we present a high-order discontinuous Galerkin (DG) method for solving the one-fluid two-temperature Euler equations for non-equilibrium hydrodynamics. In order to achieve optimal order of accuracy as well as suppress potential numerical oscillations behind strong shocks, special jump terms are applied in the DG spatial discretization for the nonconservative equation of electronic internal energy. Moreover, inspired by the solution procedure of Riemann problem, we develop a new HLLC (Harten–Lax–van Leer Contact) approximate Riemann solver for the one-fluid two-temperature Euler equations and use it as a building block for the high-order discontinuous Galerkin method. Several key features of the proposed HLLC approximate Riemann solver are analyzed. Finally, we design typical test cases to numerically verify and demonstrate the performance of the proposed method.

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Data Availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The author would like to thank Zhifang Du for helpful discussion. This work is supported by the National Natural Science Foundation of China No.12171046 and No. 12031001.

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In the appendix, we give the eigenvalues and eigenvectors for the matrixes \(\textbf{A}_x(\textbf{U})\) and \(\textbf{A}_y(\textbf{U})\) , which are obtained by rewritten ( 16 ) into a quasi-linear form as follows

The five eigenvalues of \(\textbf{A}_x(\textbf{U})\) are

The corresponding right eigenvectors of \(\textbf{A}_x(\textbf{U})\) are given as

where \(H = \frac{E+p}{\rho }\) and \(q^2=u^2+v^2\) . The left eigenvectors of \(\textbf{A}_x(\textbf{U})\) are given as

Similarly, the five eigenvalues of \(\textbf{A}_y(\textbf{U})\) are

The corresponding right eigenvectors of \(\textbf{A}_y(\textbf{U})\) are given as

and the left eigenvectors of \(\textbf{A}_y(\textbf{U})\) are given as

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Cheng, J. A High-Order Discontinuous Galerkin Method for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics. J Sci Comput 100 , 82 (2024). https://doi.org/10.1007/s10915-024-02640-z

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Received : 29 December 2023

Revised : 09 July 2024

Accepted : 22 July 2024

Published : 02 August 2024

DOI : https://doi.org/10.1007/s10915-024-02640-z

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• Non-equilibrium hydrodynamics
• One-fluid two-temperature Euler equations
• Discontinuous Galerkin method
• High-order method

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