Granular materials and funnels

Topic: Granular materials

Research question: What are the flow and mixing properties of granular materials flowing in funnels of different shapes and sizes?

Materials and Methods Outline:
You will need some sort of fine granular material. This can be sand, small spherical beads of bronze, copper, or other material. You will need some type of fan that can have a focused stream of blown air. Perhaps a hair dryer or shopvac. It is ideal to have something that has multiple options for wind speed.

The other main piece of equipment will be some sort of camera that has video capabilities. Video will be the main method of collecting data and making measurements. The key to making measurements from video is to have a ruler of some type in the video, which can be used to make calibrations within a program such as Tracker or LoggerPro. If you have access to any video hardware with high-speed options, such as on an iPhone 6 or many other cameras (instead of the standard 30 frames per second (fps), some can be turned to 60 fps, 120 fps, 240 fps, or even 480 fps or 1000 fps); note that the clarity and resolution of video gets worse with higher fps values - you will need to experiment with the settings to get the optimal balance for frame rate and clarity to get measurements you trust.

Possible parameters to test, and make your own:

• Vertical funnel, single stream of grains sliding straight down as a control
• What if funnel is angled relative to the vertical?
• Two streams of identical grains sliding down on opposite sides, colliding/mixing properties
• Two streams identical material, different diameters
• Properties of falling down the funnel as function of diameter
• Grains consisting of different materials: changes in flow patterns?
• Flow properties as a function of angle of funnel
• Flow properties as function of width of funnel spout
• Flow properties as function of entry speed of grains
• Appearance of avalanches, as a function of flow rate?
• Have grains flow into funnel at angles so they flow down in spiral motion
• What conditions must exist to clog the spout? 
• Piling properties/patterns of grains pouring out of funnel spout into a container: can vary height the grains fall into container; size and shape of container
• Some of the more interesting analyses would include two (or more) different sized grains, and mixing properties while changing the above conditions and parameters. Any segregation or stratification? 
• One stream of grains mixing with a stream of water from the other side of a funnel: dynamics of the mixing as a function of flow rates of both grains and liquid; how do the dynamics and mixing vary as the above conditions and parameters are varied?
• Perhaps some interesting changes in flow occur when the funnel is vertically vibrated at various frequencies and/or amplitudes

An interesting video of computer simulations of granular flow, courtesy of UNC. Get more ideas from what they show! Their website is here.

Links and Literature on this type of research:
- Free-flowing granular materials with two-way solid coupling (UNC math model used in simulations)

- Two-dimensional granular flow in a small angle funnel

- Rapid granular flows

Piles of Granular materials blown into walls

Topic: Granular Materials

Research Questions:
The primary idea behind this research is to see what the behavior and properties of wind-blown granular materials, such as sand or small beads, when those grains are i) blown from a pile, and ii) when those same grains collide with a wall not far away from the pile. There are numerous specific questions one can address with a system such as this, as listed below.

Try to make observations of how the pile is actually blown away. Do grains begin to be blown off the pile from the side closest to the fan, from the sides, or from the side farthest from the fan? Then, when grains hit the wall, what is the distribution of the grains as they land and begin to pile up again? Are there patterns and consistencies you observe if you do a number of trials? Is there any avalanching on either end of the process?


Materials and Methods Outline:
You will need some sort of fine granular material. This can be sand, small spherical beads of bronze, copper, or other material. You will need some type of fan that can have a focused stream of blown air. Perhaps a hair dryer or shopvac. It is ideal to have something that has multiple options for wind speed.

The other main piece of equipment will be some sort of camera that has video capabilities. Video will be the main method of collecting data and making measurements. The key to making measurements from video is to have a ruler of some type in the video, which can be used to make calibrations within a program such as Tracker or LoggerPro. If you have access to any video hardware with high-speed options, such as on an iPhone 6 or many other cameras (instead of the standard 30 frames per second (fps), some can be turned to 60 fps, 120 fps, 240 fps, or even 480 fps or 1000 fps); note that the clarity and resolution of video gets worse with higher fps values - you will need to experiment with the settings to get the optimal balance for frame rate and clarity to get measurements you trust.

Specific Research Questions can include:

• Decomposition of pile as a function of airspeed from the fan or hair dryer/blower
• How does changing the angle of airstream as it hits the pile affect decomposition?
• The height of the pile
• The diameter of the pile
• The slope of the pile
• The size of the grains making up the pile
• If the pile is a random mix of two or more sizes of grains
• If there is a small pile of one size grain, buried below another size grain
• Effect of different sized, shaped obstacles between wind source and granular pile
• What are the characteristics of any pile formed at the wall?
• Any difference(s) between a straight wall and a curved wall?
• What happens if the wall is tilted at difference angles? 
• Change the material of the wall (coefficient of restitution between grain and wall)
• How does the pile change as a function of distance between the pile and the wall?
• What is there are two piles side by side?
• What if a second pile is in between the first pile and the wall? 
• If two different grains are used, is there any segregation and/or stratification in the pile that is formed? 
• Is there avalanching of any kind on either side of the original pile(s)? In the formed pile at the wall?
• Instead of symmetric pile (more coned shaped), what is the pile is a ramp with a flat end? Try piles of different geometric shapes.

Related articles and links in the literature (if you do not have access to an article, email us at vondracekm@eths202.org):

- Transport by wind of granular materials of different grain shapes and densities

- Determination of wind induced detachment threshold for granular material on Mars

An Example of Computational Science using Computer Simulations: Climate Models

Computational science is the newest type of science research, which evolved with the development of powerful computers. It allows us to work on very hard problems with mathematical models and theories that are too hard to solve with pencil and paper. Computational research is done in all branches of science, engineering, and even in business, medicine, city planning, and on and on...it is everywhere!

If you want to see a good example of one of the most challenging scientific problems in modern science, check out the TED talk by Gavin Schmidt, who is modeling the earth's climate. See what goes into a computer simulation in terms of the math, and then how the simulation can be tested for validity and accuracy based on real data and measurements from past climate trends. Finally, and this is the power of a simulation that has been tested and has a high level of confidence it is doing what we think it is doing, he shows how the simulation can make predictions for future climate trends depending on what values the parameters in the simulation are given.

Good computer simulations allow scientists to do computer experiments on phenomena and systems they otherwise could not experiment on. Imagine trying to figure anything out about the way a star works - we obviously cannot directly test a star, or star systems. But astrophysicists can run computer simulations using the known laws of physics and compare the results to what is really out there. If there is a good match with the simulation, then the simulations can be used to see what would happen under different conditions, and predict other objects and systems that may not have even been observed yet!

Video Analysis: A Powerful technique using video cameras of any kind, even your phone's, with Tracker software

A game changer for high school research has been the advent of decent digital cameras that are widely available and affordable, such as those on smartphones or standalone cameras purchased for $100 or less at Target or Best Buy. More and more of these cameras even have high-speed capabilities of several hundred frames per second (fps), as compared to the standard 30 fps of a general camcorder. Using video as a data collection device for any type of experiment where motion or change is occurring can allow even high school students and teachers to do a good analysis of the experiment.

Video data collection and analysis has become a standard part of my classroom labs for several years, and students quickly learn the benefits of video to enhance their datasets and analysis sections of lab reports. They embrace it on an everyday basis since it is part of their phones, and often they do this for events outside of the classroom (they want to do science and analysis on their own! Great buy-in leading up to possible research projects for your students).

Some phones, such as the new iPhones (6th generation) have settings up to 240 fps or 480 fps. They also allow for frame-by-frame viewing, where the time between frames is on order of 0.0042 sec and 0.0021 sec, respectively. This allows high school students to do an analysis where one can watch time development of the system being studied at a millisecond scale. Also, for better, fuller analysis, one can use a free software package called Tracker to analyze video or still digital photos. Download Tracker onto a school computer or your own computer, and the world of video analysis is now yours!

Below is an introductory video for Tracker, by the author of the software, Douglas Brown. A second video has an introduction of how to use the autotracking feature of Tracker. There are numerous videos on YouTube about using this type of software. Note that some schools may have Vernier's Logger Pro software, which also has photo and video analysis features. An introductory video for using Logger Pro for video analysis is here. What is so nice about these is one can calibrate distances and times within the video and make measurements right from the still frames you've captured. What you may want to do is be sure a meterstick is in the video, and/or a stopwatch. This allows you to have good calibrations whether you use Tracker or not.

Here is an introduction into Tracker software:

And now to learn how to use Autotracking features in Tracker:

Hydraulic Jump Activity: Example of Finding Research Questions and Complexity from the Seemingly Simple

In this post, I want to outline an activity I do with students to demonstrate a method for finding research questions that are both doable at school or in one's basement as well as original questions where one may make a new discovery. It involves a phenomenon all of us encounter every day, since we all use sinks, bathtubs, and drinking fountains every day - the hydraulic jump. This is when a stream of water falls on a hard surface, spreads out smoothly (laminar flow) and at some radius the water flow rises up and becomes turbulent...this is the jump.

Now, it is true that the hydraulic jump has been known to exist and studied in the lab for over a century. How can we possibly find out something new? We can by thinking about every conceivable physical parameter that might have some effect, big or small, on the nature of the jump. This involves picking apart something that at a glance and without any thinking, seems utterly simple. Here, water flows out, then jumps. What's so special about this?

The activity (go to the link, click on The Science Teacher: Hydraulic Jump... article) is simple for students. I have a beaker of water, some type of hard plate sitting on top of a block in the middle of a tray or pan, which is used to collect the water you are about to spill on the plate, and that's it. Students pour the water so the stream hits the plate at a right angle, and I literally tell students to play with the system, with a goal of thinking of at least 10 things that might possibly affect the size or shape of the jump they observe. Within 5 minutes, students tend to have more than 10 possible parameters!

A list might look like this (highlighted ones are linked to papers students have done):
   height the water falls from
   the diameter of the stream of water falling towards the plate
   temperature of the water
   whether the stream is falling smoothly (laminar) or has turbulence/is winding/vibrating
   the flow rate of the water
   the material the plate/surface is made from
   whether the plate is flat or angled
   whether the plate is still or moving side to side
   whether the plate is still or moving up and down (frequency and amplitude combinations)
   whether the plate is moving on a see saw
   temperature of the plate
   if the plate is smooth or rough
   if there are engraved lines/patterns of any kind on the surface (could be numerous patterns tried, which may be symmetric or asymmetric, any of which may not have been tested in prior experiments; these could have ranges of depth in the surface, and so on)
   the viscosity of the fluid (what if one used syrup instead of water?)
   if there are multiple streams hitting the surface (i.e. jumps interact)
   does gravity matter? Would a jump form on the moon?
   the angle the stream hits the surface
   environmental factors: air pressure, air temperature, humidity in the air, any wind
   if the plate is rotating
   structure of the stream as it hits the surface
   combinations of any of these parameters/situations
 
Right there, within minutes, students may have dozens of possible experiments to try on something that does NOT require fancy equipment or a professional lab; just a little creativity and elbow grease from a teacher and/or student who puts the experiment(s) together. If one looks in journals for mathematical models of hydraulic jump, they will focus on flow rate, viscosity, and height above the surface from which the stream falls, and that is about it.

For those that have links to papers, the papers have pictures and more detailed outlines of the apparatus students built and used, and how they went about obtaining data for these studies.  Use these old papers as guides to design and build your own apparatus and experimental procedures!

Try using this method on any everyday phenomenon with which you are curious! Play with it in a controlled way, and make a list of any and all parameters that even might make any difference in the phenomenon. With some literature searches, using Google Scholar or any university database (which we can help with), you can determine if thorough and serious work has been done on the question(s) you have in mind.

What is the difference between word problems and 'math modeling' and 'computational' problems?

In math and science classes, students are all too familiar with 'word problems' that need to be solved on a homework set. These are problems that ask, in words, what a particular answer should be to an everyday type application of the topic being studied. In algebra, it may be something like "the sides of a rectangular plot of land has two sides three times as long as the short sides, and the sides add up to 120 meters. What is the length of a long side of the rectangle?"

You would need to think of an equation to solve this. These can be difficult for many students, but these types of problems at least show a practical side to the material being studied in a math class. It is also nice that there is a definite numerical answer, and only one correct answer.

Then there are the problems professional mathematicians, scientists, and engineers deal with on a daily basis: Math Modeling and Computational problems. These are generally much more complex, do not necessarily have a single correct answer, and can be open-ended, meaning you must go out and find information that can help you develop a possible solution. These types of problems have many possible ways of thinking about the problem, to the point where you must start with a series of assumptions that a solution could be built upon.

For instance, what if your problem was: For a specific city, develop an optimal recycling plan that will maximize participation by the city's inhabitants.

And that's it! No information given to you that hints at an answer, no data provided upfront. You must go out and find information, you might need to obtain information that does not yet exist, such as what is the current level of participation. There are different ways of collecting recyclables, such as given each household a recycling bin or having a central depository. There are cost restraints in the city budget. You will need a staff to do all this - how many do you hire to make this process effective, but also keep costs down so the city can afford it. You need facilities to process and separate the materials, transportation to then take those materials to plants that actually do recycling, and so on. Wow!!

These complex, open-ended problems need assumptions to be made, justified, and then used with real data to develop potential, viable solutions. When doing this type of problem, you actually need to develop equations, i.e. the mathematical model, that results from those assumptions and best-fit functions from the data, which can then be used to make predictions and find results to initial conditions that you have for the city.

Got all that?!

Check out the Moody's Mega Math Challenge Handbook for more details about mathematical modeling. There is a video with a brief explanation of math modeling from professional applied mathematicians. Check out archives of nationally winning papers from high school students, so you can see the level of work that is possible! There is a matrix of all the problem statements given for the COMAP math modeling contests, including the high school contest (HiMCM) for many more examples of what open-ended problems look like!

For an example of computational work, which typically involves writing computer simulations for complex systems, check this out. It is an example of how computational research is done for climate science.

Resources for Students

Science research in high school is the ultimate experience a student can have. And by research, this does NOT mean typical high school lab activities you might do in one or two periods, but rather longer term work on something that is not necessarily known - the goal on this site is to help you find a topic and very specific research question that you can take on and try to literally discover something new. And the kicker is to do this without the need of professional labs or equipment! We hope you can do this in your school or in your home, with everyday materials. Or, perhaps do this on a computer at school or at home with computational work or accessing data sets that are online.

Go to the various pages of this site and you will find many research questions we have formed and provided initial information and suggestions in order to help you get started. Typically, the hardest part of the research process for anyone is to find that specific question that has not been looked at before in a serious study - here, you have many options in a variety of fields of study, so have fnu with it, find something of interest to you, and think about how you can design and setup controlled experiments to collect data and possibly an answer to the question! DO THE PROCESS OF SCIENCE, from start to finish, and look for that answer that no one else knows!