Wednesday, 30 November 2011

Granular Dynamics and Asteroid Formation - Pt 2 - Modelling at Home

About half way through the lecture on Granular Systems at the University of Nottingham see Part 1 here the presenter began showing some short videos of how the particles in granular solids behaved when agitated. One of the effects shown was the "Brazil Nut Effect" and, on seeing this, Number One son leaned over and whispered "We could do this in Phun".

"Phun" is a free software program that allows you to create shapes and simple machines that can then be "run" in an environment that has gravity, air resistance and other characteristics of the real world. I could go on but, to be honest, the short demonstration video below says it all. Dear Reader, if you can watch this without a sense of "wow" and a wish to have a go yourself, then perhaps you need to check whether your heart has somehow turned to stone. . .

Awesome, isn't it! You can download the software, for free, here (scroll down to the section called "old verions" to get the free version).

Now, to get back to the lecture. NSB had a go at modelling (more or less) the "Brazil Nut Effect" in Phun.

This was done by making a box that had a load of small balls inside it, as well as one larger ball. The whole thing was then agitated by two triangular cams located below the box that were rotating at about 100rpm. Somewhat to NSB's surprise, the model worked, with the larger ball rising to the surface each time. Three screenshots of a typical run are are shown below, one from the start, one from the middle and one at the end (i.e. when the larger ball had reached the surface)

In the example above, the larger ball is twice the diameter of the other balls. What do you think would happen if the larger ball was three, four or five times the diameter of the other balls? Would it rise to the top even faster? BFTF certainly thought so and tried it. The results are shown below (they are all the time to rise to the surface, the average of three runs and are corrected for the fact the larger balls don't have to rise so far before the get to the surface)

2 x diameter of standard ball : 125sec
3 x diameter of standard ball : 107sec
4 x diameter of standard ball : 131sec
5 x diameter of standard ball : 87sec

Not exactly the clearest of trends is it? The result for the 4xdiameter ball seems a little out of place, so BFTF ran that one a further three times to get more data, and found the average to go up to 143 seconds for his trouble.

That really does seem weird, and BFTF could not really understand why there was no trend. NSB also noticed that, once it had reached the top, if the ball moved to the side it would often get "dragged down" towards the bottom of the container for a while before moving towards the centre and rising to the surface.

What was going on? NSB had no idea. . . until it noticed this article that described how particles behaved like a fluid, with convection currents (like peas in a pan of boiling water).

This would imply that the standard balls would also rise to the surface, as they were just caught in the current, as it were. NSB tried this in Phun, but found the marked ball to stay resolutely where it was and not move upwards particularly.

NSB suspects that this is because the balls are all the same size and so pack together really well, thus limiting movement, so perhaps using two or three different shapes of particles would work better.

Out of idle curiosity (and, in case you are wondering, NSB does have a day job that pays all the bills so is not actually idle), NSB then took the "4xdiameter of standard ball". . .er . . .ball and progressively reduced its density down from 2.0g/cc (the same as all the small balls) to 0.5g/cc. Dear Reader, what do you think happened this time. . .?

Well, the results are shown in Chart below:

Presuambly, giving the larger ball a density much bigger than 2g/cc would result in it being too heavy to be "pushed" to the surface, but NSB has not tried this.

So there you. "Phun" - it is brilliant, and you can do real physics on it.

If you haven't already, why not download it and have a go - you know you want to.

No comments:

Post a Comment