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Regarding static granular mixtures (pile of sand - particles with different sizes), is there an expression that will give me the entropy of such a mixture? I am interested in finding the entropy of the system initially and once it has been screened ie once the larger particles get sorted out, giving two piles (I think that ths is a reversible process, correct me if I am wrong). Would this mixing entropy be consistent with a bulk entropy such as $\Delta S = m c_p ln(T)$ ? Could I use this bulk entropy and the mixing entropy together in some free energy expression? I have looked for some references but I get nothing that I can access.


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The concept of entropy here is a little misleading--- the entropy is negligible compared to molecular entropy, the number of grains is essentially infinitely smaller than the number of atoms. So it is not useful to level-mix like this. But it is straightforward to define the configurational entropy of a granular mixture, but this is almost certainly not the right quantity for predicting the dynamics, since it can decrease (and increase the atomic entropy by hugely more in the process). – Ron Maimon Apr 25 '12 at 4:20
@Ron Good to see you Ron. It has been a long time since my days in Rock 21. The motivation for this question (and perhaps some sort of modification may be due) is: I have a screen, and lets say a binary solution - same material, different sizes. The screen separates the material inefficiently so I end up with two piles, each predominantly of one size. The screen is basically ordering the material. I know the amount of power applied. I can measure the temperatures of the piles. The machine is insulated. Can I say something about the operation in terms of entropy? – s martins Apr 26 '12 at 9:18

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