I am looking for statistical models (or results of relevant numerical simulations) to estimate the number of different types of contacts between particles in a powder mixture. The simplest case would be a mixture of particles of type A and B, both spherical and of same uniform size.
The goal would be to calculate the number of A-A, B-B and A-B contacts per unit volume.
More complex cases would include size and shape distributions (which may or may not differ between the components) and mixtures with more than two components.
Any relevant references are highly appreciated! Thanks in advance.
Hi Jan!
I'm not sure there is an answer to this since the problem as written depends on the exact packing state of the bed, which is presumably unknown at a particle level. I suggest that you make the additional assumption that the bed is entirely random and the the contacts are quite soft (you need this because otherwise the number of contacts is extremely sensitive to tiny particle positional errors).
If you allow those simplifications, then assuming the bed is large enough, you can make some progress by assuming that each particle has a coordination number determining its number of nearest neighbours. Each one of these then has a x% chance of being either A or (100-x) of being B depending on your concentration ratio, so you can construct a probability distribution for the distribution of A and B surrounding each particle. Then you can propagate this through the bed and see how/if it converges (you only need to do a 1D chain since the bed is random).
If you wanted to improve this then you would need to look at probability distributions of coordination numbers as a function of PSD and other particle properties. Standard DEM simulations routinely produce such data, although it is probably not published in an accessible form.
Pretty much all bets are off for hard, non-spherical particles...
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