On the Depletion Effect in Colloids

Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clustering in colloids. The term depletion force refers to the force (in the Newtonian sense) which is associated with the clustering. Our model is stochastic but derived from a deterministic setup in a Newtonian setting. A mathematical transition from the deterministic dynamics of several large particles and infinitely many small particles to a kinetic description of the stochastic motion of the large particles is available. Assuming that the empirical velocity distribution of the small particles is governed by a probability density, the mean-field force on the large particles can be represented as the negative gradient of a scaled version of that density. The stochastic motion of the large particles can then be described by a system of correlated Brownian motions. The scaling in the transition preserves a small parameter, the correlation length. From the limiting kinetic stochastic equations we compute the probability flux rates for the difference in ∗Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA, [email protected], 216 368 4838 (analog), 216 368 5163 (fax). †Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA, [email protected], 216 368 2890 (analog), 216 368 5163 (fax). ‡Chemical Engineeing, Case Western Reserve University, Cleveland, OH 44106, USA, [email protected], 216 368 4122 (analog), 216 368 3016 (fax).