On the Brazil Nuts Problem: Is It of Relevance to Hydrodynamics?

A recent advance in understanding the Brazil nuts phenomenon together with insight into the relative motion of different-size particles in a lattice fluid makes this phenomenon amenable to an approach based on hydrodynamic concept. Here we use this conjecture as a stimulus for solving the equation describing asymmetric transport of particles in a medium moving with constant velocity. We also consider a method for constructing invariant solutions, which enables us to study the dependence of the probability density function on the parameters controlling the asymmetry of the flow. Physical realizations of the invariant solutions are in agreement with recent computer simulations by Alexander and Lebowitz.