Developing flow of gas-particle mixtures in vertical ducts

It is well-known that during high-velocity flow of gas-particle mixtures through a vertical duct the particles are distributed nonuniformly over the cross section. We had shown in an earlier paper that such a nonuniform state is sustained under fully-developed flow conditions by the large scale fluctuations accompanying such flows. In the present study, we have carried out a simple analysis of the developing flow problem to demonstrate that the evolution of the nonuniform distribution is indeed driven by turbophoresis.