Theory for particle settling and shear-induced migration in thin-film liquid flow

Particles suspended in a film flow can either settle out of the flow, remain well mixed, or even advance faster than the fluid, accumulating at the moving contact line. Recent experiments by Zhou [Phys. Rev. Lett. 94, 117803 (2005)] have demonstrated that these three settling behaviors can be achieved by control of the average particle concentration phi and inclination angle theta. This work presents a theory for determining the settling behavior in the Stokes regime by calculating the depth profile of phi and the depth-averaged velocities of the liquid and particle phases. It is found that shear-induced particle fluxes can lead to an inversely stratified flow, in which the particles move on average faster than the liquid. The theory is directly compared to Zhou 's experimental data, and the implications of stratification for lubrication-type models are also discussed.