On the Steady Regime Assumptions in Flows Involving Short Fiber Suspensions

The present study addresses the issue of the steady regime assumption inflows involving short fibers usually introduced for the analysis of rheometric flows orin the simulation of some kind of forming processes as is the case of the extrusion.For this purpose we analyze the solution of the Fokker-Planck equation in simpleshear flows for both two-dimensional and three-dimensional systems. Despite thesimplicity of that flow, it brings the possibility of comparing exact and numericalsolutions. Thus, exact analytical solutions and results of numerical simulations basedon the finite element technique and the method of particles are presented. The effectof diffusion on the existence of steady solutions, and more particularly on the timerequired to reach that steady solution, is investigated.