A model for the evolution of sedimentation beds in the dynamic of a pipelined non-Newtonian fluid

In this work, the dynamic of particles in a non-Newtonian (Bingham) fluid is considered, developing a mathematical model (one nonlinear, free boundary, first-order PDE) for the sedimentation of particles in a cylindrical, axis symmetric flow. We proved existence and uniqueness (locally in some circumstances) of the solutions, and we tested numerically the fitting of the model with the real physical problem.