A model of the steady-state motion of suspensions

The authors examine the steady-state one-dimensional motions of suspensions whose particles have a density equal to that of the corresponding dispersion medium. As a whole, the mechanical behavior of such suspensions is described by equations of motion that coincide in form with the Navier-Stokes equations for a certain incompressible fluid whose viscosity is a known function of the particle concentration in the suspensions. To close these equations, the authors postulate a principle of minimum energy dissipation for steady-state motion, which plays the paxt of an equation of state for the suspension. This new equation permits the determination of the spatial distribution in the concentration of solids. Exact solutions are presented for certain variational problems associated with the Poiseuille flow of a fluid of this kind in circular tubes and Couette flows between concentric cylinders and parallel planes. It is shown that in most cases separation of the suspension takes place.