Phenomenological model of filtration processes: 1. Cake formation and expression

The phenomenological theory of sedimentation-consolidation processes of flo cculated suspensions is extended to pressure filtration processes. The loca l mass and linear momentum balances for the solid and liquid component toge ther with appropriate constitutive assumptions lead to a strongly degenerat e (mixed hyperbolic-parabolic) nonlinear partial differential equation for the local solids fraction, which together with initial and boundary conditi ons determines a dynamic cake filtration process. In the case of a prescrib ed applied pressure function, we obtain a free boundary problem, in which t he piston height has to be determined simultaneously with the solids concen tration, A numerical algorithm approximating the physically correct solutio n, with possible discontinuities such as the cake/suspension interface, is presented and employed to simulate various cake filtration processes. (C) 2 001 Elsevier Science Ltd. All rights reserved.