Numerical Solution of the Problem of Relaxation Filtration of a Suspension Through a Radial Filter at a Constant Flow Velocity

This paper investigates the relaxation filtration of a suspension through a radial filter surface under conditions of constant flow velocity. A mathematical model for relaxation cake growth is formulated based on the liquid-phase continuity equation, Darcy’s relaxation law, and constitutive relations for both compressive and liquid pressures. The resulting governing equation is a nonlinear partial differential equation for the compressive pressure, complemented by a Stefan condition that characterizes the motion of the cake–slurry interface. The moving-boundary problem is solved numerically using a finite difference method employing a coordinate-based front-tracking technique combined with iterative procedures. The numerical results demonstrate the influence of relaxation effects on cake formation. Increasing the relaxation time slows the compaction process, thereby maintaining higher porosity and promoting accelerated growth of the cake layer thickness.