| Compressible cake filtration is a widely used process for solid-liquid separation. Filter cakes are formed when a liquid containing solid particles is forced through a filter system which allows the liquid transport but retains the solid particles. Following a literature survey, the governing equations for the cake thickness and the concentration of solid particles are obtained by averaging the conservation of mass equations for fluid, suspended and captured solid particles along the cake thickness. Then, these first order nonlinear partial differential equations are solved simultaneously with constant average porosity. The capture mechanisms that are considered include a kinetic equation with simultaneous rate constants of particle trapping and cake erosion. The maximum cake thickness is observed when all particles are captured at the cake surface. However, if the level of turbidity is half of the slurry concentration, the cake thickness is dramatically reduced. Furthermore, it reaches a minimum when all particles penetrating the surface leave the cake without being captured.; Later, numerical solutions for the cake permeability, cake resistance, solid particle velocity and the concentration of suspended solid particles are obtained with experimentally available porosity and pressure variations along the dimensionless cake thickness. The results, compared to a simplified case obtained from literature, show excellent match. In addition to the conservation of mass equations, functional relations among porosity, permeability, and pressure are obtained from literature and solved simultaneously with the preceding one to obtain numerical solutions for the same variables in addition to pressure and porosity. At each instant of time, the porosity decreases throughout the cake from the cake surface to the filter septum where it has the smallest value. As the cake thickness increases at a given point, the porosity decreases with time.; Finally, the equation for the transport of solid particles through a finite column of soil is solved analytically and numerically. Comparison of theoretical results with experimental ones show favorable match. |
