Approximate Theory for Radial Filtration/Consolidation

Approximate solutions are developed for filtration and subsequent consolidation of compactible cakes on a cylindrical filter element. Darcy's flow equation is coupled with equations for equilibrium stress under the conditions of plane strain and axial symmetry for radial flow inwards. The solutions are based on power function forms involving the relationships of the solidosity εs (volume fraction of solids) and the permeability K to the solids effective stress p s . The solutions allow determination of the various parameters in the power functions and the ratio k0 of the lateral to radial effective stress (earth stress ratio). Measurements were made of liquid and effective pressures, flow rates, and cake thickness versus time. Experimental data are presented for a series of tests in a radial filtration cell with a central filter element. Slurries prepared from two materials (Microwate, which is mainly SrSO 4 , and kaolin) were used in the experiments. Transient deposition of filter cakes was followed by static (i.e., no flow) conditions in the cake. The no-flow condition was accomplished by introducing bentonite which produced a nearly impermeable layer with negligible flow. Measurement of the pressure at the cake surface and the transmitted pressure on the central element permitted calculation of k0 .