A model for filter cake formation on geotextiles: Theory

The equations for a numerical model that describes the accumulation of filter cake on a geotextile as flow passes through it are developed and solved numerically. The accumulation of both colloidal and settle-able particles is considered. The equations are first developed for a colloidal suspension and subsequently expanded to include settle-able particles having various settling velocities. Output from the numerical model includes: the flow rate through the geotextile/filter cake layers, the head drop through the layers, the cumulative volume of flow per unit area of geotextile and the rate of accumulation of the various size components of the filter cake. Important model parameters are Ψy0/K which relates the permittivity of the geotextile times the water level at the start of the dewatering process to the permeability of the accumulating filter cake, gΨ2/y0, a dimensionless permittivity, the αi/ɛ values that determine how much each sediment size class contributes to the filter cake’s thickness and the vi/K values that describe the settling velocities of each sediment size class. The size distribution of the particles in various layers within the filter cake can be determined from the model and an example solution is presented that shows how particle size distribution varies within the filter cake. Experiments to verify the theory are presented in Weggel and Dortch (this issue).