A Revised Approach To The Theory Of Cake Filtration

Several simplifications have been accepted in filtration theory during the past fifty years in an effort to avoid apparently intractable mathematical problems. In effect, these simplifications ignored the variation in average cake porosity and average filtration resistance with variation in pressure drop or with time. This study examines the traditional approach and shows that, in many cases, it cannot give correct design guidance. Using a set of dimensionless parameters because of the large number of significant variables, a revised theory is developed which does not require that porosity and resistance values be set constant. Graphs developed in the traditional approach (e.g., dt/dv versus v or t/v versus V) have substantial curvature near the ordinate; but this curvature is frequently ignored in theory and is easily missed in experiments. The revised theory allows more accurate design calculations, especially for compressible cakes.