Variable flow rate in compactible filter cakes

Traditional formulas used for design of filters and interpretation of experimental data depend upon a number of simplifications including negligible solid velocity u(s) and a superficial liquid flow rate q(L) which is assumed to be a function of time and independent of distance x through a filter cake. The extent of variation of u(s) and q(L) for highly compactible biosolids is discussed in this article. An approximate method based on well-known equations which rest on the assumption the q(L) is constant throughout a compressible cake at a given time is presented. Using previously available formulas, the assumption of constancy of q(L) is abandoned; and approximate equations yielding q(L) as a function of x are developed. Comparisons are made of the variation with distance of q(L), u(x), and relative velocities for cakes of different degrees of compactibility and slurries of varying concentrations. Problems related to verification of a given model are discussed.