Certain assumptions which have previously served as a basis for the conventional equations employed in constant pressure filtration are shown to be in error. It is demonstrated that the specific filtration resistance, the ratio of the mass of wet to mass of dry cake, and the rate of flow, q = dv/dθ, are not constant as has been assumed. In an example it is shown that q undergoes an eightfold variation as the liquid flows from the cake surface through to the medium.
Since the product αq appears in the basic differential equation, incorrect values of q lead to errors in the calculated values of α arising from experimental data. The errors are significant when thick slurries are employed.
New partial differential equations are presented for flow through compressible media in which q varies with cake thickness. Modifications of the conventional constant pressure equations are presented.