A rigorous, dynamic mathematical model for predicting the rate of ultrafiltration of charged colloidal dispersions is developed. The model is based on sophisticated descriptions of the particle-particle interactions within filter cakes which are responsible for controlling permeation rates. Electrostatic (double layer) interactions are accounted for by means of a Wigner-Seitz cell approach, including a numerical solution of the non-linear Poisson-Boltzmann equation, which is known to give an excellent description of the configurational electrostatic interaction energy of particle assemblages. London-van der Waals forces are calculated using a computationally efficient means of approximating screened, retarded Lifshitz-Hamaker constants. Hydration forces are included by utilising mathematical expressions derived from the latest results obtained with surface-forces apparatus. Configurational entropy effects are calculated using an equation of state giving excellent agreement with molecular dynamic data. Electroviscous effects are also accounted for.