From the development of a compressional rheology of a flocculated suspension, a number of separation processes have been modeled. With respect to the two-stage pressure filtration process of compact formation and then consolidation, the theological formulation appears at first examination to be significantly at variance with the conventional engineering approach. The present model may be reconciled to the early engineering model. Moreover the filtration parameters extracted from experiments can be related to the more fundamental rheological parameters, r(phi), the hindered settling factor, which is a function of solids volume fraction phi - it takes into account hydrodynamic interactions between local particles, which increase the drag forces. Useful estimates of the compact bed formation resistance and the formation time are provided as a function of applied pressure. The initial time dependence of the consolidation ratio on the elapsed consolidation time is not found to be a square root behavior as suggested by the conventional modeling.