Centrifugal filtration of particulate systems

Abstract

Analysis of centrifugal filtration is complicated by its formulation in radial-cylindrical coordinates and the inclusion of a significantly varying centrifugal force across the filter cake. The process often commences, however, with a filter cake of zero thickness so there will be a period of time during which one-dimensional, constant centrifugal force analysis of the process will be exact. It is important to understand the nature of flow during this time because it accurately represents the early stages of, and therefore a base from which to analyse, the more complicated system. In addition, it may emerge that, for some materials, the simplified analysis may be sufficient for practical purposes. For materials where the permeability and the effective stress are well-defined functions of the water content, the early stages of centrifugal filtration are described by a one-dimensional non-linear Fokker–Planck equation cast in a material coordinate based on the distribution of the solid phase. The analysis takes full account of the non-steady nature of flow and the non-linearity of the equations that describe it. It does not require common inaccurate assumptions that the flux of solid can be neglected nor that quasi-steady flow takes place. The analysis predicts, and experiments on a sodic bentonite confirm, that substantially non-uniform solid and liquid profiles are observed during ‘early stages’ of the process, which evolve in a manner which is effectively identical to those observed during constant pressure filtration. The generality of the approach is illustrated with material data for Red mud. Limits to the times during which flow might be regarded as one-dimensional rather than cylindrically axi-symmetric, and during which some centrifugal effects might be neglected, are discussed and shown to be readily calculated.