The intermediate stage of the dead-end filtration process

The volume-time curves in a dead-end filtration experiment can be approximated - in the intermediate stage - by a power law. The exponent of this law shows a marked dependence on the zeta potential and falls to nearly 0.5 in the vicinity of the isoelectric point. Two limiting cases have been investigated: (1) high zeta potential where the particles have a strong interaction and (2) zero zeta potential where the particles behave as a dense gas. For (1) the forming cake can be assigned a stiffness and by solving a system of Blot equations the exponent of the volume-time curve is obtained; the value of the exponent must always be greater than 0.5. For (2) the 'granular temperature' theory by McTigue and Jenkins (1992, Channel flow of a concentrated suspension. In H. H. Shen et al., Advances in macromechanics of granular materials (pp. 381-390), Amsterdam: Elsevier) is made appropriate to the geometry and the exponent of the volume-time curve is found to be exactly 0.5. The two limiting cases are associated with distinctly different cake formation processes: for (1) a smooth solidosity curve is found while for(2) the cake formation can be approximated by a solidosity step function (the 'two-solidosity' model). In all modelling in this paper the septum permeability is non-negligible, but a function of the solidosity of the filter cake at the septum. (C) 2000 Elsevier Science Ltd. All rights reserved.