Modelling of filtration: from the polarised layer to deposit formation and compaction

A theoretical study is developed for the modelling of mass accumulation from the polarised layer to the formation of a deposit. Concentrated suspension properties are accounted for through a solid pressure corresponding to osmotic pressure in the suspension and to compression resistance in the deposit. Mass and solvent transfer are depicted through balanced permeation/diffusion transport in the polarised layer and balanced friction/compaction forces in the deposit. The modelling applied to transient state for dead end filtration gives information about the coupling between mass transfer in the polarised layer and in the deposit. Consequences on specific cake resistance are presented and discussed.

This model is a first step to the description of the mass accumulation in a membrane filtration process including both polarisation, formation and — Membrane surface, L2 — Temperature, K — Filtered volume per membrane area, L — Solid accumulated volume per membrane area, L — Particle or macromolecule volume, L3 compaction of a deposit. Two major parameters are used to describe colloidal suspensions properties within the polarised layer and the deposit: the solid pressure π(φ) and the hydrodynamic coefficient K(φ). Modelling lies on two major points: • The continuous description of colloidal properties vs. volume fraction from the solid suspension in the liquid to the solid percolated by the liquid. • The analogy in equation between the description of permeation in a deposit and the diffusion in a polarised layer.