Study of a cake model during stirred dead-end microfiltration

A cake model that predicts permeation flux in dead-end microfiltration under stirred condition is proposed, and it is established based on a particle mass balance on the membrane surface in terms of Darcy's law. In this model, denudation coefficient K is introduced to quantitatively describe the back-transport of particles from the membrane surface by agitation. Moreover, the effects of operating conditions (pressure, suspension concentration and agitation velocity) on denudation coefficient K and permeation flux are studied for kaolin suspension and yeast suspension in this paper, and the results showed: (1) Denudation coefficient K has a direct proportion with agitation velocity and suspension concentration, while it has an inverse proportion with transmembrane pressure. (2) An increase in pressure results in a rise in flux, but when exceeding critical pressure, the flux rises slowly, even declines, additionally, membrane flux rises with an increase in agitation velocity, and declines when suspension concentration increases, but under higher concentration, the flux approaches the level of lower concentration. The influencing degree of operating conditions on denudation coefficient K is analyzed quantificationally by using a multivariate linear regression model, and the regression equations are K = -0.43 - 1.16P + 147.23C + 5.13 X 10(-4) omega for kaolin suspension and K = -51.92 - 271.96P + 1.06 x 10(4)C + 7.57 X 10(-2) omega for yeast suspension. Finally, the model is validated by experimental data, and the results show good agreement between model prediction and experimental observation, it indicates that agitation can decrease cake layer thickness and consequently improve permeation flux, and the cake model can be used to predict permeation flux during dead-end microfiltration.