  A mathematical model using classical cake-filtration theory and the
surface-renewal concept is formulated for describing constant flux, cross-flow
microfiltration (CFMF). The model provides explicit analytical expressions for
the transmembrane pressure drop (TMP) and cake-mass buildup on the membrane
surface as a function of filtration time. The basic parameters of the model are
the membrane resistance, specific cake resistance, and rate of surface renewal.
The surface-renewal model has two forms: the complete model, which holds for
compressible cakes, and a subsidiary model for incompressible cakes, which can
be derived from the complete model. The subsidiary model is correlated against
some of the experimental TMP data reported by Miller et al. (2014) for constant
flux CFMF of a soybean-oil emulsion in a cross-flow filtration cell having
unmodified and surface-modified, fouling-resistant membranes, and has an
average root-mean-square (RMS) error of 6.2%. The complete model is fitted to
the experimental TMP data reported by Ho and Zydney (2002) for constant flux
microfiltration of a bovine serum albumin solution in a stirred cell using
polycarbonate track-etched membranes and has an average RMS error of 11.2%.
This model is also correlated against the TMP data of Kovalsky et al. (2009)
for constant flux yeast filtration in a stirred cell (average RMS error =
9.2%).

Soft Condensed Matter;Fluid Dynamics