A comprehensive model for cross-flow filtration incorporating polydispersity of the influent

A semi-empirical model is presented for the prediction of foulant deposit thickness and concentration, and thereby, predicting the permeate flux in cross-flow microfiltration and ultrafiltration. The scope of the model is limited to colloidal suspensions (i.e. non-diffusive solutes) and its hallmark is its applicability to polydispersed influents. The theoretical model was verified with experimental observations and found to yield a fairly good agreement with an error less than 62% of the average flux over 100 min of filtration. However, evaluation of model coefficients a and b is necessary through laboratory studies. The model was successfully used to predict the effect of particle size distribution (PSD) on permeate flux. The simulation results corroborate the contention that the long-term flux decline is due to the reduction is foulant deposit permeability via infiltration of fines into the cake, thereby demonstrating the importance of influent particle size distribution (PSD) on foulant deposit permeability. The proposed model is a first step towards the modeling of polydispersed influents. As such there is a lot of scope for further refinements which is briefly discussed.