Prediction of the Limiting Flux and Its Correlation with the Reynolds Number during the Microfiltration of Skim Milk Using an Improved Model

Limiting flux (J(L)) determination is a critical issue for membrane processing. This work presents a modified exponential model for J(L) calculation, based on a previously published version. Our research focused on skim milk microfiltrations. The processing variables studied were the crossflow velocity (CFV), membrane hydraulic diameter (d(h)), temperature, and concentration factor, totaling 62 experimental runs. Results showed that, by adding a new parameter called minimum transmembrane pressure, the modified model not only improved the fit of the experimental data compared to the former version (R(2) > 97.00%), but also revealed the existence of a minimum transmembrane pressure required to obtain flux (J). This result is observed as a small shift to the right on J versus transmembrane pressure curves, and this shift increases with the flow velocity. This fact was reported in other investigations, but so far has gone uninvestigated. The J(L) predicted values were correlated with the Reynolds number (Re) for each d(h) tested. Results showed that for a same Re; J(L) increased as d(h) decreased; in a wide range of Re within the turbulent regime. Finally, from dimensionless correlations; a unique expression J(L) = f (Re, d(h)) was obtained; predicting satisfactorily J(L) (R(2) = 84.11%) for the whole set of experiments