Limiting flux and critical transmembrane pressure determination using an exponential model: The effect of concentration factor, temperature, and cross-flow velocity during casein micelle concentration by microfiltration

During microfiltration, limiting (J_L) and critical flux (J_C) are essential. Using these concepts, the operational zones, have been established for flux (J) versus transmembrane pressure (ΔP_T). However, the resistance model cannot be used for an accurate description of these operational zones. The aim of this work was to evaluate the application of an equation for process parameters' determination during skim milk microfiltration. The exponential model, J = J_L(1 - exp(-ΔP_T/(ΔP_T)_C), allowed a direct determination of J_L and the critical ΔP_T ((ΔP_T)_C) and allowed the calculation of J_C and the limiting ΔP_T ((ΔP_T)_L). The effect of temperature, concentration factor, and cross-flow velocity over J_L and (ΔP_T)_C were evaluated. For J_L and (ΔP_T)_C, a good fitting was obtained (R_adj² = 98.12%; R_adj² = 97.83%, respectively). These results allow to predict the limiting and critical points for given values of the concentration factor, cross-flow velocity and temperature. Moreover, determination of the operational zones could be established.