An analytical solution of Sherwood number in a stirred continuous cell during steady state ultrafiltration

Sherwood number relationship was developed for gel controlled steady state ultrafiltration in a stirred cell from the first principles, under the framework of boundary layer analysis. A developing mass transfer boundary layer was considered and the governing equation was solved using an integral method. Variation of viscosity in the mass transfer boundary layer was included as proposed by Aimar and Field (1992) [29]. Polyvinyl alcohol, having molecular weight of 14,000, was used as the gel forming material. A weak dependence of mass transfer coefficient on transmembrane pressure drop was observed. The final expression of Sherwood number was obtained using 50% of the experimental data of the steady state. Permeate flux values were calculated for the rest 50% of the experiments using the developed relation in the predictive mode. In all cases, the predictions lie within ±10% of the experimental data. Using the expression of Sherwood number, the transient profile of flux decline was also estimated.

► An analytical solution of Sherwood number for stirred cell is derived.
► Integral method is used to solve the mass transfer boundary layer.
► Sherwood number expression is developed for gel controlling filtration including the viscosity and pressure variations.
► Using the Sherwood number relationship, the transient flux decline profile is also estimated.