Simulation of unstirred batch ultrafiltration system based on analytical solution of boundary layer equation

A mass transfer model based on an unsteady-state mass balance over the conc entration boundary layer, coupled with diffusive backtransport opposing the ultrafiltrate flux, has been developed in the present study. This model ca n be used to simulate flux and rejection at any desired time in an unstirre d batch ultrafiltration module. This model uses the semi-infinite considera tion to solve the governing partial differential equation by the Laplace tr ansform technique, which gives the analytical solution of the concentration profile. In the partial differential equation, volumetric flux is assumed to be constant in accordance with pseudosteady-state assumption, often used in diffusive mass transfer analysis. Once the analytical expression for th e concentration profile has been found, an iterative technique has been use d in conjunction with other membrane and solute properties to predict the f lux and rejection at any desired time under a specified operating condition . Concentration profiles as a function of time for different experiments ar e also computed in order to analyze the effect of different operating param eters on the concentration boundary layer. The prediction from this model i s found to be in good agreement with the experimental results obtained duri ng ultrafiltration of PEG-6000 in an unstirred batch module using a cellulo se acetate membrane of MWCO-5000, and in most cases the variation of concen tration within the boundary layer is found to be limited within a very shor t distance over the membrane surface.