Separation Science and Technology, Vol.34, No.13, 2485-2500, 1999
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 concentration boundary layer, coupled with diffusive backtransport opposing the ultrafiltrate flux, has been developed in the present study. This model can be used to simulate flux and rejection at any desired time in an unstirred batch ultrafiltration module. This model uses the semi-infinite consideration to solve the governing partial differential equation by the Laplace transform 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 the concentration profile has been found, an iterative technique has been used in conjunction with other membrane and solute properties to predict the flux and rejection at any desired time under a specified operating condition. Concentration profiles as a function of time for different experiments are also computed in order to analyze the effect of different operating parameters on the concentration boundary layer. The prediction from this model is found to be in good agreement with the experimental results obtained during ultrafiltration of PEG-6000 in an unstirred batch module using a cellulose acetate membrane of MWCO-5000, and in most cases the variation of concentration within the boundary layer is found to be limited within a very short distance over the membrane surface.
Keywords:MEMBRANE SEPARATION PROCESSES;CROSS-FLOW ULTRAFILTRATION;KRAFT BLACK LIQUOR;LIMITING FLUX;CONCENTRATION POLARIZATION;MACROMOLECULAR SOLUTIONS;PREDICTION;CELL;FILTRATION