Mass Transfer Coefficient and Wall Concentration

The mass transfer coefficient of the stirred cell was estimated using the method described below. Dextran (T-70) was purchased from Pharmacia Biotech (Uppsala, Sweden) and a stock solution of about 60 g/L was used. The molecular weight of Dextran T-70 ([CcHioOsJn) is 70.3 kDa. The MW per unit is 162.2 Da, and the carbon content is 44.4%. 

Applying the osmotic pressure model, assuming negligible fouling of the membranes with Dextran and a negligible permeate concentration, the wall concentration of Dextran can be calculated using equations (7.8) and (7.9) and the relationship between osmotic pressure and Dextran concentration developed by Wijmans et al. (1985) 

This equation can be resolved to calculate the concentration from the measured osmotic pressure 

The mass transfer coefficient was determined as a function of membrane t)pe and stirrer speed. Results obtained for various membranes are within 5%, and thus no impact of the membrane was found. The average mass transfer coefficient at 400 rpm was (1.81 0.10) 10 ms h Rejection of Dextran was 99.5% for all membranes used. 

Stirring had a large effect on the mass transfer coefficient with the mass transfer coefficients var)hng from 0.14 lO ms at 0 rpm (unstirred) to 2.18 10 ms at 560 rpm. This indicates that unstirred filtration will cause significandy higher wall concentrations, which explains the differences observed in rejection and fouling experiments. 

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