Initial Response Method for Simultaneous Determination of Both Diffusivity and Distribution Coefficients in Symmetric Reverse Osmosis Membrane by Dialysis.

Abstract

A partial differential diffusion equation for dialysis phenomenon is derived considering the effect of osmosis flux jw of which the initial value jw0 was observed very high and decreased exponentially with time toward jw∞ with a time constant τ. Numerical integration of the equation with time, gives dialysis curve which shifts toward right with the increase of pushing back effect (jw0/jw∞) and prolonging effect τ. Therefore, the intercept on T(=tD/l2)-axis, TL, for the asymptotic line of dialysis curve which is usually 0.17 for gas separation membranes (special case for no osmosis), increases with the increase of the both effects, for example TL=1.0 for jw0/jw∞=10 and τD/l2=0.5.With cellulose acetate symmetric membranes, it was observed that the shape of dialysis curve changed from convex for the new membrane to concave at the 2nd, 3rd and 4th run. With the dialysis curve of 4th run and the measured osmosis flux, the best fit combination of distribution coefficient Kc and diffusivity Dc was obtained for the minimum error squared, as Kc=0.05 and Dc=2.2×10-14[m2·s-1].The diffusion coefficient De and distribution coefficient Ke were measured as De=2.5×10-14[m2·s-1] and Ke=0.05, respectively which agree quite well with the calculated Dc and Kc.