Analysis of facilitated transport membrane with modified boundary conditions

The performance of the steady state carrier-mediated transport has been investigated. A modified boundary condition is proposed according to the fact that a flowing sweep gas in the receiving phase of the membrane sweeps the permeant molecules, thus the concentration of permeant in the interface of membrane-receiving phases is a function of mass transfer coefficient in the receiving phase. Based on the method of orthogonal collocation, the system of coupled integro-differential boundary value equations is solved. It is confirmed that the facilitation factors calculated by the present approach are much closer to the experimental data. A superior efficiency has also been shown with respect to the previous results of simple Dirichlet type boundary conditions. The proposed method well predicts the system over the entire range of operating conditions, from the physical diffusion to the chemical equilibrium region as well as equal/unequal carrier and complex diffusivities. More studies reveal that increasing Sherwood number and thus reducing the receiving phase resistance would cause an increase in the mass transfer coefficient as well as trans-membrane flux. Also, a decrease in concentration of permeant in the receiving phase, “C_M,b”, shows the same results as increasing Sherwood number.