A numerical method for mass transfer by a thin moving membrane with selective permeabilities

We propose a numerical method for mass transfer by membrane movement in the framework of the non-conforming mesh with respect to the membrane. The method treats the discontinuity at the membrane by incorporating the concentration jump into the finite element discretization. Through coupling the weak forms of the unsteady convection-diffusion equation and membrane permeability equation, an implicit treatment of the jump value is derived, which is capable of handling both permeable and non-permeable membranes. Through some comparisons of the numerical tests with analytical solutions, the validity of the proposed method is established. The analytical solutions include the steady concentration distributions as well as transient state during the movement of the membrane. The method is applied to the mass transfer with a membrane of curved geometry, and the applicability for the membrane with arbitrary shape is demonstrated.