Liquid-liquid phase membrane contactors are increasingly being used for mixing and reaction. The principle is the following: component A flows through the membrane device inlet to mix/react with component B which comes from the membrane pores. This study presents a numerical simulation using computational fluid dynamics (CFD) of momentum and mass transfer in a tubular membrane contactor for laminar flow conditions. The velocity and concentration profiles of components A-C are obtained by resolution of the Navier-Stokes and convection-diffusion equations. The numerical simulations show that mixing between A and B is obtained by diffusion along the streamlines separating both components. The mixing/reaction zone width is within the region of a few hundred of microns, and depends on the diffusion coefficients of A and B. Hollow fiber membrane devices are found to be of particular interest because their inner diameter is close to the mixing zone width.