Microfluidic modeling and simulation of flow in membrane microreactors

We study the development of a mathematical model that describes isothermal microfluidic steady flow in a membrane microreactor, i.e., a silicon microreactor that houses a permeable membrane in one wall. The model employs the Navier-Stokes equation with appropriate boundary conditions for fluid permeation through the membrane and velocity slip at the walls to account for high Knudsen number. The model equations are solved analytically using finite Fourier transforms. The model solution is used to evaluate the effect of fluid permeation through the membrane and the Knudsen number on the velocity profile and pressure drop. For the simplified cases of no permeation and/or no slip, the derived solution is in excellent agreement with published experimental and theoretical results available in the literature. The utility of the model is illustrated by applying the results to a membrane microseparator used to separate hydrogen from the other effluents in a microreformer.