Finite element methods for multicomponent convection-diffusion

Francis R. A. Aznaran, Patrick E. Farrell, Charles W. Monroe, Alexander J. Van-Brunt

Published 2022-08-25Version 1

We develop finite element methods for coupling the steady-state Onsager-Stefan-Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Employing a novel variational formulation for general non-ideal fluids, we prove well-posedness of a Picard-type linearization, and convergence of its discretization with appropriate finite elements. The application of the method to non-ideal fluids is illustrated with a simulation of the microfluidic mixing of hydrocarbons.