Finite element methods for electroneutral multicomponent convection-diffusion

Abstract: Multicomponent fluids are those consisting of multiple chemical species. Complex physical processes occur within these fluids; examples include cross-diffusion, chemical reactions, momentum transport, thermality and (for charged species) electrical effects. Despite their ubiquity in science and engineering, multicomponent fluids have received limited attention from the finite element community, and many important applications remain out of reach from current numerical methods. In this talk, we present novel high-order finite element methods for multicomponent cross-diffusion and momentum transport. Our model can also incorporate local electroneutrality when the species carry electrical charge, making the methods particularly desirable for simulating liquid electrolytes in electrochemical applications. We discuss challenges that arise when discretising the governing partial differential equations, as well as some salient theoretical properties of the numerical schemes. Finally, we present numerical simulations involving (i) the microfluidic non-ideal mixing of hydrocarbons and (ii) a lithium-ion battery electrolyte in a Hull cell electrode.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)