Evaluation of Grid-Based and Grid-Free Methods to Model Microchannel Transport-Reaction

The goal of this paper is to investigate the spectral element method (SEM), a grid-based computational approach, and the grid-free particle strength exchange method (PSEM) for solving the advection-diffusion-reaction equation in a microfluidic channel. We identify the dimensionless parameter regimes at which each algorithm provides a satisfactory solution in terms of accuracy and computational time. We also compare the velocity field computed in microchannel geometries for nonzero and zero Reynolds numbers by solving the full Navier–Stokes equations with the SEM and solving the inertia-free Stokes equations with the boundary element method, which does not require an internal mesh. The methods discussed may be utilized in any appropriate combination to solve high and low Péclet number and zero and nonzero Reynolds number transport problems to allow fast, accurate evaluation of a binding reaction between two species. We show that the grid-free particle and boundary element methods are suitable for solving the convection-dominated, irregular geometry problems expected for microfluidic applications where the Reynolds number is near zero and the Péclet number is very high. The SEM transport solver is appropriate for cases in which diffusion plays a greater role and the concentration gradients are not as steep. These methods may be applied to the design and optimization of microchannel geometries for mixing and other microfluidic applications.