A combined continuum/DSMC technique for multiscale analysis of microfluidic filters

A multiscale method that combines continuum fluid models with the direct simulation Monte Carlo (DSMC) method is presented. The continuum regions are treated by Stokes equations and a scattered point based finite cloud method is employed to solve the Stokes equations. The continuum and DSMC regions are combined by an overlapped Schwarz alternating method with Dirichlet-Dirichlet type boundary conditions. A scattered point interpolation scheme is developed to interpolate the solution between subdomains. The convergence characteristics of the multiscale approach are investigated in detail. Specifically, the dependence of convergence on the overlap size, the DSMC noise, and the number of time steps employed in the DSMC algorithm are studied. While the convergence depends weakly on the DSMC noise and the overlap size, the number of DSMC time steps simulated in each coupling iteration should be selected so that the total time steps simulated until convergence of the coupled process is close to the time constant of the DSMC subsystem. Steady-state analysis of microfluidic filters is studied in detail using the multiscale approach. The multiscale approach is also applied for the simulation of a membrane with an array of microfluidic filters and a dual-stage microfluidic device with an array of microfluidic filters for particle trapping and sorting.