Assessment of mesoscopic particle-based methods in microfluidic geometries

We assess the accuracy and efficiency of two particle-based mesoscopic simulation methods, namely, Dissipative Particle Dynamics (DPD) and Stochastic Rotation Dynamics (SRD) for predicting a complex flow in a microfluidic geometry. Since both DPD and SRD use soft or weakly interacting particles to carry momentum, both methods contain unavoidable inertial effects and unphysically high fluid compressibility. To assess these effects, we compare the predictions of DPD and SRD for both an exact Stokes-flow solution and nearly exact solutions at finite Reynolds numbers from the finite element method for flow in a straight channel with periodic slip boundary conditions. This flow represents a periodic electro-osmotic flow, which is a complex flow with an analytical solution for zero Reynolds number. We find that SRD is roughly ten-fold faster than DPD in predicting the flow field, with better accuracy at low Reynolds numbers. However, SRD has more severe problems with compressibility effects than does DPD, which limits the Reynolds numbers attainable in SRD to around 25-50, while DPD can achieve Re higher than this before compressibility effects become too large. However, since the SRD method runs much faster than DPD does, we can afford to enlarge the number of grid cells in SRD to reduce the fluid compressibility at high Reynolds number. Our simulations provide a method to estimate the range of conditions for which SRD or DPD is preferable for mesoscopic simulations.