# Mesoscale particle-based simulations of flow in expansion-contraction microchannels at low Reynolds number

## TL;DR

This study compares analytical and mesoscale simulation methods for low Reynolds number flow in sinusoidal microchannels, finding good agreement and highlighting the strengths and limitations of each approach.

## Contribution

It extends prior analytical solutions to tenth order and evaluates mesoscale particle-based methods against these solutions for complex microchannel flows.

## Key findings

- DPD and MPCD simulations agree well with series solutions for flow rates and velocities.
- Mesoscale models show slight wall slip, overpredicting flow parameters.
- Series solutions fail for short channels and large amplitudes, but mesoscale methods remain effective.

## Abstract

We computationally study the flow of Newtonian fluids through sinusoidal expansion-contraction microchannels at low Reynolds number. We first use a perturbation method to analytically derive series solutions for the stream function and volumetric flow rate that extend prior work [P.K. Kitanidis and B.B. Dykaar, Transport in Porous Media 26, 89-98 (1997)] up to tenth order. We then employ two particle-based mesoscale methods, dissipative particle dynamics (DPD) and multiparticle collision dynamics (MPCD), to simulate the same flows. We find that the fluid velocity at the expansion and contraction points as well as the volumetric flow rate are in good agreement between DPD, MPCD, and the fourth-order series solution for a wide range of microchannel geometries. The mesoscale fluid models exhibit some slip at the walls, leading to a small but consistent overprediction of the velocity and volumetric flow rate. The series solution fails for short microchannel lengths and large amplitudes; we identify lengths and amplitudes for which it converges to a given order. Overall, we find that DPD and MPCD are convenient and reasonably accurate methods, particularly for microchannel geometries where the series solution fails or is cumbersome to implement.