A particle flow specific boundary element formulation for microfluidic applications

Abstract

In this study, a special formulation to obtain velocities of particles flowing within a microchannel is presented. The formulation is based on boundary element method, and the large system matrices resulting from the analysis is reduced to a system of linear equations with the unknowns being the rigid-body motion parameters of the particles. This reduction is achieved through matrix multiplications which increases computational efficiency when compared with the solution of a large system of equations. Since the formulation involves mainly matrix multiplications, parallelization is straightforward. With the presented algorithm, only the position of the particle(s) are tracked through the solution of their rigid-body velocities and an explicit time integration to obtain displacements. Due to the boundary-only nature of the boundary element method, the particle flow in close proximity to the channel walls are very effectively modeled without any need for specific model. The presented method is given in 2D, where the 3D formulation is straightforward. To demonstrate the applicability of the method, besides some benchmark problems, two fundamental processes, namely flow cytometry and hydrodynamic-based particle separation, are studied. It is observed that present formulation offers an efficient numerical model to be used for the simulation of the particle trajectory for 2D microfluidic applications and can easily be extended for 3D multiphysics simulations.