Mathematical modelling of inertial particle migration in curved microfluidic ducts

Abstract

Particles suspended in flow through a closed duct migrate in the cross section of the duct due to the forces acting on them and may focus to different equilibrium positions in the cross section. This has been used for particle sorting in microfluidic devices, one example being "liquid biopsy", the isolation of circulating tumour cells from a blood sample. In this talk we will consider the migration of spherical neutrally-buoyant particles in curved microfluidic ducts. In addition to the primary flow along the duct, the curvature results in Dean vortices in the cross section. Particle migration is due to a balance between the inertial lift arising, primarily, from the flow along the duct, and drag arising from the cross-sectional vortices. In a spiral duct, the changing bend radius results in bifurcations in the particle equilibria and consequential changes in the particle dynamics, so that different spirals yield different outcomes. Recent mathematical modelling, aimed at predicting the migration of a spherical particle in such ducts under the assumptions that the particle Reynolds number is small and the bend radius of the duct changes slowly, will be discussed. The goal is to develop a model that might be used to determine a duct geometry for a specific application requiring separation of particles of different size. This is joint work with Dr Brendan Harding, Dr Rahil Valani, Dr Kyung Ha and Prof Andrea Bertozzi.