# Prediction of inertial particle focusing in curved microfluidic channels.

Professor Yvonne Stokes, Mathematical Sciences, The University of Adelaide

Inertial lift and drag forces on particles suspended in flow through a curved microfluidic duct cause their migration in the cross section of the duct and focusing by size to different regions of the cross section. This has been used in microfluidic devices for particle sorting as required for “liquid biopsy”, the isolation of cancer cells in a routine blood sample. I will discuss a recently developed model to predict the migration of a spherical particle under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane. Depending on its initial position, a particle migrates towards one of these. The Navier-Stokes equations determine the hydrodynamic forces acting on a particle. A leading order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. The model is used to predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales, specifically the particle radius, duct height, and duct bend radius. We will consider ducts with rectangular and trapezoidal shaped cross-sections in order to demonstrate how changes in the cross-section design influence the dynamics of particles. This is joint work with Dr Brendan Harding and Prof Andrea Bertozzi.

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