Numerical study of particle migration and equilibrium positions in inertial particle microfluidics: effect of channel cross-section*

Inertial particle microfluidics (IPMF) is a technique used to separate cells on the microscale, such as circulating tumour cells (CTCs) for disease diagnosis, by focusing cells to a lateral equilibrium position which depends on cell properties. IPMF is a passive technique which, aside from a pump to generate a flow inside the device, solely relies on the intrinsic hydrodynamic forces between the channel, fluid, and particles. Two key forces in IPMF are the wall lift force and the shear gradient lift force, which are influenced by a number of parameters, such as the Reynolds number, particle confinement (particle size relative to the channel size), and velocity profile. The velocity profile is determined by the shape of the channel's cross-section, leading to variations in the number and location of equilibrium positions of the particles. 

In our study, we employ a 3D immersed-boundary-lattice-Boltzmann method to numerically analyze the dynamics of both soft and rigid particles, including their migration paths and equilibrium positions. 

By simulating particle migration in channels with different cross-sectional shapes, we demonstrate that changes in the channel geometry significantly impact the behaviour of particles by modifying the particle trajectory and the location and number of equilibrium positions, while keeping the Reynolds number and particle size constant. The results will enable improved designs in order to more finely manipulate particles in microfluidic channels for applications such as cell cytometry and separation.