Inertial focusing of a neutrally buoyant particle in stratified flows

Abstract

Particles in microfluidic channels experience two dominant lift forces in the direction transverse to the flow—the shear gradient lift force and the wall lift force. These forces contribute to the lift experienced by the particle and cause their cross stream migration until they attain an equilibrium position where the net lift force in the transverse direction is zero. Stratified coflow of two liquids with different viscosities is a stable flow-regime observed under some operating conditions. The presence of the second fluid alters the shear gradient induced lift force and the wall force acting on the particle at each point, changing the final equilibrium position. These positions can be tuned and controlled by altering the viscosity or the flow rates of the two fluids so that the particles focus in one fluid. A numerical method based on the combined Immersed Boundary-Lattice Boltzmann Method is used to study inertial focusing of neutrally buoyant particles in stratified Couette flows and pressure driven flows. We analyze how different factors such as the Reynolds number, flow rate ratio, viscosity ratio of the fluids, and particle size affect the particle migration in two-dimensional (2D) and three-dimensional (3D) geometries. Our study shows that in Couette flows, the particle focuses in the low viscosity fluid when the interface is at the center. We also found that a critical viscosity ratio exists beyond which particle focusing in low viscous fluid is guaranteed, for a given flow rate ratio in pressure driven flows.