Inertial focusing of spherical particles in curved microfluidic ducts at moderate Dean numbers

Abstract

We examine the effect of Dean number on the inertial focusing of spherical particles suspended in flow through curved microfluidic ducts. Previous modelling of particle migration in curved ducts assumed the flow rate was small enough that a leading order approximation of the background flow with respect to the Dean number produces a reasonable model. Herein, we extend our model to situations having a moderate Dean number (in the microfluidics context) while the particle Reynolds number remains small. This extension allows us to capture changes in the background flow that occur with increasing flow rate, namely a shift in local extrema towards the outside wall. The change in the axial velocity profile of the background flow has an effect on the inertial lift force, while the change in the cross-sectional components directly affects the secondary flow drag. In keeping the particle Reynolds number small we approximate the inertial lift force in a similar manner to previous studies while capturing subtle effects do to the modified background flow profile. Capturing and understanding these effects is an important step towards accurately modelling inertial migration across a wide range of practical applications. Our results reveal how the changing background flow profile modifies the inertial focusing of particles. We illustrate enhanced lateral separation of particles by size in a number of scenarios and find that focusing times can be roughly separated into two regimes. These results suggest our model might aid with parameter choices for separation of particles by size.