# Focusing and splitting of particle streams in microflows via viscosity gradients

## TL;DR

This paper introduces a novel mechanism where viscosity gradients in microflows cause soft particles to migrate across streamlines, enabling potential applications in particle focusing and separation.

## Contribution

It reveals how viscosity gradients induce cross-streamline migration and focusing of soft particles, supported by analytical and simulation methods.

## Key findings

- Viscosity gradients cause particles to migrate towards lower viscosity regions.
- Viscosity variations can lead to splitting of particle attractors in flows.
- Particle properties influence the location of attracting streamlines.

## Abstract

Microflows are intensively used for investigating and controlling the dynamics of particles, including soft particles such as biological cells and capsules. A classic result is the tank-treading motion of elliptically deformed soft particles in linear shear flows, which do not migrate across straight stream lines in the bulk. However, soft particles migrate across straight streamlines in Poiseuille flows. In this work we describe a new mechanism of cross-streamline migration of soft particles. If the viscosity varies perpendicular to the stream lines then particles migrate across stream lines towards regions of a lower viscosity, even in linear shear flows. An interplay with the repulsive particle-boundary interaction causes then focusing of particles in linear shear flows with the attractor stream line closer to the wall in the low viscosity region. Viscosity variations perpendicular to the stream lines in Poiseuille flows leads either to a shift of the particle attractor or even to a splitting of particle attractors, which may give rise to interesting applications for particle separation. The location of attracting streamlines depend on the particle properties, like their size and elasticity. The cross-stream migration induced by viscosity variations is explained by analytical considerations, Stokesian dynamics simulations with a generalized Oseen tensor and Lattice-Boltzmann simulations.