# Inertial migration and axial control of deformable capsules

## TL;DR

This study investigates how deformable capsules behave in microfluidic channels under inertial flow, revealing how their equilibrium positions depend on deformability, size, and external axial forces, with potential applications in cell separation.

## Contribution

The paper introduces a comprehensive simulation analysis of deformable capsule migration in inertial microfluidics, highlighting a master curve for equilibrium positions and control mechanisms for particle focusing.

## Key findings

- Equilibrium position depends on size and deformability.
- Deformability influences migration direction opposite to inertial lift.
- External axial forces can focus particles at the same position regardless of deformability.

## Abstract

The mechanical deformability of single cells is an important indicator for various diseases such as cancer, blood diseases and inflammation. Lab-on-a-chip devices allow to separate such cells from healthy cells using hydrodynamic forces. We perform hydrodynamic simulations based on the lattice-Boltzmann method and study the behavior of an elastic capsule in a microfluidic channel flow in the inertial regime. While inertial lift forces drive the capsule away from the channel center, its deformability favors migration in the opposite direction. Balancing both migration mechanisms, a deformable capsule assembles at a specific equilibrium distance depending on its size and deformability. We find that this equilibrium distance is nearly independent of the channel Reynolds number and falls on a single master curve when plotted versus the Laplace number. We identify a similar master curve for varying particle radius. In contrast, the actual deformation of a capsule strongly depends on the Reynolds number. The lift-force profiles behave in a similar manner as those for rigid particles. Using the Saffman effect, the capsule's equilibrium position can be controlled by an external force along the channel axis. While rigid particles move to the center when slowed down, very soft capsules show the opposite behavior. Interestingly, for a specific control force particles are focused on the same equilibrium position independent of their deformability.