# Cross-stream migration of a Brownian droplet in a polymer solution under Poiseuille flow

## TL;DR

This study uses simulations to explore how polymer solutions influence the lateral migration of Brownian droplets in microchannels under flow, revealing polymer-induced focusing effects and shape dynamics.

## Contribution

It demonstrates that adding polymers causes droplets to focus at the channel centerline, contrasting with inertial migration in Newtonian fluids, and explores the effects of polymer length and concentration.

## Key findings

- Droplets migrate toward walls in Newtonian fluids due to inertia.
- Polymers cause droplets to focus at the channel centerline.
- Flow-rate and polymer properties influence droplet shape and position.

## Abstract

The migration of a Brownian fluid droplet in a parallel-plate microchannel was investigated using dissipative particle dynamics computer simulations. In a Newtonian solvent, the droplet migrated toward the channel walls due to inertial effects at the studied flow conditions, in agreement with theoretical predictions and recent simulations. However, the droplet focused onto the channel centerline when polymer chains were added to the solvent. Focusing was typically enhanced for longer polymers and higher polymer concentrations with a nontrivial flow-rate dependence due to droplet and polymer deformability. Brownian motion caused the droplet position to fluctuate with a distribution that primarily depended on the balance between inertial lift forces pushing the droplet outward and elastic forces from the polymers driving it inward. The droplet shape was controlled by the local shear rate, and so its average shape depended on the droplet distribution.