# The flow field around a confined active droplet

## TL;DR

This study experimentally measures and analytically models the complex flow field around a confined active droplet, revealing significant effects of wall confinement and providing a simplified yet accurate flow description.

## Contribution

First experimental 3D flow measurements around a swimming droplet and an analytical model incorporating wall effects and singularities.

## Key findings

- Confinement significantly alters the flow field compared to unbounded flow.
- A superposition of dipole and quadrupole singularities accurately models the flow.
- The model captures the monopolar flow component due to Marangoni propulsion.

## Abstract

We present here first-of-a-kind experimental measurements of the flow field around a swimming water droplet, using confocal PIV in three dimensions. The droplet is denser than the continuous oil phase, and swims close and parallel to the bottom wall. The measured flow field is first quantitatively characterized and compared to the flow field obtained for an axisymmetric swimmer in unbounded flow. Important qualitative differences are observed, in particular the emergence of a strong isotropic radial flow field in the planes parallel to the wall. These fundamental differences stress the critical impact of confinement on the flow field around the swimming droplet. We then propose an analytical formulation, based on a reduced order description of the swimming droplet in terms of fundamental hydrodynamic singularities as well as the classical method of images. This model is able to account exactly for the effect of the wall and provides a simplified description of the flow field as the superposition of axisymmetric dipole and quadrupole singularities. We demonstrate that this simplified description quantitatively captures the effect of the wall on the dipolar and quadrupolar components of the flow field. Further including the confinement-induced asymmetry of the concentration field responsible for the droplet's Marangoni propulsion, our model is also able to account for the monopolar contribution to the experimental flow field which drives the dominant far-field signature of the droplet.