Vorticity Determines the Force on Bodies Immersed in Active Fluids

TL;DR

This paper links the forces on bodies in active fluids to vorticity and density currents, showing how shape and boundary effects influence motion, with implications for designing propulsion in active matter systems.

Contribution

It introduces a theoretical framework connecting vorticity and force generation in active fluids, enabling shape-based control of propulsion.

Findings

Vorticity near bodies determines propulsion direction.

Force scales with system boundary in bounded systems.

Shape curvature influences local vorticity and motion.

Abstract

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by--but far away from--the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a non-vanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We demonstrate that vorticity is localized close to the body and to points at which the local curvature changes, enabling the rational design of particle shapes with desired propulsion properties.