Optimal transport and control of active drops

TL;DR

This paper develops an optimal control framework for transporting active fluid drops, revealing strategies that minimize dissipation and optimize displacement, with implications for manipulating active matter.

Contribution

It introduces a low-order lubrication theory model combined with optimal control to determine efficient active stress profiles for drop transport.

Findings

Identifies a 'gather-move-spread' transport strategy.

Reveals complex morphologies due to active-passive interactions.

Provides bounds on maximum displacement relative to drop size.

Abstract

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural ''gather-move-spread'' strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension, and active controls generates richer behaviour with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework, and begins to pave the way for the spatiotemporal manipulation of active matter.