Capillary wave formation in conserved active emulsions

TL;DR

This paper investigates how non-equilibrium chemical interactions induce instabilities and capillary waves at interfaces in active emulsions, revealing mechanisms for controlling interfacial dynamics and mass transport in soft matter systems.

Contribution

It introduces a minimal model coupling conserved species with a chemical field, identifying conditions for interfacial instabilities and characterizing capillary waves in active emulsions.

Findings

Non-reciprocal chemotactic interactions induce interface instabilities.

Capillary waves can propagate along phase boundaries due to oscillatory instability.

Simulations show secondary instabilities leading to complex wave superpositions.

Abstract

The dynamics of phase-separated interfaces shape the behavior of both passive and active condensates. While surface tension in equilibrium systems minimizes interface length, non-equilibrium fluxes can destabilize flat or constantly curved interfaces, giving rise to complex interface morphologies. Starting from a minimal model that couples a conserved, phase-separating species to a self-generated chemical field, we identify the conditions under which interfacial instabilities may emerge. Specifically, we show that non-reciprocal chemotactic interactions induce two distinct types of instabilities: a stationary (non-oscillatory) instability that promotes interface deformations, and an oscillatory instability that can give rise to persistent capillary waves propagating along the boundaries of phase-separated domains. To characterize these phenomena, we develop a perturbative framework that predicts the onset, wavelength, and velocity of capillary waves, and quantitatively validate these predictions through numerical simulations. Beyond the linear regime, our simulations reveal that capillary waves undergo a secondary instability, leading to either stationary or dynamically evolving superpositions of different wave modes. Finally, we investigate whether capillary waves can facilitate directed mass transport, either along phase boundaries (conveyor belts) or through self-sustained liquid gears crawling along a solid wall. Taken together, our results establish a general framework for interfacial dynamics in active phase-separating systems and suggest new strategies for controlling mass transport in soft matter and biological condensates.