Active Young-Dupr\'e Equation: How Self-organized Currents Stabilize Partial Wetting

TL;DR

This paper develops an Active Young-Dupré equation to describe how self-organized currents stabilize partial wetting in active particle systems, revealing new physics beyond equilibrium theories.

Contribution

It introduces a microscopic definition of surface tension for active systems and demonstrates how steady currents stabilize interfaces and influence droplet shapes.

Findings

Steady currents emerge from symmetry breaking and stabilize interfaces.

Negative liquid-gas surface tension causes objects to be expelled from the liquid phase.

The theory explains partial wetting and droplet size selection in active matter.

Abstract

The Young-Dupr\'e equation is a cornerstone of the equilibrium theory of capillary and wetting phenomena. In the biological world, interfacial phenomena are ubiquitous, from the spreading of bacterial colonies to tissue growth and flocking of birds, but the description of such active systems escapes the realm of equilibrium physics. Here we show how a microscopic, mechanical definition of surface tension allows us to build an Active Young-Dupr\'e equation able to account for the partial wetting observed in simulations of active particles interacting via pairwise forces. Remarkably, the equation shows that the corresponding steady interfaces do not result from a simple balance between the surface tensions at play but instead emerge from a complex feedback mechanism. The interfaces are indeed stabilized by a drag force due to the emergence of steady currents, which are themselves a by-product of the symmetry breaking induced by the interfaces. These currents also lead to new physics by selecting the sizes and shapes of adsorbed droplets, breaking the equilibrium scale-free nature of the problem. Finally, we demonstrate a spectacular consequence of the negative value of the liquid-gas surface tensions in systems undergoing motility-induced phase separation: partially-immersed objects are expelled from the liquid phase, in stark contrast with what is observed in passive systems. All in all, our results lay the foundations for a theory of wetting in active systems.