Active Model H: Scalar Active Matter in a Momentum-Conserving Fluid

TL;DR

This paper develops a continuum model for scalar active matter in a momentum-conserving fluid, revealing how activity influences phase separation and interface dynamics, with predictions confirmed numerically.

Contribution

It introduces a novel scalar active matter theory incorporating hydrodynamics and activity-induced stresses, highlighting effects on phase separation and interface behavior.

Findings

Activity modifies interfacial tension, leading to unique phase separation dynamics.

Numerical simulations confirm domain growth halts at a finite length scale.

Active stresses can be contractile, affecting coarsening processes.

Abstract

We present a continuum theory of self-propelled particles, without alignment interactions, in a momentum-conserving solvent. To address phase separation we introduce a scalar concentration field $\phi$ with advective-diffusive dynamics. Activity creates a contribution $\Sigma_{ij}=-\zeta((\partial_i\phi)(\partial_j\phi)-(\nabla\phi)^{2}\delta_{ij}/d)$ to the deviatoric stress, where $\zeta$ is odd under time reversal and $d$ is the number of spatial dimensions; this causes an effective interfacial tension contribution that is negative for contractile swimmers. We predict that domain growth then ceases at a length scale where diffusive coarsening is balanced by active stretching of interfaces, and confirm this numerically. Thus the interplay of activity and hydrodynamics is highly nontrivial, even without alignment interactions.