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

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 $\varphi$ with advective-diffusive dynamics. Activity creates a contribution ${\Sigma }_{ij}=-\zeta (({\partial }_i\varphi )({\partial }_j\varphi )-(\nabla \varphi {)}^2{\delta }_{ij}/d)$ 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.

7 pages, 4 figures

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