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

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 $ϕ$ with advective-diffusive dynamics. Activity creates a contribution $Σ_{ij}=-ζ((\partial_iϕ)(\partial_jϕ)-(\nablaϕ)^{2}δ_{ij}/d)$ to the deviatoric stress, where $ζ$ 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.