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 dimensionless scalar concentration field. with advective-diffusive dynamics. Activity creates a contribution Sigma(ij) = -(kappa) over cap[(partial derivative(i)phi)(partial derivative(j)j) - (del phi)(2)delta(ij)/d] to the deviatoric stress, where (kappa) over cap 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, there is a subtle interplay of activity and hydrodynamics, even without alignment interactions.