The need for inertia in nonequilibrium steady states of sheared binary fluids

Abstract

We study numerically phase separation in a binary fluid subject to an applied shear flow in two dimensions, with full hydrodynamics. To do so, we introduce a mixed finite-differencing/spectral simulation technique, with a transformation to render trivial the implementation of Lees-Edwards sheared periodic boundary conditions. For systems with inertia, we reproduce the nonequilibrium steady states reported in a recent lattice Boltzmann study. The domain coarsening that would occur in zero shear is arrested by the applied shear flow, which restores a finite domain size set by the inverse shear rate. For inertialess systems, in contrast, we find no evidence of nonequilibrium steady states free of finite size effects: coarsening persists indefinitely until the typical domain size attains the system size, as in zero shear. We present an analytical argument that supports this observation, and that furthermore provides a possible explanation for a hitherto puzzling property of the nonequilibrium steady states with inertia.

arXiv comment18 pages, 8 figures

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• Two-dimensional Turbulence in Symmetric Binary-Fluid Mixtures: Coarsening Arrest by the Inverse Cascade
• Bridging length and time scales in sheared demixing systems: from the Cahn-Hilliard to the Doi-Ohta model
• Advection selects pattern in multistable emulsions of active droplets
• The intertwined physics of active chemical reactions and phase separation