Role of 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.

Non-equilibrium steady states of entangled polymer mixtures under shear flow

“…Since eliminating the finite-size effects requires a large system size, we must ensure the typical domain size L ( L x, y . Most of the recent publications 15,16,18 about the non-equilibrium phase separation tune the system size between 512 and 1024, and it is found that the finite-size effects are under control with such a system size. In this study, all simulations are done for asymmetric quenches on a L x 3 L y = 1024 3 512 mesh.…”

“…While under shear the system is no longer periodic and the morphology will in general be anisotropic, we define the length scales using a gradient statistic for f A across the simulation box. We define a symmetric matrix 16,18,35 …”

Hybrid lattice Boltzmann model for binary fluid mixtures

“…At each time step we update ϕ n → ϕ n+1 using Eq. (10) in two successive partial steps [29]. This allows to have a better numerical stability.…”

Role of viscoelasticity in non-equilibrium steady states of sheared entangled polymer mixtures

“…to characterize the long and short principal axes of the domain morphology using a gradient statistic for f A across the simulation box. They are the reciprocal eigenvalues of the symmetric matrix 1,17,24 …”

“…; _ g À3=4 using the Lattice Boltzmann approach. After that, Fielding 17 took a further research and found no evidence for nonequilibrium steady states in inertialess systems, which confirmed the irreplaceable role of inertia in nonequilibrium steady states.…”