Phase separating binary fluids under oscillatory shear

TL;DR

This study uses lattice Boltzmann simulations to explore how oscillatory shear influences phase separation in binary fluids, revealing complex behaviors depending on frequency and viscosity, including isotropic growth, anisotropic patterns, and slowed segregation.

Contribution

It introduces a detailed simulation approach to analyze the effects of oscillatory shear on binary fluid phase separation, highlighting new phenomena related to frequency and viscosity variations.

Findings

High-frequency shear leads to isotropic domain growth with known exponents.

Oscillatory shear can induce anisotropic patterns and coexistence of lamellar and isotropic domains.

Low-frequency shear results in lamellar order similar to steady shear conditions.

Abstract

We apply lattice Boltzmann methods to study the segregation of binary fluid mixtures under oscillatory shear flow in two dimensions. The algorithm allows to simulate systems whose dynamics is described by the Navier-Stokes and the convection-diffusion equations. The interplay between several time scales produces a rich and complex phenomenology. We investigate the effects of different oscillation frequencies and viscosities on the morphology of the phase separating domains. We find that at high frequencies the evolution is almost isotropic with growth exponents 2/3 and 1/3 in the inertial (low viscosity) and diffusive (high viscosity) regimes, respectively. When the period of the applied shear flow becomes of the same order of the relaxation time $T_R$ of the shear velocity profile, anisotropic effects are clearly observable. In correspondence with non-linear patterns for the velocity profiles, we find configurations where lamellar order close to the walls coexists with isotropic domains in the middle of the system. For particular values of frequency and viscosity it can also happen that the convective effects induced by the oscillations cause an interruption or a slowing of the segregation process, as found in some experiments. Finally, at very low frequencies, the morphology of domains is characterized by lamellar order everywhere in the system resembling what happens in the case with steady shear.