Phase separation under shear in two-dimensional binary fluids

Abstract

We use lattice Boltzmann simulations to study the effect of shear on the phase ordering of a two-dimensional binary fluid. The shear is imposed by generalising the lattice Boltzmann algorithm to include Lees-Edwards boundary conditions. We show how the interplay between the ordering effects of the spinodal decomposition and the disordering tendencies of the shear, which depends on the shear rate and the fluid viscosity, can lead to a state of dynamic equilibrium where domains are continually broken up and re-formed.

Binary fluids under steady shear in three dimensions

“…(We define the mean velocity as u x =γy so that x, y, z are velocity, velocity gradient and vorticity directions respectively;γ is the shear rate. )Our recent simulations, building on earlier work of others [4,5], have shown that in two dimensions (2D), a NESS is indeed achieved [6]. In 3D, the situation is more subtle.…”

“…Another crucial difference is that in 2D fluid bicontinuity is possible only by fine tuning to a percolation threshold at 50:50 composition (assuming fluids of equal viscosity) so that the generic situation is one of droplets. (Indeed, for topological reasons, droplets are implicated even at threshold [4].) In contrast, in 3D both fluids remain continuously connected across the sample throughout a broad composition window either side of 50:50.…”

“…Fig. 2 shows time series for L x,y,z from runs R030 and R019 as measured by a standard order parameter gradient statistic [4] that effectively measures the mean distance between interfaces crossing the chosen direction. In [12], finite size effects (in the absence of shear) were considered quantitatively under control when the correlation length L was less than 1/4 of the system size Λ.…”

“…Linear least-squares fits to these data suggest scaling exponents for L x,y,z of, respectively, −0.54 ± 0.03, −0.65 ± 0.03, and −0.60 ± 0.04 at the 95% confidence level. An alternative scaling, using the principal axes of the gradient statistic [4,6], gives exponents for L 3 , L 1 , L 2 of −0.53 ± 0.04, −0.67 ± 0.03, and −0.64 ± 0.06 (data not shown). These results appear to rule out L y ∼γ −3/4 which was found in 2D [6].…”

Rheological Properties of Binary and Ternary Amphiphilic Fluid Mixtures

“…It is very important to understand how these uids behave under high shear forces, in order to b e able to build reliable machines and choose the proper uid for di erent applications. In our simulations we use Lees Edwards boundary conditions, which were originally developed for molecular dynamics simulations in 1972 15] and have been used in lattice Boltzmann simulations by di erent authors before 25,24,10]. We apply our model to study the b ehaviour of binary immiscible and ternary amphiphilic uids under constant and oscillatory shear.…”