Structure and rheology of binary mixtures in shear flow

Abstract

Results are presented for the phase separation process of a binary mixture subject to an uniform shear flow quenched from a disordered to a homogeneous ordered phase. The kinetics of the process is described in the context of the time-dependent Ginzburg-Landau equation with an external velocity term. The large-n approximation is used to study the evolution of the model in the presence of a stationary flow and in the case of an oscillating shear.For stationary flow we show that the structure factor obeys a generalized dynamical scaling. The domains grow with different typical lengthscales Rx and R ⊥ respectively in the flow direction and perpendicularly to it. In the scaling regime R ⊥ ∼ t α ⊥ and Rx ∼ γt αx (with logarithmic corrections), γ being the shear rate, with αx = 5/4 and α ⊥ = 1/4. The excess viscosity ∆η after reaching a maximum relaxes to zero as γ −2 t −3/2 . ∆η and other observables exhibit log-time periodic oscillations which can be interpreted as due to a growth mechanism where stretching and break-up of domains cyclically occur.In the case of an oscillating shear a cross-over phenomenon is observed: Initially the evolution is characterized by the same growth exponents as for a stationary flow. For longer times the phase separating structure cannot align with the oscillating drift and a different regime is entered with an isotropic growth and the same exponents of the case without shear.47.20.Hw; 05.70.Ln; 83.50.Ax

Growth and scaling in anisotropic spinodal decomposition

“…(A Ginzburg-Landau model for sheared mixtures has been shown to exhibit a similar property, though with two lengths both behaving differently than ℓ(t) here. [5]) Fig. 3 also illustrates that data for different square lattices scale…”

“…[3]- [5] We studied the kinetics of the driven lattice gas (DLG) [6] by extensive Monte Carlo (MC) simulation. This is appealing on several grounds.…”

“…That is, initial formation of small anisotropic clusters (inducing a larger growth rate along the flow than in the other directions), and stringlike domains extending macroscopically have been reported in fluids. [3,5] After the initial (anisotropic) nucleation regime, strings coarsen further into well defined, relatively narrow stripes; fig.1c. The resulting multistripe states are not stable.…”

Role of inertia in nonequilibrium steady states of sheared binary fluids

“…Despite previous experimental [4,5,6,7,8,9,10,11,12,13,14], numerical [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] and theoretical [18,19,20,21,29,32,33,34,35,36,37] work, this question remained open until the recent simulation studies of Stansell et al in Refs [38,39]. Using Lattice Boltzmann techniques, they gave convincing evidence for the formation of nonequilibrium steady states, with domains of a finite size set by the inverse shear rate, independent of the system size.…”

Equilibrium and dynamical behavior in the Vicsek model for self-propelled particles under shear

“…Even in passive materials an imposed flow may lead to flow-sustained non-equilibrium steady states. For instance, wormlike micelles and liquid crystals form bands when sheared [12][13][14], whereas a sheared binary fluid arrests spinodal decomposition, leaving domains of a well-defined size, provided that hydrodynamic coupling between the order parameter and the velocity field is retained [15][16][17][18][19][20]. The self-driving characteristics of SPP suspensions is likely to add even more richness to this already fascinating physics.…”