Phase separation of binary mixtures in shear flow: A numerical study

Active Surface Flows Accelerate the Coarsening of Lipid Membrane Domains

Phase separation of multicomponent lipid membranes is characterized by the nucleation and coarsening of circular membrane domains that grow slowly in time as ∼t^{1/3}, following classical theories of coalescence and Ostwald ripening. In this Letter, we study the coarsening kinetics of phase-separating lipid membranes subjected to nonequilibrium forces and flows transmitted by motor-driven gliding actin filaments. We experimentally observe that the activity-induced surface flows trigger rapid coarsening of noncircular membrane domains that grow as ∼t^{2/3}, a 2x acceleration in the growth exponent compared to passive coalescence and Ostwald ripening. We analyze these results by developing analytical theories based on the Smoluchowski coagulation model and the phase field model to predict the domain growth in the presence of active flows. Our Letter demonstrates that active matter forces may be used to control the growth and morphology of membrane domains driven out of equilibrium.

Hierarchical Morphology of Polymer Blend Films Induced by Convection-Driven Solvent Evaporation

Homogeneous thin films of polymer blends with a desired morphology are necessary because of their applications in the fields such as optoelectronics, sensors, biomedicine, and so on. The frequently employed approach for the thin film preparation, spin coating is only able to achieve a homogeneous film for a small area because of the overwhelming spin-driven solvent evaporation with increased size. Here, a convection-guided morphology formation for polystyrene:poly(methyl methacrylate) blend films is reported. In situ observation shows that the morphology changed from homogeneous deposition with a scale less than 10 μm to a self-organized cellular pattern with a scale of more than 100 μm after the fluid flow is involved. Selective dissolution of the hierarchical films reveals that the cellular morphology is attributed to the flow-field-guided deposition of sequentially generated precipitates. The coupling of phase separation and fluid convection results in the hierarchical morphology that includes Voronoi cellular division as the primary structure and the detailed heterogeneous inner-cell features as the secondary structure. Isolated modulation of either micro- or mesoscale in the hierarchical morphology could be carried out via adjusting phase interaction or the convection disturbance correspondingly, providing a flexible and straightforward strategy to construct designed hierarchical structures for polymer thin films toward desired function or property.

Lattice Boltzmann simulation of phase separation under dynamic temperature and shear: Coupling effects of shear convection and thermal diffusion

This paper presents an exploration of the separation behavior and pattern formation in a shear binary fluid with dynamic temperature after slow cooling via coupled lattice Boltzmann method. The phase separation procedure can be divided into three different stages: spinodal decomposition, domain growth, and domain stretch. The effect of thermal diffusion was observed to be more significant than that of shear convection in the spinodal decomposition stage, while the opposite was observed in the domain growth stage. The slow cooling temperature field significantly prolonged the spinodal decomposition stage, and decreased the separated domain size in domain growth stage. The phase behavior and pattern formation from the disordered state into the coexistence state after slow cooling was investigated during the domain stretch stage. Two typical length scales were obtained according to the equilibrium of two phases, where the number of layers in the corresponding domains was controllable by adjusting the Prandtl number for systems of different scales. The manner in which various viscosities and thermal diffusivities influence the morphologies and kinetic characterizations of the materials was also demonstrated: numerical results indicated that decrease in viscosity can cause increase in the growth exponents of separation fronts and velocity of domain growth, as well as increase in thermal diffusion.

Polymerization-induced spinodal decomposition of ethylene glycol∕phenolic resin solutions under electric fields

Temporal evolution of polymerization-induced spinodal decomposition (PISD) under electric fields was investigated numerically in ethylene glycol∕phenolic resin solutions with different initial composition. A model composed of the nonlinear Cahn-Hilliard-Cook equation for spinodal decomposition and a rate equation for curing reaction was utilized to describe the PISD phenomenon. As initial composition varied, deformed droplet-like and aligned bi-continuous structures were observed in the presence of an electric field. Moreover, the anisotropic parameter (D), determined from the 2D-FFT power spectrum, was employed to quantitatively characterize the degree of morphology anisotropy. The value of D increased quickly in the early stage and then decreased in the intermediate stage of spinodal decomposition, which was attributed to the resistance of coarsening process to morphology deformation and the decline of electric stress caused by polymerization reaction. The results can also provide a guidance on how to control the morphology of monolithic porous polymer and carbon materials with anisotropic structures.

Bridging length and time scales in sheared demixing systems: from the Cahn-Hilliard to the Doi-Ohta model

We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse-grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.

Role of inertia in nonequilibrium steady states of sheared binary fluids

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 and 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.

Binary fluids under steady shear in three dimensions

We simulate by the lattice Boltzmann method the steady shearing of a binary fluid mixture with full hydrodynamics in three dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite correlation lengths in all three spatial directions. Using large simulations, we obtain at moderately high Reynolds numbers apparent scaling exponents comparable to those found by us previously in two dimensions (2D). However, in 3D there may be a crossover to different behavior at low Reynolds number: accessing this regime requires even larger computational resources than used here.

Structural transitions and arrest of domain growth in sheared binary immiscible fluids and microemulsions

We investigate spinodal decomposition and structuring effects in binary immiscible and ternary amphiphilic fluid mixtures under shear by means of three-dimensional lattice Boltzmann simulations. We show that the growth of individual fluid domains can be arrested by adding surfactant to the system, thus forming a bicontinuous microemulsion. We demonstrate that the maximum domain size and the time of arrest depend linearly on the concentration of amphiphile molecules. In addition, we find that for a well-defined threshold value of amphiphile concentration, the maximum domain size and time of complete arrest do not change. For systems under constant and oscillatory shear we analyze domain growth rates in directions parallel and perpendicular to the applied shear. We find a structural transition from a sponge to a lamellar phase by applying a constant shear and the occurrence of tubular structures under oscillatory shear. The size of the resulting lamellae and tubes depends strongly on the amphiphile concentration, shear rate, and shear frequency.

Long-time behavior and different shear regimes in quenched binary mixtures

The dependence on applied shear of the morphological and rheological properties of diffusive binary systems after a quench from the disordered state into the coexistence region is investigated. In particular the behavior of the late-time transversal size of domains L_{y} and of the maximum of excess viscosity (Deltaeta)_{M} is considered. Numerical results show the existence of two regimes corresponding to weak and strong shear separated by a shear rate of the order of gamma_{c} approximately 1t_{D} where t_{D} is the diffusive time. L_{y} and (Deltaeta)_{M} behave as L_{y} approximately gamma;{-alpha} and (Deltaeta)_{M} approximately gamma;{nu} with alpha=alpha_{s}=0.18+/-0.02 , nu=nu_{s}=-2.00+/-0.01 and alpha=alpha_{w}=0.25+/-0.01 , nu=nu_{w}=-0.68+/-0.04 in the strong- and weak-shear regimes, respectively. Differently from what was found in systems with fluctuating velocity field, it is confirmed that domains continue to grow at all times.

Nonequilibrium steady states in sheared binary fluids

We simulate by lattice Boltzmann the steady shearing of a binary fluid mixture undergoing phase separation with full hydrodynamics in two dimensions. Contrary to some theoretical scenarios, a dynamical steady state is attained with finite domain lengths L(x,y) in the directions (x,y) of velocity and velocity gradient. Apparent scaling exponents are estimated as Lx approximately gamma (-2/3) and Ly approximately gamma(-3/4). We discuss the relative roles of diffusivity and hydrodynamics in attaining steady state.

Dynamics of a drop at a fluid interface under shear

We analyze the dynamics of a two-dimensional drop lying on a fluid interface, sometimes called a liquid lens, subjected to simple shear flow. The three fluids, the drop and the two external fluids, meet at a triple point (or a triple line in three dimensions). A requirement for steady drop shapes is that the triple points are stationary. This leads to a flow topology different than that of a freely suspended drop. Results are substantiated with numerical results using a level set method for interface evolution and treatment of triple points. Possible implications for new drop instabilities are also discussed.