Domain growth in computer simulations of segregating two-dimensional binary fluids

Pattern dynamics of density and velocity fields in segregation of fluid mixtures

We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H.

Modeling multiphase flow using fluctuating hydrodynamics

Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single-component, multiphase flow in the neighborhood of the critical point. The system is modeled using a compressible flow formulation with a van der Waals equation of state, incorporating a Korteweg stress term to treat interfacial tension. We present a numerical algorithm for modeling this system based on an extension of algorithms developed for fluctuating hydrodynamics for ideal fluids. The scheme is validated by comparison of measured structure factors and capillary wave spectra with equilibrium theory. We also present several nonequilibrium examples to illustrate the capability of the algorithm to model multiphase fluid phenomena in a neighborhood of the critical point. These examples include a study of the impact of fluctuations on the spinodal decomposition following a rapid quench, as well as the piston effect in a cavity with supercooled walls. The conclusion in both cases is that thermal fluctuations affect the size and growth of the domains in off-critical quenches.

Growth dynamics of domains in ternary fluid vesicles

We have studied the growth dynamics of domains on ternary fluid vesicles composed of saturated (dipalmitoylphosphatidylcholine), unsaturated (dioleoylphosphatidylcholine) phosphatidylcholine lipids, and cholesterol using a fluorescence microscopy. The domain coarsening processes are classified into two types: normal coarsening and trapped coarsening. For the normal coarsening, the domains having flat circular shape grow in a diffusion-and-coalescence manner and phenomenologically the mean size grows as a power law of approximately t(2/3). The observed growth law is not described by a two-dimensional diffusion-and-coalescence growth mechanism following the Saffman and Delbrück theory, which may originate from the two-body hydrodynamic interactions between domains. For trapped coarsening, on the other hand, the domain coarsening is suppressed at a certain domain size because the repulsive interdomain interactions obstruct the coalescence of domains. The two-color imaging of the trapped domains reveals that the repulsive interactions are induced by the budding of domains. The model free energy consisting of the bending energy of domains, the bending energy of matrix, the line energy of domain boundary, and the translation energy of domains can describe the observed trapped coarsening. The trapping of domains is caused by the coupling between the phase separation and the membrane elasticity under the incompressibility constraint.

Diffuse-interface model for rapid phase transformations in nonequilibrium systems

A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables, we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing. To describe transformations within the diffuse interface, we use the phase-field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface. Governing equations of the phase-field model are derived for the hyperbolic model, a model with memory, and a model of nonlinear evolution of transformation within the diffuse interface. The consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation-dissipation theorem. A comparison with existing sharp-interface and diffuse-interface versions of the model is given.

Scale invariance in coarsening of binary and ternary fluids

Phase separation in binary and ternary fluids is studied using a two-dimensional lattice gas automata. The lengths given by the the first zero crossing point of the correlation function and the total interface length is shown to exhibit power law dependence on time. In binary mixtures, our data clearly indicate the existence of a regime having more than one length scale, where the coarsening process proceeds through the rupture and reassociation of domains. In ternary fluids; in the case of symmetric mixtures there exists a regime with a single length scale having dynamic exponent 1/2, while in asymmetric mixtures our data establish the break down of scale invariance.

Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions

We investigate the domain growth and phase separation of hydrodynamically correct binary immiscible fluids of differing viscosity as a function of minority phase concentration in both two and three spatial dimensions using dissipative particle dynamics. We also examine the behavior of equal-viscosity fluids and compare our results to similar lattice-gas simulations in two dimensions.

Phase separation in two-dimensional fluids: the role of noise

We use a lattice Boltzmann scheme within which the noise can be turned on and off to investigate the effect of stochastic terms on the phase ordering of a two-dimensional binary fluid. Sufficiently strong noise slows the growth in the hydrodynamic regime, changing the growth exponent alpha=2/3 to alpha=1/2.