Phase Separation Of Binary Fluids Research Articles

Response of chemically active dimer motor in phase-separating binary fluid mixture: Motility regulation and self-aggregation

Response of chemically active dimer motor in phase-separating binary fluid mixture: Motility regulation and self-aggregation

Hydrodynamic effects in kinetics of phase separation in binary fluids: Critical versus off-critical compositions.

Via hydrodynamics-preserving molecular dynamics simulations we study growth phenomena in a phase-separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap, for various mixture compositions. For compositions at the symmetric or critical value we capture the rapid linear viscous hydrodynamic growth due to advective transport of material through tubelike interconnected domains. For state points very close to any of the branches of the coexistence curve, the growth in the system, following nucleation of disconnected droplets of the minority species, occurs via a coalescence mechanism. Using state-of-the-art techniques, we have identified that these droplets, between collisions, exhibit diffusive motion. The value of the exponent for the power-law growth, related to this diffusive coalescence mechanism, has been estimated. While the exponent nicely agrees with that for the growth via the well-known Lifshitz-Slyozov particle diffusion mechanism, the amplitude is stronger. For the intermediate compositions we observe initial rapid growth that matches the expectations for viscous or inertial hydrodynamic pictures. However, at later times these types of growth cross over to the exponent that is decided by the diffusive coalescence mechanism.

Nonlocal Cahn-Hilliard-Brinkman System with Regular Potential: Regularity and Optimal Control

In this paper, we study an optimal control problem for nonlocal Cahn-Hilliard-Brinkman system, which models phase separation of binary fluids in porous media. The system evolves with regular potential in a two-dimensional bounded domain. We extend the existence of weak solution results for the system to prove the existence of strong solution under extra assumptions on the forcing term and initial datum. Further, using our regularity results, we study the tracking type optimal control problem. We prove the existence of optimal control and establish the first-order optimality condition. Lastly, we characterise optimal control in terms of the solution of the corresponding adjoint system. The existence of the solution for the adjoint system is also established.

Curvature dynamics and long-range effects on fluid-fluid interfaces with colloids.

We investigate the dynamics of a phase-separating binary fluid, containing colloidal dumbbells anchored to the fluid-fluid interface. Extensive lattice Boltzmann-immersed boundary method simulations reveal that the presence of soft dumbbells can significantly affect the curvature dynamics of the interface between phase-separating fluids, even though the coarsening dynamics is left nearly unchanged. In addition, our results show that the curvature dynamics exhibits distinct non-local effects, which might be exploited for the design of new soft mesoscale materials. We point out that the inspection of the statistical dynamics of the curvature can disclose new insights into local inhomogeneities of the binary fluid configuration, as a function of the volume fraction and aspect ratio of the dumbbells.

Hydrodynamics of binary-fluid mixtures —An augmented Multiparticle Collison Dynamics approach

The Multiparticle Collision Dynamics technique (MPC) for hydrodynamics simulations is generalized to binary-fluid mixtures and multiphase flows, by coupling the particle-based fluid dynamics to a Ginzburg-Landau free-energy functional for phase-separating binary fluids. To describe fluids with a non-ideal equation of state, an additional density-dependent term is introduced. The new approach is verified by applying it to thermodynamics near the critical demixing point, and interface fluctuations of droplets. The interfacial tension obtained from the analysis of the capillary-wave spectrum agrees well with the results based on the Laplace-Young equation. Phase separation dynamics follows the Lifshitz-Slyozov law.

Lattice Boltzmann Method for Simulating Phase Separation of Sheared Binary Fluids with Reversible Chemical Reaction

AbstractA lattice Boltzmann method is utilized for governing equations which control phase separation of binary fluids with reversible chemical reaction in presence of a shear flow in this paper. We first present the morphology modeling of sheared binary fluids with reversible chemical reaction. We then validate the model by taking the unsheared binary fluids as an example. It is found that the results fit well with the references. The paper shows structures of the sheared system and gives the detailed analysis for the morphology of sheared binary fluids with reversible chemical reaction. The phase separation of the domain structures with different chemical reaction rates is discussed. Through simulations of the sheared binary fluids, two interesting phenomena are observed, which do not exist in a binary mixture without reversible chemical reaction. One is that the same results appear in both low and high viscosity, and the other is that the domain growth exponent with both low and high viscosities presents wave due to the competition of the viscosity and phase separation. In addition, we find that the finite size effects resulting in the growth exponent decreasing appear faster than that of the unsheared blend at a large time when the size of domains is comparable with the lattice size.

Controlled motion of Janus particles in periodically phase-separating binary fluids.

We numerically investigate the propelled motions of a Janus particle in a periodically phase-separating binary fluid mixture. In this study, the surface of the particle tail prefers one of the binary fluid components and the particle head is neutral in the wettability. During the demixing period, the more wettable phase is selectively adsorbed to the particle tail. Growths of the adsorbed domains induce the hydrodynamic flow in the vicinity of the particle tail, and this asymmetric pumping flow drives the particle toward the particle head. During the mixing period, the particle motion almost ceases because the mixing primarily occurs via diffusion and the resulting hydrodynamic flow is negligibly small. Repeating this cycle unboundedly moves the Janus particle toward the head. The dependencies of the composition and the repeat frequency on the particle motion are discussed.

Crossover in growth laws for phase-separating binary fluids: Molecular dynamics simulations

Pattern and dynamics during phase separation in a symmetrical binary (A+B) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50) systems to temperatures below the critical one. The morphology of the domains, rich in A or B particles, is observed to be bicontinuous. The early-time growth of the average domain size is found to be consistent with the Lifshitz-Slyozov law for diffusive domain coarsening. After a characteristic time, dependent on the temperature, we find a clear crossover to an extended viscous hydrodynamic regime where the domains grow linearly with time. Pattern formation in the present system is compared with that in solid binary mixtures, as a function of temperature. Important results for the finite-size and temperature effects on the small-wave-vector behavior of the scattering function are also presented.

Interfacial and wetting behaviour of phase-separating ultrasoft mixtures

We apply density functional theory to study the interfacial properties of a phase-separating binary fluid of ultrasoft particles, whose interaction potentials belong to the family of the so-called generalized exponential models (GEM). By using the formalism of the density functional theory within the mean-field approximation, we investigate the equilibrium density profiles for each component at the free interface as well as at a repulsive, flat wall. We show that the studied system can lead to first-order wetting transition which is characterized by a layering-like behaviour due to the clustering properties of GEM particles.

Phase separation of binary fluids with dynamic temperature

Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high viscosity, different morphologies are observed by varying the thermal diffusivity. In the range of thermal diffusivities with domains growing parallel to the walls, temperature and phase separation fronts propagate toward the inner of the system with power-law behavior. At low viscosity hydrodynamics favors rounded shapes, and complex patterns with different length scales appear. Off-symmetrical systems behave similarly but with more ordered configurations.

Modelling of phase separation in binary fluid under vibration with LBM

Fluid dynamics in phase separation system subject to a vibration perpendicular to gravity is analysed by using a lattice Boltzmann method (LBM) based on the He-Shan-Doolen (HSD) model. The vibrations considered correspond to sinusoidal translations of a rigid cavity at a fixed frequency. Interaction between gravity and vibration-induced convection is studied. The ability of applied vibration to influence the phase separation behaviour and deposition is investigated.

Bounds on the mixing enhancement for a stirred binary fluid

The Cahn–Hilliard equation describes phase separation in binary liquids. Here we study this equation with spatially-varying sources and stirring, or advection. We specialize to symmetric mixtures and time-independent sources and discuss stirring strategies that homogenize the binary fluid. By measuring fluctuations of the composition away from its mean value, we quantify the amount of homogenization achievable. We find upper and lower bounds on our measure of homogenization using only the Cahn–Hilliard equation and the incompressibility of the advecting flow. We compare these theoretical bounds with numerical simulations for two model flows: the constant flow, and the random-phase sine flow. Using the sine flow as an example, we show how our bounds on composition fluctuations provide a measure of the effectiveness of a given stirring protocol in homogenizing a phase-separating binary fluid.

Dynamics of Colloidal Particles in Soft Matters

We developed numerical methods for studying the dynamics of colloidal particles suspended in complex fluids. It is essential to employ a coarse-grained model for studying slow dynamics of these systems. Our methods are based on the “fluid particle dynamics (FPD)” method, which we have developed to deal with hydrodynamic interactions in colloidal systems in an efficient manner. We regard a solid particle as an undeformable fluid one. It has a viscosity much higher than the solvent, which smoothly changes to the solvent viscosity at the interface. This methods allows us to avoid troublesome boundary conditions to be satisfied on the surfaces of mobile particles. Since we express the spatial distribution of colloids as a continuum field, we can easily introduce the order parameter describing a complex solvent, e.g., ion distribution for charged colloids, director field for nematic liquid crystal, and concentration for phase-separating binary fluid. Then we solve coupled dynamic equations of three relevant parameters, i.e., particle positions, flow field, and the order parameter. We demonstrate a few examples of such simulations.

Convection-driven pattern formation in phase-separating binary fluids

Using a thermal-lattice Boltzmann model, we examine the rich phase behavior that develops when partially miscible fluids evolve in the presence of a vertical temperature gradient, which encompasses the critical temperature T(c) of the mixture. In particular, a binary AB fluid is confined between two plates in a gravitational field. The upper plate is fixed below T(c) and hence, the nearby fluid phase separates into A-rich and B-rich domains. The lower plate is fixed above the temperature T(c), and the surrounding fluid is in the homogeneous phase. A coupling between convection (driven by the temperature gradient) and phase separation gives rise to unique pattern formation. A number of regimes are identified: regularly spaced stripes, convective steady-state columns, the periodic disturbance of these columns, and finally, chaotic dripping from the upper surface. These results highlight dynamical behavior in partially miscible mixtures.

Instability of interfaces in phase-separating binary fluids at a finite Reynolds number

We investigate a stability of a lamellar domain in phase-separating binary fluids under an external flow. Using the Navier–Stokes and the Cahn–Hilliard equations, we take into account effects of diffusion and surface tension at an interface. Stability eigenvalues are evaluated for various values of the Péclet number, the spacing between the interfaces, and the Reynolds number. It is found that the lamellar domain becomes unstable at a finite wavenumber before the flow when the Reynolds number increases. The instability of the interface occurs on conditions that the interface is situated near a wall or the Péclet number is large. The instability stems from the interaction between disturbances of the flow and the diffusive interface.

Phase separation dynamics in binary fluids containing quenched or mobile filler particles

The dynamics of phase separation of binary fluids in the presence of quenched or mobile filler particles, with preferential attraction for one of the two fluid components, is investigated by means of extensive molecular dynamics simulations in two dimensions. When the filler particles are quenched, we found that they lead to a slowing-down of the kinetics that is enhanced as the density of the filler particles is increased. The domain growth in this case is found to follow a crossover scaling form which links domain growth in pure binary mixtures to that in the presence of quenched filler particles. On the other hand, when the filler particles are annealed, systematic simulations for various values of single filler particle mass, μc, and filler particle density, ρc, show that the filler particles only affect the nonuniversal prefactor of the power law. The power law itself remains given by t2/3, characteristic of inertial growth that is typically observed in pure binary fluid mixtures. The prefactor is found to depend on μc as μc−1/3 as expected in phase separating fluid in the inertial regime.

Phase-separating binary fluids under oscillatory shear.

We apply the 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 nonlinear 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.

Stability of Cylindrical Domain under Poiseuille Flow

We investigate stability of a cylindrical domain in a phase-separating binary fluid under a Poiseuille flow. Linearization for a couple of the Navier–Stokes and Cahn–Hilliard equations around stationary solutions leads to an eigenvalue problem, a solution of which yields a stability eigenvalue. The stability eigenvalue is composed of a term originated from the hydrodynamic Rayleigh instability and that from the diffusive instability. Concerning the stability eigenvalue of the hydrodynamic instability, a set of equations is obtained from boundary conditions at an interface and a solution of the equations yields the stability eigenvalue. In case of equal viscosity, the analytic formula of the solution is obtained without an external flow. The Tomotika's stability eigenvalue with the equal viscosity [Proc. R. Soc. London, Ser. A 150 (1935) 322] is shown to agree with the Stone and Brenner's result [J. Fluid Mech. 318 (1996) 373] explicitly. The Poiseuille flow has an effect of mixing an unstable axisymmetric...

Binary star-polymer solutions: bulk and interfacial properties

Using an effective logarithmic–Gaussian pair potential that models theinteraction between star polymers, we compare the hypernetted chain(HNC) and random phase approximations (RPA) for calculating the bulkstructure (including the Fisher–Widom and Lifshitz lines), thermodynamicfunctions and phase diagram of a phase-separating binary fluid of starpolymers, of two-arm length ratio 2:1. Thereby, the stars considered hereare equivalent to linear chains in the mid-point representation of theireffective interaction. We find that at densities where the star coronasoverlap, the quasi-exact HNC and RPA give very similar results. Using adensity functional approach, with a functional which generates the RPA, wecalculate properties of the inhomogeneous binary fluid. We determinethe surface tension and one-body density profiles at the free fluid–fluidinterface. For states well removed from the critical point the profiles exhibitpronounced oscillations. For a purely repulsive planar wall potential thatmodels the effective potential between a star polymer and a hard wall, wefind a first-order wetting transition with the associated pre-wetting line.

Parallel implementation of the fluid particle model for simulating complex fluids in the mesoscale

AbstractDissipative particle dynamics (DPD) and its generalization—the fluid particle model (FPM)—represent the ‘fluid particle’ approach for simulating fluid‐like behavior in the mesoscale. Unlike particles from the molecular dynamics (MD) method, the ‘fluid particle’ can be viewed as a ‘droplet’ consisting of liquid molecules. In the FPM, ‘fluid particles’ interact by both central and non‐central, short‐range forces with conservative, dissipative and Brownian character. In comparison to MD, the FPM method in three dimensions requires two to three times more memory load and a three times greater communication overhead. Computational load per step per particle is comparable to MD due to the shorter interaction range allowed between ‘fluid particles’ than between MD atoms. The classical linked‐cells technique and decomposing the computational box into strips allow for rapid modifications of the code and for implementing non‐cubic computational boxes. We show that the efficiency of the FPM code depends strongly on the number of particles simulated, the geometry of the box and the computer architecture. We give a few examples from long FPM simulations involving up to 8 million fluid particles and 32 processors. Results from FPM simulations in three dimensions of the phase separation in binary fluid and dispersion of the colloidal slab are presented. A scaling law for symmetric quench in phase separation has been properly reconstructed. We also show that the microstructure of dispersed fluid depends strongly on the contrast between the kinematic viscosities of this fluid phase and the bulk phase. This FPM code can be applied for simulating mesoscopic flow dynamics in capillary pipes or critical flow phenomena in narrow blood vessels. Copyright © 2002 John Wiley & Sons, Ltd.