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

Phase behavior of AB/CD diblock copolymer blends via coarse-grained simulation

The phase diagram of equimolar blends of AB and CD diblock copolymers has been studied using dissipative particle dynamics. All unlike blocks interacted with the same χ, except for the B-C interaction, for which χ_BC < 0 in order to prevent macrophase separation. The BC interaction was able to prevent macrophase separation except for low volume fractions of B and C (φ_BC⪅ 0.1) and relatively equal fractions of A and D. For high φ_BC (φ_BC⪆ 0.92), a disordered state was obtained. For all microphase separated states the shapes/morphologies were described by the ratios of the eigenvalues of the radius of gyration tensor and their sphericity. These were used to classify the domains as forming sphere, cylinders, lamellae, or branched/gyroidal structures. For φ_BC < 0.5 the BC domains acted as an interfacial region which compatibilized the A and D domains, while for φ_BC > 0.5 the BC domain filled in the space between A and D domains. Several interesting structures were formed including a novel connected/branched spheres morphology, hierarchical lamellae, concentric spheres/cylinders, and a combination of cylinders/lamellae. Comparisons are made with the linear diblock and linear triblock phase diagrams.

Phase separation in binary fluid mixtures with symmetric and asymmetric Schmidt numbers: A DPD study

We investigate the effect of the Schmidt number (Sc) on phase separation dynamics of two immiscible fluids in a two-dimensional periodic box using dissipative particle dynamics. The range of Sc investigated spans liquid-liquid separation processes. Phase separation is characterized by a domain size r(t), which typically follows a power law t^β in time t, where β is a characteristic exponent corresponding to the coarsening mechanism at play. The phase separation dynamics is studied for strongly (deep quench) separating mixtures. We consider cases of critical (ϕ ∼ 0.5) and off-critical (ϕ < 0.5) mixtures of fluids A and B for both Sc_A = Sc_B and Sc_A ≠ Sc_B. In all cases, the growth dynamics slow down with the increasing Schmidt number of either fluid. We observe the power law exponent β = 0.5 for symmetric (Sc_A = Sc_B) critical mixtures and β = 0.33 for all other cases. However, for off-critical mixtures, the exponent is 0.33 irrespective of the Schmidt number ratio of the two fluids. We explain these results from an analysis of the competition between diffusive effects vis-á-vis dynamical forces.

A new equation of state for homo-polymers in dissipative particle dynamics

A chain-revised Groot-Warren equation of state (crGW-EOS) was developed and tested to describe systems of homo-oligomeric chains in the framework of dissipative particle dynamics (DPD). First, thermodynamic perturbation theory is applied to introduce correction terms that account for the reduction in pressure with an increasing number of bonds at constant bead number density. Then, this EOS is modified by introducing a set of switching functions that yields an accurate second virial coefficient in the low-density limit. The crGW-EOS offers several improvements over the revised Groot-Warren equation of state and Groot-Warren equation of state for chain molecules. We tested the crGW-EOS by using it to predict the pressure of oligomeric systems and the B₂ virial coefficient of chain DPD particles for a range of bond lengths. Additionally, a method is developed for determining the strength of cross-interaction parameters between chains of different compositions and sizes and for thermal and athermal mixtures. We explored how different levels of coarse-graining affect the upper-critical solution temperature.

Dissipative particle dynamics study of phase separation in binary fluid mixtures in periodic and confined domains

We investigate the phase separation behavior of binary mixtures in two-dimensional periodic and confined domains using dissipative particle dynamics. Two canonical problems of fluid mechanics are considered for the confined domains: square cavity with no-slip walls and lid-driven cavity with one driven wall. The dynamics is studied for both weakly and strongly separating mixtures and different area fractions. The phase separation process is analyzed using the structure factor and the total interface length. The dynamics of phase separation in the square cavity and lid-driven cavity are observed to be significantly slower when compared to the dynamics in the periodic domain. The presence of the no-slip walls and the inertial effects significantly influences the separation dynamics. Finally, we show that the growth exponent for the strongly separating case is invariant to changes in the inter-species repulsion parameter.

Fragmentation and limits to dynamical scaling in viscous coarsening: an interrupted in situ x-ray tomographic study

X-ray microtomography was used to follow the coarsening of the structure of a ternary silicate glass experiencing phase separation in the liquid state. The volumes, surfaces, mean, and Gaussian curvatures of the domains of minority phase were measured after reconstruction of the 3D images and segmentation. A linear growth law of the characteristic length scale ℓ∼t was observed. A detailed morphological study was performed. While dynamical scaling holds for most of the geometrical observables under study, a progressive departure from scaling invariance of the distributions of local curvatures was evidenced. The latter results from a gradual fragmentation of the structure in the less viscous phase that also leads to a power-law size distribution of isolated domains.

Continuum theory of phase separation kinetics for active Brownian particles

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

Bottom-up construction of interaction models of non-Markovian dissipative particle dynamics

We derive the equation of motion for non-Markovian dissipative particle dynamics (NMDPD) by introducing the history effects on the time evolution of the system. Our formulation is based on the generalized Langevin equation, which describes the motions of the centers of mass of clusters comprising microscopic particles. The mean, friction, and fluctuating forces in the NMDPD model are directly constructed from an underlying molecular dynamics (MD) system without any scaling procedure. For the validation of our formulation, we construct NMDPD models from high-density Lennard-Jones systems, in which the typical time scales of the coarse-grained particle motions and the fluctuating forces are not fully separable. The NMDPD models reproduce the temperatures, diffusion coefficients, and viscosities of the corresponding MD systems more accurately than the dissipative particle dynamics models based on a Markovian approximation. Our results suggest that the NMDPD method is a promising alternative for simulating mesoscale flows where a Markovian approximation is not valid.

Arrest of fluid demixing by nanoparticles: a computer simulation study

We use lattice Boltzmann simulations to investigate the formation of arrested structures upon demixing of a binary solvent containing neutrally wetting colloidal particles. Previous simulations for symmetric fluid quenches pointed to the formation of "bijels": bicontinuous interfacially jammed emulsion gels. These should be created when a glassy monolayer of particles forms at the fluid-fluid interface, arresting further demixing and rigidifying the structure. Experimental work has broadly confirmed this scenario, but it shows that bijels can also be formed in volumetrically asymmetric quenches. Here, we present new simulation results for such quenches, compare these to the symmetric case, and find a crossover to an arrested droplet phase at strong asymmetry. We then make extensive new analyses of the postarrest dynamics in our simulated bijel and droplet structures, on time scales comparable to the Brownian time for colloid motion. Our results suggest that, on these intermediate time scales, the effective activation barrier to ejection of particles from the fluid-fluid interface is smaller by at least 2 orders of magnitude than the corresponding barrier for an isolated particle on a flat interface.

Effect of hydrodynamic interactions on the evolution of chemically reactive ternary mixtures

We investigate the structural evolution of an A/B/C ternary mixture in which the A and B components can undergo a reversible chemical reaction to form C. We developed a lattice Boltzmann model for this ternary mixture that allows us to capture both the reaction kinetics and the hydrodynamic interactions within the system. We use this model to study a specific reactive mixture in which C acts as a surfactant, i.e., the formation of C at the A/B interface decreases the interfacial tension between the A and B domains. We found that the dynamics of the system is different for fluids in the diffusive and viscous regimes. In the diffusive regime, the formation of a layer of C at the interface leads to a freezing of the structural evolution in the fluid; the values of the reaction rate constants determine the characteristic domain size in the system. In the viscous regime, where hydrodynamic interactions are important, interfacial reactions cause a slowing down of the domain growth, but do not arrest the evolution of the mixture. The results provide guidelines for controlling the morphology of this complex ternary fluid.

Vapor-liquid coexistence in many-body dissipative particle dynamics

Many-body dissipative particle dynamics is constructed to exhibit vapor-liquid coexistence, with a sharp interface, and a vapor phase of vanishingly small density. The application to fluid mechanics problems involving free surfaces is illustrated by simulation of a pendant drop. The model is an unusual example of a soft-sphere liquid with a potential energy built out of local-density-dependent one-particle self-energies.

Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids

We use a modified Shan-Chen, noiseless lattice-BGK model for binary immiscible, incompressible, athermal fluids in three dimensions to simulate the coarsening of domains following a deep quench below the spinodal point from a symmetric and homogeneous mixture into a two-phase configuration. The model is derivable from a continuous-time Boltzmann-BGK equation in the presence of an intercomponent body force. We find the average domain size grows with time as t(gamma), where gamma increases in the range 0.545+/-0.014<gamma<0.717+/-0.002, consistent with a crossover between diffusive t(1/3) and hydrodynamic viscous, t(1.0), behavior. We find good collapse onto a single scaling function, yet the domain growth exponents differ from previous results for similar values of the unique characteristic length L0 and time T0 that can be constructed out of the fluid's parameters. This rebuts claims of universality for the dynamical scaling hypothesis. For Re=2.7 and small wave numbers q we also find a q(2)<-->q(4) crossover in the scaled structure function, which disappears when the dynamical scaling reasonably improves at later stages (Re=37). This excludes noise as the cause for a q(2) behavior, as analytically derived from Yeung and proposed by Appert et al. and Love et al. on the basis of their lattice-gas simulations. We also observe exponential temporal growth of the structure function during the initial stages of the dynamics and for wave numbers less than a threshold value, in accordance with the diffusive Cahn-Hilliard Model B. However, this exponential growth is also present in regimes proscribed by that model. There is no evidence that regions of parameter space for which the scheme is numerically stable become unstable as the simulations proceed, in agreement with finite-difference relaxational models and in contradistinction with an unconditionally unstable lattice-BGK free-energy model previously reported. Those numerical instabilities that do arise in this model are the result of large intercomponent forces which turn the equilibrium distribution negative.

Lattice Boltzmann study of spinodal decomposition in two dimensions

A lattice Boltzmann model using the Shan-Chen prescription for a binary immiscible fluid is described, and the macroscopic equations obeyed by the model are derived. The model is used to quantitatively examine spinodal decomposition of a two-dimensional binary fluid. This model allows examination of the early-time period corresponding to interface formation, and shows agreement with analytical solutions of the linearized Cahn-Hilliard equation, despite the fact that the model contains no explicit free-energy functional. This regime has not, to the knowledge of the authors, been previously observed using any lattice Boltzmann method. In agreement with other models, a scaling law with the exponent 2/3 is observed for late-time domain growth. Breakdown of scaling is also observed for certain sets of simulation parameters.

Hydrodynamic bubble coarsening in off-critical vapor-liquid phase separation

Late-stage coarsening in off-critical vapor-liquid phase separation is reexamined. In the limit of bubbles of vapor distributed throughout a continuous liquid phase, it is argued that coarsening proceeds via inertial hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner mechanism seen in binary liquid mixtures. The arguments are strongly supported by simulations in two dimensions using a novel single-component soft-sphere fluid.

Thermodynamically consistent mesoscopic fluid particle model

We present a finite volume Lagrangian discretization of the continuum equations of hydrodynamics through the Voronoi tessellation. We then show that a slight modification of these discrete equations satisfies the first and second laws of thermodynamics. This is done by casting the model into the GENERIC structure. The GENERIC structure ensures thermodynamic consistency and allows for the introduction of correct thermal fluctuations in simple terms. In this way, we obtain a consistent discrete model for Lagrangian fluctuating hydrodynamics. Simulation results are presented that show the validity of the model for simulating hydrodynamic problems at mesoscopic scales.

Three-dimensional hydrodynamic lattice-gas simulations of domain growth and self-assembly in binary immiscible and ternary amphiphilic fluids

We simulate the dynamics of phase assembly in binary immiscible fluids and ternary microemulsions using a three-dimensional hydrodynamic lattice-gas approach. For critical spinodal decomposition we perform the scaling analysis in reduced variables introduced by Jury et al. [Phys. Rev. E 59, R2535 (1999)] and by Bladon et al. [Phys. Rev. Lett. 83, 579 (1999)]. We find a late-stage scaling exponent consistent with the R approximately t(2/3) inertial regime. However, as observed with the previous lattice-gas model of Appert et al. [J. Stat. Phys. 81, 181 (1995)] our data do not fall in the same range of reduced length and time as those of Jury et al. and Bladon et al. For off-critical binary spinodal decomposition we observe a reduction of the effective exponent with decreasing volume fraction of the minority phase. However, the n=1 / 3 Lifshitz-Slyzov-Wagner droplet coalescence exponent is not observed. Adding a sufficient number of surfactant particles to a critical quench of binary immiscible fluids produces a ternary bicontinuous microemulsion. We observe a change in scaling behavior from algebraic to logarithmic growth for amphiphilic fluids in which the domain growth is not arrested. For formation of a microemulsion where the domain growth is halted we find that a stretched exponential growth law provides the best fit to the data.