Spinodal decomposition of two-dimensional fluid mixtures: A spectral analysis of droplet growth

Growth regimes in three-dimensional phase separation of liquid-vapor systems

The liquid-vapor phase separation is investigated via lattice Boltzmann simulations in three dimensions. After expressing length and time scales in reduced physical units, we combined data from several large simulations (on 512^{3} nodes) with different values of viscosity, surface tension, and temperature, to obtain a single curve of rescaled length l[over ̂] as a function of rescaled time t[over ̂]. We find evidence of the existence of kinetic and inertial regimes with growth exponents α_{d}=1/2 and α_{i}=2/3 over several time decades, with a crossover from α_{d} to α_{i} at t[over ̂]≃1. This allows us to rule out the existence of a viscous regime with α_{v}=1 in three-dimensional liquid-vapor isothermal phase separation, differently from what happens in binary fluid mixtures. An in-depth analysis of the kinetics of the phase separation process, as well as a characterization of the morphology and the flow properties, are further presented in order to provide clues into the dynamics of the phase-separation process.

Pattern formation by bacteria-phage interactions

The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.

Chemotactic Motility-Induced Phase Separation

Collectives of actively moving particles can spontaneously separate into dilute and dense phases-a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS-in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Kinetics of domain growth and aging in a two-dimensional off-lattice system

We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single-component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth, and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-"liquid" as well as vapor-"solid" coexistence. For the vapor-liquid phase separation we observe that ℓ, the average domain length, grows with time (t) as t^{1/2}, a behavior that has connection with hydrodynamics. At low-enough temperature, a sharp crossover of this time dependence to a much slower, temperature-dependent, growth is identified within the timescale of our simulations, implying "solid"-like final state of the high-density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data collapse with respect to ℓ/ℓ_{w}, ℓ, and ℓ_{w} being the average domain lengths at times t and t_{w} (≤t), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: ∼(ℓ/ℓ_{w})^{-λ} for t≫t_{w}. The decay exponent λ, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.

Phase behavior and morphology of multicomponent liquid mixtures

Multicomponent systems are ubiquitous in nature and industry. While the physics of few-component liquid mixtures (i.e., binary and ternary ones) is well-understood and routinely taught in undergraduate courses, the thermodynamic and kinetic properties of N-component mixtures with N > 3 have remained relatively unexplored. An example of such a mixture is provided by the intracellular fluid, in which protein-rich droplets phase separate into distinct membraneless organelles. In this work, we investigate equilibrium phase behavior and morphology of N-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with N = 4 and 5 components. We report on both the coarsening behavior of such systems, as well as the resulting morphologies in three spatial dimensions. We discuss how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-means clustering algorithms. Finally, we discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested "Russian dolls" and encapsulated Janus droplets.

Flow-parametric regulation of shear-driven phase separation in two and three dimensions

The Cahn-Hilliard equation with an externally prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical simulation as the basis for the study. The model flow is parametrized by its amplitudes (thereby admitting the possibility of anisotropy), length scales, and multiple time scales, and the outcome of the phase separation is investigated as a function of these parameters as well as the dimensionality. In this way, a parameter regime is identified wherein the phase separation and the associated coarsening phenomenon are not only arrested but in fact the concentration variance decays, thereby opening up the possibility of describing the dynamics of the concentration field using the theories of advection diffusion. This parameter regime corresponds to long flow correlation times, large flow amplitudes and small diffusivities. The onset of this hyperdiffusive regime is interpreted by introducing Batchelor length scales. A key result is that in the hyperdiffusive regime, the distribution of concentration (in particular, the frequency of extreme values of concentration) depends strongly on the dimensionality. Anisotropic scenarios are also investigated: for scenarios wherein the variance saturates (corresponding to coarsening arrest), the direction in which the domains align depends on the flow correlation time. Thus, for correlation times comparable to the inverse of the mean shear rate, the domains align in the direction of maximum flow amplitude, while for short correlation times, the domains initially align in the opposite direction. However, at very late times (after the passage of thousands of correlation times), the fate of the domains is the same regardless of correlation time, namely alignment in the direction of maximum flow amplitude. A theoretical model to explain these features is proposed. These features and the theoretical model carry over to the three-dimensional case, albeit that an extra degree of freedom pertains, such that the dynamics of the domain alignment in three dimensions warrant a more detailed consideration, also presented herein.

Morphological evolution of domains in spinodal decomposition

Domain growth in spinodal decomposition is usually described by a single time-evolving length scale. We show that the evolution of morphology of domains is nonmonotonic. The domains elongate rapidly at first and then, with the help of hydrodynamics, return to a more circular shape. The initial elongation phase does not alter with hydrodynamics. A small deviation from critical composition changes the morphology dramatically.

Dynamic scaling in phase separation kinetics for quasi-two-dimensional membranes

We consider the dynamics of phase separation in lipid bilayer membranes, modeled as flat two-dimensional liquid sheets within a bulk fluid, both in the creeping flow approximation. We present scaling arguments that suggest asymptotic coarsening in these systems is characterized by a length scale R(t) ~ t(1/2) for critical (bicontinuous) phase separation and R(t) ~t(1/3) for off-critical concentrations (droplet morphology). In this limit, the bulk fluid is the primary source of dissipation. We also address these questions with continuum stochastic hydrodynamic simulations. We see evidence of scaling violation in critical phase separation, where isolated circular domains coarsen slower than elongated ones. However, we also find a region of apparent scaling where R(t) ~ t(1/2) is observed. This appears to be due to the competition of thermal and hydrodynamic effects. We argue that the diversity of scaling exponents measured in experiment and prior simulations can in part be attributed to certain measurements lying outside the asymptotic long-length-scale regime, and provide a framework to help understand these results. We also discuss a few simple generalizations to confined membranes and membranes in which inertia is relevant.

Spinodal decomposition of polymer solutions: molecular dynamics simulations of the two-dimensional case

As a generic model system for phase separation in polymer solutions, a coarse-grained model for hexadecane/carbon dioxide mixtures has been studied in two-dimensional geometry. Both the phase diagram in equilibrium (obtained from a finite size scaling analysis of Monte Carlo data) and the kinetics of state changes caused by pressure jumps (studied by large scale molecular dynamics simulations) are presented. The results are compared to previous work where the same model was studied in three-dimensional geometry and under confinement in slit geometry. For deep quenches the characteristic length scale ℓ(t) of the formed domains grows with time t according to a power law close to [Formula: see text]. Since in this problem both the polymer density ρ(p) and the solvent density ρ(s) matter, the time evolution of the density distribution P(L)(ρ(p),ρ(s),t) in L × L subboxes of the system is also analyzed. It is found that in the first stage of phase separation the system separates locally into low density carbon dioxide regions that contain no polymers and regions of high density polymer melt that are supersaturated with this solvent. The further coarsening proceeds via the growth of domains of rather irregular shapes. A brief comparison of our findings with results of other models is given.

Beyond the creeping viscous flow limit for lipid bilayer membranes: theory of single-particle microrheology, domain flicker spectroscopy, and long-time tails

Recent experiments suggest that lipid bilayer membranes may be viscoelastic. We present a generalized "Saffman-Einstein" relation that may be used to determine the linear viscoelastic shear modulus from single-bead microrheology experiments on membranes. We show that viscoelastic parameters can also be extracted from membrane domain flicker spectroscopy experiments. Contributions from fluid inertia are expected to be negligible in both microrheology and domain flicker spectroscopy experiments, but can create a "long-time tail" in the membrane velocity autocorrelation function. In a viscous membrane, this tail crosses over from t(-1) at intermediate times, as in a two-dimensional fluid, to t(-3/2) at long times, as in a three-dimensional fluid. If the membrane is viscoelastic, the velocity autocorrelation function may be negative at intermediate times.

Solvation effects in phase transitions in soft matter

Phase transitions in polar binary mixtures can be drastically altered by even a small amount of salt. This is because the preferential solvation strongly depends on the ambient composition. Together with a summary of our research on this problem, we present some detailed results on the role of antagonistic salt composed of hydrophilic and hydrophobic ions. These ions tend to segregate at liquid-liquid interfaces and selectively couple to water-rich and oil-rich composition fluctuations, leading to mesophase formation. In our two-dimensional simulation, the coarsening of the domain structures can be stopped or slowed down, depending on the interaction parameter (or the temperature) and the salt density. We realize stripe patterns at the critical composition and droplet patterns at off-critical compositions. In the latter case, charged droplets emerge with considerable size dispersity in a percolated region. We also give the structure factors among the ions, accounting for the Coulomb interaction and the solvation interaction mediated by the composition fluctuations.

Hydrodynamic effects on spinodal decomposition kinetics in planar lipid bilayer membranes

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, domain growth in the presence of hydrodynamic interactions both within the (effectively) two-dimensional membrane and in the three-dimensional solvent in which the membrane is immersed has received little attention. In this work, we explore the role of hydrodynamic effects on spinodal decomposition kinetics via continuum simulations of a convective Cahn-Hilliard equation for membrane composition coupled to the Stokes equation. Our approach explicitly includes hydrodynamics both within the planar membrane and in the three-dimensional solvent in the viscously dominated flow regime. Numerical simulations reveal that dynamical scaling breaks down for critical lipid mixtures due to distinct coarsening mechanisms for elongated versus more isotropic compositional lipid domains. The breakdown in scaling should be readily observable in experiments on model membrane systems.

Cooperative photoinduced two-dimensional condensation in Langmuir films observed using nanosecond pump-probe Brewster angle microscopy

Two-dimensional condensation was initiated in a self-assembled mixed monolayer of spiropyran and octadecanol by a nanosecond laser pulse. The dynamics of the process were monitored using nanosecond pump-probe Brewster angle microscopy. Domain growth followed a power law with a growth exponent of 0.47 at a velocity approaching 20 ms(-1). This represents a limit for the rate of longitudinal signaling of pressure waves through a self-assembled amphiphilic layer at an interface and adds to our understanding of signal transmission rates in biomimetic membranes where morphological change in one region can be signaled to a more remote region.

Bubbles and filaments: stirring a Cahn-Hilliard fluid

The advective Cahn-Hilliard equation describes the competing processes of stirring and separation in a two-phase fluid. Intuition suggests that bubbles will form on a certain scale, and previous studies of Cahn-Hilliard dynamics seem to suggest the presence of one dominant length scale. However, the Cahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we show that, by stirring the mixture at a sufficiently large amplitude, we excite the diffusion and overwhelm the segregation to create a homogeneous liquid. At intermediate amplitudes we see regions of bubbles coexisting with regions of hyperdiffusive filaments. Thus, the problem possesses two dominant length scales, associated with the bubbles and filaments. For simplicity, we use a chaotic flow that mimics turbulent stirring at large Prandtl number. We compare our results with the case of variable mobility, in which growth of bubble size is dominated by interfacial rather than bulk effects, and find qualitatively similar results.

Spinodal decomposition in thin films: molecular-dynamics simulations of a binary Lennard-Jones fluid mixture

We use molecular dynamics (MD) to simulate an unstable homogeneous mixture of binary fluids (AB), confined in a slit pore of width D. The pore walls are assumed to be flat and structureless and attract one component of the mixture (A) with the same strength. The pairwise interactions between the particles are modeled by the Lennard-Jones potential, with symmetric parameters that lead to a miscibility gap in the bulk. In the thin-film geometry, an interesting interplay occurs between surface enrichment and phase separation. We study the evolution of a mixture with equal amounts of A and B, which is rendered unstable by a temperature quench. We find that A-rich surface enrichment layers form quickly during the early stages of the evolution, causing a depletion of A in the inner regions of the film. These surface-directed concentration profiles propagate from the walls towards the center of the film, resulting in a transient layered structure. This layered state breaks up into a columnar state, which is characterized by the lateral coarsening of cylindrical domains. The qualitative features of this process resemble results from previous studies of diffusive Ginzburg-Landau-type models [S. K. Das, S. Puri, J. Horbach, and K. Binder, Phys. Rev. E 72, 061603 (2005)], but quantitative aspects differ markedly. The relation to spinodal decomposition in a strictly two-dimensional geometry is also discussed.

Molecular dynamics study of phase separation kinetics in thin films

We use molecular dynamics to simulate experiments where a symmetric binary fluid mixture (AB), confined between walls that preferentially attract one component (A), is quenched from the one-phase region into the miscibility gap. Surface enrichment occurs during the early stages, yielding a B-rich mixture in the film center with well-defined A-rich droplets. The droplet size grows with time as l(t) proportional t(2/3) after a transient regime. The present atomistic model is also compared to mesoscopic coarse-grained models for this problem.

Turbulence and coarsening in active and passive binary mixtures

Phase separation between two fluids in two dimensions is investigated by means of direct numerical simulations of coupled Navier-Stokes and Cahn-Hilliard equations. We study the phase ordering process in the presence of an external stirring acting on the velocity field. For both active and passive mixtures we find that, for a sufficiently strong stirring, coarsening is arrested in a stationary dynamical state characterized by a continuous rupture and formation of finite domains. Coarsening arrest is shown to be independent of the chaotic or regular nature of the flow.

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.

Phase separation in two-dimensional binary fluid mixtures: spontaneous pinning effect

The dynamics of phase separation, under asymmetric quench, is studied for binary mixtures by molecular dynamics simulations. We consider two kinds of systems, i.e., the small molecular liquid mixture and the flexible chain blend. The domain growth is found to be dependent crucially upon the relative composition of the mixture. For a near symmetric quench with volume fraction not far away from the critical value, we find that the domain growth is obviously slowed down (the spontaneous pinning effect) when the phase-separating structure undergoes the percolation-to-cluster transition. However, as the volume fraction of the minority phase is decreased, a pinning-depinning transition of the domain growth is observed for certain asymmetric quenches, due to the correlated motion of droplets. For sufficiently asymmetric quenches where the volume fraction of the minority phase is low, the domain growth is suppressed at late stages for the flexible polymer blend, in contrast to the fast growth for the small molecular system. The results are in good agreement with previous studies, and confirm the possibility of the intermittent or final pinning of phase separation for isolated droplets structure.

Self-assembling morphology induced by nanoscale rods in a phase-separating mixture

A symmetric binary mixture containing mobile nanoscale rods is quenched from a one-phase state into an unstable phase-separating region. Incorporating the motion of rods, the system undergoes spinodal decomposition to form a dropletlike structure. The rod-rod interaction and the preferential adsorption of one of the two immiscible phases onto the mobile rods play an important role in driving the system to self-assemble into this special structure. Within each cluster of the wetting phase, the rods align parallel to each other as in a nematic liquid crystal, while the rod orientations between these clusters are randomly distributed. However, an interconnected structure is recovered in the presence of hydrodynamic interaction. In the present phase-separating mixture with rods, the growth dynamics is examined in detail, and our simulations reveal a crossover from a rod-mobility-dependent to an independent regime. The system always exhibits slowing-down growth behavior where the well-known diffusive Lifshitz-Slyozov mechanism and hydrodynamic effects are both suppressed.