Phase separation in thermal systems: a lattice Boltzmann study and morphological characterization

The impact of colloid-solvent dynamic coupling on the coarsening rate of colloidal phase separation

Phase separation, a fundamental phenomenon in both natural and industrial settings, involves the coarsening of domains over time t to reduce interfacial energy. While well-understood for simple viscous liquid mixtures, the physical laws governing coarsening dynamics in complex fluids, such as colloidal suspensions, remain unclear. Here, we investigate colloidal phase separation through particle-based simulations with and without hydrodynamic interactions (HIs). The former incorporates many-body HIs through momentum conservation, while the latter simplifies their effects into a constant friction coefficient on a particle. In cluster-forming phase separation with HIs, the domain size ℓ grows as ℓ∝t1/3, aligning with the Brownian-coagulation mechanism. Without HIs, ℓ∝t1/5, attributed to an improper calculation of cluster thermal diffusion. For network-forming phase separation, ℓ∝t1/2 with HIs, while ℓ∝t1/3 without HIs. In both cases, network coarsening is governed by the mechanical stress relaxation of the colloid-rich phase, yet with distinct mechanisms: slow solvent permeation through densely packed colloids for the former and free draining for the latter. Our results provide a clear and concise physical picture of colloid-solvent dynamic coupling via momentum conservation, offering valuable insights into the self-organization dynamics of particles like colloids, emulsions, and globular proteins suspended in a fluid.

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.

Thermodynamic nonequilibrium effects in bubble coalescence: A discrete Boltzmann study

The thermodynamic nonequilibrium (TNE) effects in a coalescence process of two initially static bubbles under thermal conditions are investigated by a discrete Boltzmann model. The spatial distributions of the typical nonequilibrium quantity, i.e., nonorganized momentum fluxes (NOMFs), during evolutions are investigated in detail. The density-weighted statistical method is used to highlight the relationship between the TNE effects and the morphological and kinetics characteristics of bubble coalescence. The results show that the xx component and yy component of NOMFs are antisymmetrical; the xy component changes from an antisymmetric internal and external double quadrupole structure to an outer octupole structure during the coalescence process. Moreover, the evolution of the averaged xx component of NOMFs provides two characteristic instants, which divide the nonequilibrium process into three stages. The first instant, when the averaged xx component of the NOMFs reaches its first local minimum, corresponds to the moment when the mean coalescence speed gets the maximum, and at this time the ratio of minor and major axes is about 1/2. The second instant, when the averaged xx component of the NOMFs gets its second local maximum, corresponds to the moment when the ratio of minor and major axes becomes 1 for the first time. It is interesting to find that the three quantities, TNE intensity, acceleration of coalescence, and the slope of boundary length, show a high degree of correlation and attain their maxima simultaneously. The surface tension and the heat conduction accelerate the process of bubble coalescence, while the viscosity delays it. Both the surface tension and the viscosity enhance the global nonequilibrium intensity, whereas the heat conduction restrains it. These TNE features and findings present some insights into the kinetics of bubble coalescence.

Lattice Boltzmann simulation for phase separation with chemical reaction controlled by thermal diffusion

This study investigates phase separation behavior and pattern formation in a binary fluid with chemical reaction controlled by thermal diffusion. By incorporating the Arrhenius equation into the lattice Boltzmann method (LBM), the coupling effects of the pre-exponential factor K, viscosity [Formula: see text], and thermal diffusion D on phase separation were successfully evaluated. The effect of the competition between thermal diffusion and concentration on the phase separation morphology and dynamics of binary mixtures under a chemically reacting controlled by slow cooling is assessed based on the extended LBM. The calculations indicated that increases in viscosity and thermal diffusion can obtain interconnected structures (ISs) and lamellar structures (LSs) for cases with small K. However, concentric phase-separated structures (CSs) were observed in cases with large K. The increase in the degree and efficiency of phase separation were significantly greater in cases with decreased viscosity and increased thermal diffusion.

Temperature and initial composition dependence of pattern formation and dynamic behavior in phase separation under deep-quenched conditions

Phase separation of SCN-H2O ([CH2CN]2-H2O) transparent solutions is simulated in two dimensions and the effects of quenching temperature and initial composition on the pattern formation and dynamic behavior of the second phase are examined via Minkowski functionals. The simulation is based on model H where the molar free energy of the SCN-H2O solution is obtained by the CALPHAD approach. We find that the composition and temperature do not affect the exponent in the domain growth law, where the average domain size with time yields R(t)-t n . However, they influence the pattern formation and dynamic behavior of the second phase in phase separation. Lower temperature leads to a finer bicontinuous structure in spinodal decomposition and promotes the nucleation rate, which accelerates the phase separation and results in more liquid droplets with smaller size. As the initial composition diverges from the critical value, the spatial patterns change gradually from bicontinuous into a droplet-like structure. When the initial composition is closer to the critical value, for spinodal decomposition, the diffusion-driven growth lasts for a longer time and the average domain size of liquid droplets is larger. For nucleation-driven growth, in contrast, the single phase separates more quickly and the average size of liquid droplets is smaller.

Entropy production in thermal phase separation: a kinetic-theory approach

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.

Insights from inside the spinodal: Bridging thermalization time scales with smoothed particle hydrodynamics

We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a 1/2 ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.

Effects of temperature on spinodal decomposition and domain growth of liquid-vapor systems with smoothed particle hydrodynamics

We present a numerical method for simulations of spinodal decomposition of liquid-vapor systems. The results are in excellent agreement with theoretical predictions for all expected time regimes from the initial growth of "homophase fluctuations" up to the inertial hydrodynamics regime. The numerical approach follows a modern formulation of the smoothed particle hydrodynamics method with a van der Waals equation of state and thermal conduction. The dynamics and thermal evolution of instantaneously temperature-quenched systems are investigated. Therefore, we introduce a simple scaling thermostat that allows thermal fluctuations at a constant predicted mean temperature. We find that the initial stage spinodal decomposition is strongly affected by the temperature field. The separated phases react on density changes with a change in temperature. Although, the thermal conduction acts very slowly, thermal deviations are eventually compensated. The domain growth in the late stage of demixing is found to be rather unaffected by thermal fluctuations. We observe a transition from the Lifshitz-Slyozov growth rate with 1/3 exponent to the inertial hydrodynamics regime with a rate of 2/3, only excepted from simulations near the critical point where the liquid droplets are observed to nucleate directly in a spherical shape. The transition between the growth regimes is found to occur earlier for higher initial temperatures. We explain this time dependency with the phase interfaces that become more diffuse and overlap with approaching the critical point. A prolonging behavior of the demixing process is observed and also expected to depend on temperature. It is further found that the observations can excellently explain the growth behavior for pure nonisothermal simulations that are performed without thermostat.

Enhanced permeation of a hydrophobic fluid through particles with hydrophobic and hydrophilic patterned surfaces

The wetting properties of solid surfaces are significant in oil/gas and liquid displacement processes. It is difficult for hydrophobic fluids to permeate channels filled with hydrophilic particles and an aqueous phase, and this is thought to be the primary cause of low yields in low permeability reservoir operations. Using three-dimensional lattice Boltzmann simulations, we show that particles with hydrophobic and hydrophilic patterned surfaces can greatly improve hydrophobic fluid permeation. Specifically, a hydrophobic fluid can easily access micro-channels in the hydrophobic regions, which extend rapidly even to the hydrophilic regions and accelerate hydrophobic fluid escape. This work enriches understanding of multiphase flow in porous media at the pore scale and fracture conductivity and is expected to have great significance in the exploitation of low permeability reservoirs and shale gas.

Pattern formation in liquid-vapor systems under periodic potential and shear

In this paper the phase behavior and pattern formation in a sheared nonideal fluid under a periodic potential is studied. An isothermal two-dimensional formulation of a lattice Boltzmann scheme for a liquid-vapor system with the van der Waals equation of state is presented and validated. Shear is applied by moving walls and the periodic potential varies along the flow direction. A region of the parameter space, where in the absence of flow a striped phase with oscillating density is stable, will be considered. At low shear rates the periodic patterns are preserved and slightly distorted by the flow. At high shear rates the striped phase loses its stability and traveling waves on the interface between the liquid and vapor regions are observed. These waves spread over the whole system with wavelength only depending on the length of the system. Velocity field patterns, characterized by a single vortex, will also be shown.

Polar-coordinate lattice Boltzmann modeling of compressible flows

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.