Binary Fluid Mixtures Research Articles

Early time wetting kinetics in surface-directed spinodal decomposition for off-critical quenches: A molecular dynamics study.

We present results from the molecular dynamics simulation of surface-directed spinodal decomposition in binary fluid mixtures (A + B) with off-critical compositions. The aim is to elucidate the role of composition ratio in the early time wetting kinetics under the influence of long-range surface potential. In our simulations, the attractive part of surface potential varies as V(z) = -ϵa/zn, with ϵa being the surface-potential strength. The surface prefers the "A" species to form the wetting layer. Its thickness [R1(t)] for the majority wetting (number of A-type particles [NA] > number of B-type particles [NB]) grows as a power-law with an exponent of 1/(n + 2). This is consistent with the early time kinetics in the form of potential-dependent growth present in the Puri-Binder model. However, for minority wetting (NA < NB), the growth exponent in R1(t) is less than 1/(n + 2). Furthermore, on decreasing the field strength ϵa, we recover 1/(n + 2) for a minority wetting case. We provide phenomenological arguments to explain the early time wetting kinetics for both cases.

Transport of topological defects in a biphasic mixture of active and passive nematic fluids

Collectively moving cellular systems often contain a proportion of dead cells or non-motile genotypes. When mixed, nematically aligning motile and non-motile agents are known to segregate spontaneously. However, the role that topological defects and active stresses play in shaping the distribution of the two phases remains unresolved. In this study, we investigate the behaviour of a two-dimensional binary mixture of active and passive nematic fluids to understand how topological defects are transported between the two phases and, ultimately, how this leads to the segregation of topological charges. When the activity of the motile phase is large, and the tension at the interface of motile and non-motile phases is weak, we find that the active phase tends to accumulate +1/2 defects and expel −1/2 defects so that the motile phase develops a net positive charge. Conversely, when the activity of the motile phase is comparatively small and interfacial tension is strong, the opposite occurs so that the active phase develops a net negative charge. We then use these simulations to develop a physical intuition of the underlying processes that drive the charge segregation. Lastly, we quantify the sensitivity of this process on the other model parameters, by exploring the effect that anchoring strength, orientational elasticity, friction, and volume fraction of the motile phase have on topological charge segregation. As +1/2 and −1/2 defects have very different effects on interface morphology and fluid transport, this study offers new insights into the spontaneous pattern formation that occurs when motile and non-motile cells interact.

Binary phase separation in strongly coupled plasma

We investigated the two-dimensional binary phase separation process of plasma species using classical molecular dynamics in the strongly coupled regime. Both the plasma species interact via a pairwise screened Coulomb (Debye–Hückel) potential; however, the screening parameter κ is different for like- and unlike-species and is the cause for phase separation. We characterize the separation process by measuring the domain growth of equilibrium phases as a function of time—generally, the more significant the inhomogeneity in pairwise interaction, the faster the domain growth. Typically, the domain growth follows a power law in time with an exponent β characterizing the underlying coarsening mechanism. We demonstrate that the growth law exponent is β=1/2 for equal-number-density mixtures and 1/3 otherwise. Further, by comparing these with the corresponding growth laws in binary mixtures of viscous fluids, we show that the viscoelastic nature of plasma fluid modifies the coarsening dynamics, which in turn leads to the observed growth law exponents, notably in the unequal-number-density case.

Convective Instability Driven by Diffusiophoresis of Colloids in Binary Liquid Mixtures.

In a binary fluid mixture, the concentration gradient of a heavier molecular solute leads to a diffusive flux of solvent and solute to achieve thermodynamic equilibrium. If the solute concentration decreases with height, the system is always in a condition of stable mechanical equilibrium against gravity. We show experimentally that this mechanical equilibrium becomes unstable in case colloidal particles are dispersed uniformly within the mixture and that the resulting colloidal suspension undergoes a transient convective instability with the onset of convection patterns. By means of a numerical analysis, we clarify the microscopic mechanism from which the observed destabilization process originates. The solute concentration gradient drives an upward diffusiophoretic migration of colloids, in turn causing the development of a mechanically unstable layer within the sample, where the density of the suspension increases with height. Convective motions arise to minimize this localized rise in gravitational potential energy.

Phase ordering in binary mixtures of active nematic fluids.

We use a continuum, two-fluid approach to study a mixture of two active nematic fluids. Even in the absence of thermodynamically driven ordering, for mixtures of different activities we observe turbulent microphase separation, where domains form and disintegrate chaotically in an active turbulent background. This is a weak effect if there is no elastic nematic alignment between the two fluid components, but is greatly enhanced in the presence of an elastic alignment or substrate friction. We interpret the results in terms of relative flows between the two species which result from active anchoring at concentration gradients. Our results may have relevance in interpreting epithelial cell sorting and the dynamics of multispecies bacterial colonies.

Predicting phase coexistence and adsorption isotherms of classical and quantum fluids using the microcanonical-ensemble perturbation theory (MEPT)

The Microcanonical-Ensemble Perturbation Theory (MEPT) of Sastre et al. (2018) [7] has been extended to study the vapor-liquid phase coexistence of binary and ternary mixtures of fluids. The attractive interactions between chains of molecules are represented as monomer segments interacting via a square-well pair potential. Calculations for the thermodynamic properties and phase behavior of square-well monomer chains are considered and compared with experimental data. Molecular parameters have been obtained to model the phase behavior of real fluids such as n-alkanes (from C1 to C12), nitrogen, perfluoromethane, carbon dioxide, i-butane, i-pentane, neon, and hydrogen. Furthermore, the capability of the MEPT approach in predicting critical and azeotropic lines of binary and ternary mixtures is explored. The results demonstrate that the MEPT approach provides a robust description of the phase behavior of mixtures containing chains of fluids. Additionally, we have integrated the MEPT approach with the two-dimensional Statistical Associating Fluid Theory for fluids interacting via variable range potentials (SAFT-VR-2D) to investigate the effect of quantum contributions on both phase behavior and adsorption. Remarkable improvements are observed when both higher order perturbation terms of the Helmholtz free energy and quantum contributions are included in the predictions of the phase behavior of quantum fluids such as neon and hydrogen. In all cases, the theoretical results exhibit favorable comparisons with experimental data in a wide range of compositions, pressures, and temperatures.

Thermo-osmosis of a near-critical binary fluid mixture: A general formulation and universal flow direction.

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause preferential adsorption of one component onto the tube's wall. The adsorption layer can become much thicker than the molecular size, which enables us to apply hydrodynamics based on a coarse-grained free-energy functional. For transport processes induced by gradients of the pressure, composition, and temperature along a cylindrical tube, we obtain the formulas of the Onsager coefficients to extend our previous results on isothermal transport, assuming the critical composition in the middle of each reservoir in the reference equilibrium state. Among the processes, we focus on thermo-osmosis-mass flow due to a temperature gradient. We explicitly derive a formula for the thermal force density, which is nonvanishing in the adsorption layer and causes thermo-osmosis. This formula for a near-critical binary fluid mixture is an extension of the conventional formula for a one-component fluid, expressed in terms of local excess enthalpy. We predict that the direction of thermo-osmotic flow of a mixture near the upper (lower) consolute point is the same as (opposite to) that of the temperature gradient, irrespective of which component is adsorbed on the wall. Our procedure would also be applied to dynamics of a soft material, whose mesoscopic inhomogeneity can be described by a coarse-grained free-energy functional.

Effects of inclination angle and fluid parameters on binary fluid convection in a tilted rectangular cavity

Thermal convection of binary fluid mixtures with negative separation ratios in a tilted rectangular cavity heated from below is numerically investigated using a high-accuracy finite-difference method. The fluids under consideration are Newtonian fluids with the Prandtl number (Pr) and Lewis number (Le) in the ranges of 0.01≤Pr≤10 and 0.001≤Le≤1, respectively. Extensive direct numerical simulations are conducted to explore the dynamics of the system by varying the control parameters, namely, the relative Rayleigh number (r) and the inclination angle of the cavity (β) together with the separation ratio (ψ) in the ranges of 1.0≤r≤2.0, 0°≤β≤90°, and −0.6≤ψ≤0. It is found that the inclination angle leads to a distinct trend for heat and mass transfer: the Nusselt number first decreases for small β, then gradually increases for moderate β, and finally decreases again for large β when r varies from 1.4 to 2.0. The optimal inclination angle lies in the range of 54°≤β∗≤64°, where the heat transport peaks. The Sherwood number initially decreases for small β, then increases with increasing β, and finally remains constant for large β. We present the bifurcation diagram of the solutions for different separation ratios, focusing on the distinct variation trends of the inclination angle. The corresponding heat- and mass-transfer properties of the flow on different branches of the bifurcation diagram are investigated. Furthermore, we explore the effect of the relative Rayleigh number, Prandtl number and Lewis number as well as the separation ratio on heat and mass transfer for various inclination angles, and obtain the Nusselt number as a function of the separation ratio and inclination angle.

Optimal distributed control for a Cahn-Hilliard-Darcy system with mass sources, unmatched viscosities and singular potential

We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for the averaged velocity u as well as homogeneous Neumann boundary conditions for the phase function ϕ and the chemical potential µ. The source term in the convective Cahn-Hilliard equation contains a control R that can be thought as a drug or a nutrient in applications. Our goal is to study a distributed optimal control problem in the two-dimensional setting with a cost functional of tracking-type. In the physically relevant case with unmatched viscosities for the binary fluid mixtures and a singular potential, we first prove the existence and uniqueness of a global strong solution with ϕ being strictly separated from the pure phases ±1. This well-posedness result enables us to characterize the control-to-state mapping S: R→ϕ. Then we obtain the existence of an optimal control, the Frechet differentiability of S and first-order necessary optimality conditions expressed through a suitable variational inequality for the adjoint variables. Finally, we prove the differentiability of the control-to-costate operator and establish a second-order sufficient condition for the strict local optimality.

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.

On the separation property and the global attractor for the nonlocal Cahn-Hilliard equation in three dimensions

We consider the nonlocal Cahn-Hilliard equation with constant mobility and singular potential in three dimensional bounded and smooth domains. This model describes phase separation in binary fluid mixtures. Given any global solution (whose existence and uniqueness are already known), we prove the so-called instantaneous and uniform separation property: any global solution with initial finite energy is globally confined (in the L∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^\\infty $$\\end{document} metric) in the interval [-1+δ,1-δ]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[-1+\\delta ,1-\\delta ]$$\\end{document} on the time interval [τ,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[\ au ,\\infty )$$\\end{document} for any τ>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au >0$$\\end{document}, where δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document} only depends on the norms of the initial datum, τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} and the parameters of the system. We then exploit such result to improve the regularity of the global attractor for the dynamical system associated to the problem.

Thermodynamic analysis of novel mixtures including siloxanes and cyclic hydrocarbons for high-temperature heat pumps

This paper presents the investigation of zeotropic binary fluid mixtures containing cyclohexane (critical temperature above 200 °C) as the base fluid with R600, R600a, R601, R601a, R1336mzz(Z), R1234ze(Z), R1233zd(E) and cyclopropane (critical temperatures between 100 °C and 200 °C). For pure components and their mixtures, the performance of the vapor compression system with an internal heat exchanger was analysed at 50 °C and 80 °C heat source and sink inlet, respectively. Variation of the heat source temperature difference and the internal heat exchanger pinch point temperature difference at supply temperatures (140–170 °C) were also investigated. A pinch point temperature difference of 5 K was maintained for the evaporator and condenser. An increase of 6.59 % in COP was obtained with the zeotropic mixture of cyclohexane/cyclopropane compared to that of pure cyclopropane. The design point analysis showed that increasing the heat source temperature difference and internal heat exchanger pinch point temperature difference reduces the COP. The adopted mixture criteria increased the performance between 3.23 % and 3.91 % with respect to standard working fluids like R1233zd(E) and R601, for a 170 °C supply temperature. With this promising thermodynamic analysis in a subcritical operation, the cyclohexane/cyclopropane mixture has prospect of full integration heat pump design.

Lithium-ion battery thermal management system using MWCNT-based nanofluid flowing through parallel distributed channels: An experimental investigation

In the present research, a newly designed liquid-based battery thermal management system (BTMS) for lithium-ion batteries (LIBs) is developed and its thermal performance at different discharge rates (C-rates) is experimentally examined. The influence of various performance parameters such as the number of channels, flow configurations, working fluids, and C-rates on the cooling performance of the proposed BTMS is evaluated. Pure water, binary fluid (70 % water + 30 % ethylene glycol (EG)), and multi-walled carbon nanotubes (MWCNTs)-based nanofluids at different volume fractions (ϕv) (0.15 %, 0.30 %, and 0.45 %) in the binary fluid are used in this study and their cooling effectiveness to keep battery temperature within ideal ranges is compared. The experiments are performed at 0.5C, 1.2C, and 2.1C rates and it is discovered that nanofluids provide superior cooling performance compared to water and binary fluid mixture. Results demonstrate that the cooling performance is enhanced with the number of channels, nanoparticle concentration, and flow configurations. Nanofluid with 0.45 % ϕv of MWCNTs shows the maximum drop in battery temperature which is about 8.7 °C for configuration I, 11.8 °C for configuration II, and 17.1 °C for configuration III, respectively. Among all the flow configurations, configuration III gives the best cooling effectiveness and lowers the average temperature of cells by 10–17.01 °C using different working fluids. Configuration III also enhances the battery temperature uniformity and maintains the maximum temperature deviation within the battery module (∆Tmax) inside 1.5–2.4 °C for different working fluids at a 2.1C rate, which is well below 5 °C, and hence it helps to prevent the thermal runaway (TR) condition. Additionally, nanofluid with 0.45 % ϕv increases pressure drop (Δp) by 23.98 % and 17.91 % compared to water for single and dual channel arrangements, respectively.

Mixing/segregation characteristics and bubble behaviors of density-segregated binary particles in a pressurized fluidized bed

To enhance comprehension and achieve more targeted optimization of pressurized fluidized beds, experiments were carried out in a “cold” pseudo 2D pressurized fluidized bed with binary mixtures differing in densities via high-speed digital image analysis. The impacts of operating pressure and gas velocity on fluidization pattern, mixing/segregation characteristics, and bubble behaviors were comprehensively analyzed. Results show that the fluidization of binary mixtures is a gradual process which occurs within the range between the minimum fluidization velocity of flotsam and jetsam components. Particles with lighter density tend to produce larger size of bubbles, larger bubble fraction and increased fluctuation compared to the heavier ones when particle sizes are similar. Increasing the pressure results in an overall decreased bubble diameter and bubble fraction, which prohibits the bubble-particle interaction and ultimately deteriorates the mixing quality. The carried-out whole-field, non-intrusive measurements in this work would provide the much-needed database for validation of CFD models.

Novel turbulence and coarsening arrest in active-scalar fluids.

We uncover a new type of turbulence - activity-induced homogeneous and isotropic turbulence - in a model that has been employed to investigate motility-induced phase separation (MIPS) in a system of microswimmers. The active Cahn-Hilliard-Navier-Stokes (CHNS) equations, also called active model H, provide a natural theoretical framework for our study. In this CHNS model, a single scalar order parameter ϕ, positive (negative) in regions of high (low) microswimmer density, is coupled with the velocity field u. The activity of the microswimmers is governed by an activity parameter ζ that is positive for extensile swimmers and negative for contractile swimmers. With extensile swimmers, this system undergoes complete phase separation, which is similar to that in binary-fluid mixtures. By carrying out pseudospectral direct numerical simulations (DNSs), we show, for the first time, that (a) this model develops an emergent nonequilibrium, but statistically steady, state (NESS) of active turbulence, for the case of contractile swimmers, if ζ is sufficiently large and negative, and (b) this turbulence arrests the phase separation. We quantify this suppression by showing how the coarsening-arrest length scale does not grow indefinitely, with time t, but saturates at a finite value at large times. We characterise the statistical properties of this active-scalar turbulence by employing energy spectra and fluxes and the spectrum of ϕ. For sufficiently high Reynolds numbers, the energy spectrum (k) displays an inertial range, with a power-law dependence on the wavenumber k. We demonstrate that, in this range, the flux Π(k) assumes a nearly constant, negative value, which indicates that the system shows an inverse cascade of energy, even though energy injection occurs over a wide range of wavenumbers in our active-CHNS model.

Kinetics of phase separation and aging dynamics of segregating fluid mixtures in the presence of quenched disorder.

Quenched or frozen-in structural disorder is ubiquitous in real experimental systems. Much of the progress is achieved in understanding the phase separation of such systems using the diffusion-driven coarsening in an Ising model with quenched disorder. But there is a paucity of research on the phase-separation kinetics in fluids with quenched disorder. In this paper, we present results from a detailed molecular dynamics simulation, showing the effects of randomly placed localized impurities on the phase separation kinetics of binary fluid mixtures. Two different models are offered for representing the impurities. We observe a dramatic slowing down in the pattern formation with increasing impurity concentration. This sluggish domain growth kinetics follows a power-law with a disorder-dependent exponent. The correlation function and structure factor show a non-Porod behavior, indicating the roughening of the domain interfaces. We have also studied the effect of quenched disorder on the aging dynamics by calculating the two-time order parameter auto correlation function and find that the Fisher and Huse scaling law holds good in the presence of quenched disorder.

Controlling liquid-liquid phase behaviour with an active fluid.

Demixing binary liquids is a ubiquitous transition explained using a well-established thermodynamic formalism that requires the equality of intensive thermodynamics parameters across phase boundaries. Demixing transitions also occur when binary fluid mixtures are driven away from equilibrium, but predicting and designing such out-of-equilibrium transitions remains a challenge. Here we study the liquid-liquid phase separation of attractive DNA nanostars driven away from equilibrium using a microtubule-based active fluid. We find that activity lowers the critical temperature and narrows the range of coexistence concentrations, but only in the presence of mechanical bonds between the liquid droplets and reconfiguring active fluid. Similar behaviours are observed in numerical simulations, suggesting that the activity suppression of the critical point is a generic feature of active liquid-liquid phase separation. Our work describes a versatile platform for building soft active materials with feedback control and providing an insight into self-organization in cell biology.

Determination of diffusivities in binary fluid mixtures with various Lewis numbers as well as positive and negative Soret coefficients by the shadowgraph method.

The present work demonstrates the accessibility of the Fick diffusion coefficient D11 and/or the thermal diffusivity a of the binary mixtures dicyclohexylmethane/diphenylmethane, n-hexane/carbon dioxide, 1-hexanol/carbon dioxide, and methane/propane by the analysis of the dynamics of non-equilibrium fluctuations using the shadowgraph method. It is evidenced that D11 and a can be simultaneously determined for binary mixtures with Lewis numbers Le = a/D11 ranging over two orders of magnitude down to Le ≈ 5 or in the presence of minor advection for binary mixtures possessing a negative Soret coefficient in the investigated temperature and pressure ranges from (298.15 to 473.15) K and from about (0.5 to 25) MPa. The determined diffusivities are compared with those measured by heterodyne dynamic light scattering or obtained from the literature, with a focus on achievable uncertainties. By this comparison, it is shown that the determination of a by the shadowgraph method was hindered by mode-coupling effects for Le ≈ 5, whereas a determination of D11 was always possible for mixtures with Le ≥ 5. Furthermore, it is demonstrated that even in the presence of solutal advection, the description of the purely diffusive behavior of non-equilibrium fluctuations in concentration remains valid.

Theoretical Prediction of the Number of Bénard Cells in Low-Porosity Cylindrical/Rectangular Enclosures Saturated by a Fast Chemically Reacting Fluid

Many applications including chemical engineering and meteorology require the study of a chemically driven convection in cylindrical, as well as rectangular enclosures. The present paper reports a unified analysis of a chemically driven convection in densely packed porous cylindrical/rectangular enclosures saturated by a chemically reactive binary fluid mixture. Employing the degeneracy technique and the single-term Galerkin method involving Bessel functions in a linear stability analysis, an analytical expression for the critical Rayleigh number, Rac, was obtained. An analytical expression for the number of cells that manifest in a given enclosure, at the onset of convection, was derived from Rac. The connection between the stabilizing and destabilizing effects of various parameters and the size or the number of Bénard cells that manifest are described in detail. The results depicted that the chemical parameters related to the heat of reaction destabilize and the parameter depending inversely on the rate of the chemical reaction stabilizes the system. In the latter case, a greater number of smaller cells were formed in the system compared to the former case. Hence, we concluded that the chemically reactive fluid advances the onset of convection compared to the chemically non-reactive fluid. The results of a similar problem in rectangular enclosures of infinite horizontal extent and chemically non-reactive liquid-saturated porous medium were recovered as limiting cases. Thus, the present model presents a unified analysis of six individual problems.

Linear and conservative IMEX Runge–Kutta finite difference schemes with provable energy stability for the Cahn–Hilliard model in arbitrary domains

The Cahn–Hilliard (CH) equation is a classical mathematical equation which models the spinodal decomposition in binary fluid mixtures. In the real world, the phase change in a two-phase system usually occurs in irregular domains. To efficiently and accurately simulate this dynamics, we herein develop linear temporally first- and second-order accurate methods for the CH equation in arbitrary domains. The implicit-explicit (IMEX) Runge–Kutta method is adopted to construct discrete schemes in time. By introducing a simple boundary control function, we transform the original equations into equivalent forms in irregular domains and discretize the space by using the standard second-order finite difference stencil. In each temporal step, the proposed numerical schemes are highly efficient and easy to implement because we only need to solve several linear elliptic type equations. The mass conservation and unconditional energy stability of the proposed schemes are analytically proved. The multigrid algorithm is adopted for fast computation. The numerical results confirm the desired accuracy in time and space, mass conservation, and energy dissipation property. Moreover, the extensive calculations in two- and three-dimensional spaces indicate that the proposed method has good capability to simulate spinodal decomposition in arbitrarily irregular domains.