Binary fluid mixtures are examples of complex fluids whose microstructure and flow are strongly coupled. For pairs of simple fluids, the microstructure consists of droplets or bicontinuous demixed domains and the physics is controlled by the interfaces between these domains. At continuum level, the structure is defined by a composition field whose gradients which are steep near interfaces drive its diffusive current. These gradients also cause thermodynamic stresses which can drive fluid flow. Fluid flow in turn advects the composition field, while thermal noise creates additional random fluxes that allow the system to explore its configuration space and move towards the Boltzmann distribution. This article introduces continuum models of binary fluids, first covering some well-studied areas such as the thermodynamics and kinetics of phase separation, and emulsion stability. We then address cases where one of the fluid components has anisotropic structure at mesoscopic scales creating nematic (or polar) liquid-crystalline order; this can be described through an additional tensor (or vector) order parameter field. We conclude by outlining a thriving area of current research, namely active emulsions, in which one of the binary components consists of living or synthetic material that is continuously converting chemical energy into mechanical work.
We investigate numerically the behaviour of a phase-separating mixture of a blue phase I liquid crystal with an isotropic fluid. The resulting morphology is primarily controlled by an inverse capillary number, $χ$, setting the balance between interfacial and elastic forces. When $χ$ and the concentration of the isotropic component are both low, the blue phase disclination lattice templates a cubic array of fluid cylinders. For larger $χ$, the isotropic phase arranges primarily into liquid emulsion droplets which coarsen very slowly, rewiring the blue phase disclination lines into an amorphous …
An important strategy to stabilize emulsions is to arrest coalescence of the constituent droplets with an opposing rheological force. Colloidal particles adsorbed on the surface of emulsion droplets in a Pickering emulsion become increasingly crowded during successive coalescence events because the combined surface area of coalescing droplets is less than that of the constituent droplets. Beyond a critical density, the particles form a rigid shell around the droplet and inhibit both relaxation of the droplet shape and further coalescence. The resulting droplets have a nonuniform distribution o…
The morphology of a mixture made of a polar active gel immersed in an isotropic passive fluid is studied numerically. Lattice Boltzmann method is adopted to solve the Navier-Stokes equation and coupled to a finite-difference scheme used to integrate the dynamic equations of the concentration and of the polarization of the active component. By varying the relative amounts of the mixture phases, different structures can be observed. In the contractile case, at moderate values of activity, elongated structures are formed when the active component is less abundant, while a dynamic emulsion of pass…
A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011)). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics o…
The work deals with the experimental study of the emulsion whose dispersion medium is a magnetic fluid while the disperse phase is formed by a glycerin-water mixture. It is demonstrated that under effect of a magnetic field chain aggregates form from the disperse phase drops. Such emulsion microstructure change affects its macroscopic properties. The emulsion dielectric permeability and specific electrical conductivity have been measured. It is demonstrated that under the effect of relatively weak external magnetic fields (~ 1 kA/m) the emulsion electrical parameters may change several fold. T…
Protein-stabilised emulsions can be seen as mixtures of unadsorbed proteins and of protein-stabilised droplets. To identify the contributions of these two components to the overall viscosity of sodium caseinate o/w emulsions, the rheological behaviour of pure suspensions of proteins and droplets were characterised, and their properties used to model the behaviour of their mixtures. These materials are conveniently studied in the framework developed for soft colloids. Here, the use of viscosity models for the two types of pure suspensions facilitates the development of a semi-empirical model th…
Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，法兰西学院，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎西岱大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理学卓越集群）；Faculty of Mathematics, Natural Sciences, and Materials Engineering: Institute of Physics, University of Augsburg（奥格斯堡大学数学、自然科学与材料工程学院：物理研究所）
These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a mixture: coalescence, Ostwald ripening, its prevention by trapped species, coarsening of bicontinuous states, and the role of shear flow. The third topic addressed is the stabilization of emulsions by using surfactants to reduce or even eliminate the interfacial tension between phases; the physics of bending energy, which becomes relevant in the latter case, is the…
Using controlled spinodal decomposition, we have created a fluid-bicontinuous structure stabilized by colloidal particles. We present confocal microscopy studies of these structures and their variation with kinetic pathway. Our studies reveal a rigid multilayer of colloidal particles jammed at the interface which prevents the liquids demixing for many hours. The arrangement of two-fluid domains, interpenetrating on the meso-scale, could be useful as a microreaction medium.
Aqueous mixtures of small molecules, such as lower n-alkanols for example, are known to be micro-segregated, with domains in the nano-meter range. One consequence of micro-segregated domains would be the existence of long range domain-domain oscillatory correlations in the various atom- atom pair correlation functions, and subsequent pre-peaks in the corresponding atom atom structure factors, in the q-vector range corresponding to nano-sized domains. However, no such pre-peak have ever been observed in the large corpus of radiation scattering data published so far. Here, through large scale si…
It is demonstrated that the often observed broadness of the molecular weight distribution obtained from latex particles synthesized by means of surfactant-free emulsion polymerization results from the multistage kinetics. The initial stage of the polymerization, by which the primary particles are formed, is of the 01-kind which means that it can be assumed that the particles are so small that at any moment of time there is no more than one radical chain per particle. After the aggregation of primary particles into secondary particles, the so called coagulative nucleation step, the polymerizati…
A mathematical model to describe the emulsion polymerization kinetics of co- and ter-polymerizations is developed. The model is based on the classical Smith-Ewart (SE) equations, within the pseudo-homopolymerization approach, with state-of-the-art models for radical entry and desorption. For co- and ter-polymerizations there are unknown parameters in the model which are related to monomer-specific gel-effect coefficients, that are needed to compute the bimolecular termination reaction rates. The unknown parameters are determined through extensive calibration of the model on literature data for…
We conduct direct numerical simulation (DNS) of the Cahn-Hilliard-Navier-Stokes (CHNS) equations to investigate the statistical properties of the turbulent phase-separating symmetric binary-fluid mixture. Turbulence causes an arrest of the phase-separation which leads to the formation of a statistically steady emulsion. We characterize turbulent velocity fluctuations in an emulsion for different values of the Reynolds number and the Weber number. Our scale-by-scale kinetic energy budget analysis shows that the interfacial terms in the CHNS provide an alternate route for the kinetic energy tran…
Surface phase transitions in surfactant adsorption layers are known to affect the dynamic properties of foams and to induce surface nucleation in freezing emulsion drops. Recently, these transitions were found to play a role in several other phenomena, opening new opportunities for controlling foam and emulsion properties. This review presents a brief outlook of the emerging opportunities in this area. Three topics are emphasized: (1) The use of surfactant mixtures for inducing phase transitions on bubble surfaces in foams; (2) The peculiar properties of natural surfactants saponins which form…
We use computer simulations to study the morphology and rheological properties of a bidimensional emulsion resulting from a mixture of a passive isotropic fluid and an active contractile polar gel, in the presence of a surfactant that favours the emulsification of the two phases. By varying the intensity of the contractile activity and of an externally imposed shear flow, we find three possible morphologies. For low shear rates, a simple lamellar state is obtained. For intermediate activity and shear rate, an asymmetric state emerges, which is characterized by shear and concentration banding a…
We numerically study the energy transfer in a multi-component $2d$ film, made of an active polar gel and a passive isotropic fluid in presence of surfactant favoring emulsification. We show that by confining the active behavior into the localized component, the typical scale where chemical energy is transformed in mechanical energy can be substantially controlled. Quantitative analysis of kinetic energy spectra and fluxes shows the presence of a multi-scale dynamics due to the existence of a flux induced by the active stress only, without the presence of a turbulent cascade. An increase in the…
A mixture of hard-sphere particles and model emulsion droplets is studied with a Brownian dynamics simulation. We find that the addition of nonwetting emulsion droplets to a suspension of pure hard spheres can lead to both gas-liquid and fluid-solid phase separations. Furthermore, we find a stable fluid of hard-sphere clusters. The stability is due to the saturation of the attraction that occurs when the surface of the droplets is completely covered with colloidal particles. At larger emulsion droplet densities a percolation transition is observed. The resulting networks of colloidal particles…
We study numerically the behaviour of a mixture of a passive isotropic fluid and an active polar gel, in the presence of a surfactant favouring emulsification. Focussing on parameters for which the underlying free energy favours the lamellar phase in the passive limit, we show that the interplay between nonequilibrium and thermodynamic forces creates a range of multifarious exotic emulsions. When the active component is contractile (e.g., an actomyosin solution), moderate activity enhances the efficiency of lamellar ordering, whereas strong activity favours the creation of passive droplets wit…
Protein-based high internal phase emulsions (HIPEs) have gained tremendous attention in diverse fields, but their mechanism in the emulsification process remains elusive. In this article, HIPEs were stabilized directly by food-grade proteins, depending on a self-organized process featuring a fluid laminarization. We elucidated that the emulsification with the rotor-stator mixer is a typical non-equilibrium process. The crucial factor for the process is related to the irreversible energy dissipation, while the internal phase volume fraction is the threshold determining the laminarization. The f…
Microswimmers create bicontinuous emulsions in binary fluids
Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）；EMBL Barcelona（欧洲分子生物学实验室巴塞罗那分部）；Barcelona Collaboratorium for Modelling and Predictive Biology（巴塞罗那建模与预测生物合作组织）；Univ. Bordeaux（波尔多大学）
Self-organized flows break morphological symmetry in active/passive systems
Institute of Scientific Computing, Technische Universität Dresden（德累斯顿工业大学科学计算研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Cluster of Excellence, Physics of Life, Technische Universität Dresden（德累斯顿大学生命物理卓越集群）
We use the Self Consisten Generalized Langevin Equation theory (SCGLE) to study the dynamic arrest transitions of a system of three species of hard sphere colloidal system in the size ratio 1:3:9. We find that the inclusion of the smallest species has a depletion effect that drives the system to a second glass-liquid-glass re-entrance in a similar way that the inclusion of a small species in an otherwise monodisperse system leads to a (first) re-entrance. And we also find that the new glass after the second reentrance has very small localization length. Additionally we compare the kinetic phas…
We use state-of-the-art molecular dynamics simulations to study the effects of annealed disorder on the phase separating kinetics and aging phenomena of a segregating binary fluid mixture. In the presence of disorder, we observe a dramatic slowing down in the phase separation dynamics. The domain growth follows the power-law with a disorder-dependent exponent. Due to the energetically favorable positions, the domain boundary roughens which modifies the correlation function and structure factor to a non-Porod behavior. The correlation function and structure factor provide clear evidence that th…
Comment on the paper J. Solsvik and E. Manger, "Kinetic theory models for granular mixtures with unequal granular temperature: Hydrodynamic velocity," Phys. Fluids \textbf{33}, 043321 (2021).
The steady state and phase ordering kinetics in a pure active Borwnian particle system are studied in recent years. In binary mixture of active and passive Brownian particles passive particles are used as probe to understand the properties of active medium. In our present study we study the mixture of passive and active Brownian particles. Here we aim to understand the steady state and kinetics of small passive particles in the mixture. In our system,the passive particles are small in size and large in number, whereas ABPs are large in size and small in number. The system is studied on a two-d…
Purely entropic systems such as suspensions of hard rods, platelets and spheres show rich phase behavior. Rods and platelets have successfully been used as models to predict the equilibrium properties of liquid crystals for several decades. Over the past years hard particle models have also been studied in the context of non-equilibrium statistical mechanics, in particular regarding the glass transition, jamming, sedimentation and crystallization. Recently suspensions of hard anisotropic particles also moved into the focus of materials scientists who work on conducting soft matter composites. …
In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson and Tsimring [Phys. Rev. E {\bf 74}, 031915 (2006)] we model the motor-induced reorientation of microtubules as collision rules, and devise a semi-analytical method to calculate the corresponding interaction integrals. This procedure yields an infinite hierarchy of kinetic equations that we terminate by employing a well-established closure strategy, develope…
Based on numerical simulations of a lattice kinetic model for soft-glassy materials, we characterize the global rheology of a dense emulsion-like system, under three representative load conditions: Couette flow, time-oscillating Strain and Kolmogorov flow. It is found that in all cases the rheology is described by a Herschel-Bulkley (HB) relation, $σ= σ_{Y} + A S^β$, with the yield stress $σ_{Y}$ largely independent of the loading scenario. A proper rescaling of the HB parameters permits to describe heterogeneous flows with space-dependent stresses, based on the notion of cooperativity, as rec…
We present theory and simulation of simultaneous chemical demixing and phase ordering in a polymer-liquid crystal mixture in conditions where isotropic- isotropic phase separation is metastable with respect to isotropic-nematic phase transition. It is found that mesophase formation proceeds by a transient metastable phase that surround the ordered phase, and whose lifetime is a function of the ratio of diffusional to orientational mobilities. It is shown that kinetic phase ordering in polymer-mesogen mixtures is analogous to kinetic crystallization in polymer solutions.
The adsorption at the interface between an aqueous solution of several surface-active agents and another fluid (air or oil) phase is addressed theoretically. We derive the kinetic equations from a variation of the interfacial free energy, solve them numerically and provide an analytic solution for the simple case of a linear adsorption isotherm. Calculating asymptotic solutions analytically, we find the characteristic time scales of the adsorption process and observe the behavior of the system at various temporal stages. In particular, we relate the kinetic behavior of the mixture to the prope…
Morphologies in phase separating systems can significantly influence the final properties of materials. We present extensive Monte Carlo (MC) simulation results on the segregation kinetics of the critical binary (AB) mixture with a fraction of bond disorder (BD) introduced in a regular manner. We focus on studying the effect of various quench temperatures on the growth kinetics and scaling properties of evolving morphologies. The two-dimensional (2d) kinetic Ising system with conserved spin exchange kinetics is used to model the system. We observe that domain morphologies change from their usu…
We study the rheological behavior of mixtures of foams and pastes, which can be described as suspensions of bubbles in yield stress fluids. Model systems are designed by mixing monodisperse aqueous foams and concentrated emulsions. The elastic modulus of the suspensions decreases with the bubble volume fraction. This decrease is all the sharper as the elastic capillary number (defined as the ratio of the paste elastic modulus to the bubble capillary pressure) is high, which accounts for the softening of the bubbles as compared to the paste. By contrast, the yield stress of most studied materia…
Study of the Liquid/Vapor Interfacial Properties of Concentrated Polyelectrolyte-Surfactant Mixtures Using Surface Tensiometry and Neutron Reflectometry: Equilibrium, Adsorption Kinetics and Dilational Rheology
Microcapsules allow for the controlled containment, transport, and release of cargoes ranging from pharmaceuticals to fragrances. Given the interest from a variety of industries in microcapsules and other core-shell structures, a multitude of fabrication strategies exist. Here, we report on a method relying on a mixture of temperature-responsive microgel particles, poly(N-isopropylacrylamide) (pNIPAM), and a polymer which undergo fluid-fluid phase separation. At room temperature this mixture separates into colloid-rich (liquid) and colloid-poor (gas) fluids. By heating the sample above a criti…
An isolated mixture of smooth, inelastic hard spheres supports a homogeneous cooling state with different kinetic temperatures for each species. This phenomenon is explored here by molecular dynamics simulation of a two component fluid, with comparison to predictions of the Enskog kinetic theory. The ratio of kinetic temperatures is studied for two values of the restitution coefficient, $α=0.95$ and 0.80, as a function of mass ratio, size ratio, composition, and density. Good agreement between theory and simulation is found for the lower densities and higher restitution coefficient; significan…
The rheological properties for dilute and moderately dense granular binary mixtures of smooth, inelastic hard disks/spheres under uniform shear flow in steady state conditions are reported. The results are based on the Enskog kinetic theory, numerically solved by a dense gas extension of the Direct Simulation Monte Carlo method for dilute gases. These results are confronted to the ones also obtained by performing molecular dynamics simulations with very good agreement for the lower densities and higher coefficients of restitution. It appears that the range of densities for which the Enskog equ…
We study phase separation and transient gelation in a mixture consisting of polydisperse colloids and non-adsorbing polymers, where the ratio of the average size of the polymer to that of the colloid is approximately 0.063. Unlike what has been reported previously for mixtures with somewhat lower colloid polydispersity, the addition of polymers does not expand the fluid-solid coexistence region. Instead, we find a region of fluid-solid coexistence which has an approximately constant width but an unexpected re-entrant shape. We detect the presence of a metastable gas-liquid binodal, which gives…
In this paper we calculate the transfer coefficients for evaporation and condensation of mixtures. We use the continuous profiles of various thermodynamic quantities through the interface, obtained in our previous works using the square gradient model. Furthermore we introduce the Gibbs surface and obtain the excess entropy production for a surface. Following the traditional non-equilibrium thermodynamic approach we introduce the surface transfer coefficients which we are able to determine from the continuous solution. The knowledge of these coefficients is important for many industrial applic…
Kinetic Theory for the Shear Viscosity of Dense Binary Dipolar Fluid Mixtures
Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology（挪威科技大学机械与工业工程系）；Instituto de Alta Investigación, Universidad de Tarapacá（塔拉帕卡大学高等研究所）
It is well-recognized that granular media under rapid flow conditions can be modeled as a gas of hard spheres with inelastic collisions. At moderate densities, a fundamental basis for the determination of the granular hydrodynamics is provided by the Enskog kinetic equation conveniently adapted to account for inelastic collisions. A surprising result (compared to its molecular gas counterpart) for granular mixtures is the failure of the energy equipartition, even in homogeneous states. This means that the partial temperatures $T_i$ (measuring the mean kinetic energy of each species) are differ…
The evolution of the microstructure due to spinodal decomposition in phase separated mixtures has a strong impact on the final material properties. In the late stage of coarsening, the system is characterized by the growth of a single characteristic length scale $L\sim C t^α$. To understand the structure-property relationship, the knowledge of the coarsening exponent $α$ and the coarsening rate constant $C$ is mandatory. Since the existing literature is not entirely consistent, we perform phase field simulations based on the Cahn-Hilliard equation. We restrict ourselves to binary mixtures usin…
Many features of granular media can be modelled as a fluid of hard spheres with {\em inelastic} collisions. Under rapid flow conditions, the macroscopic behavior of grains can be described through hydrodynamic equations. At low-density, a fundamental basis for the derivation of the hydrodynamic equations and explicit expressions for the transport coefficients appearing in them is provided by the Boltzmann kinetic theory conveniently modified to account for inelastic binary collisions. The goal of this chapter is to give an overview of the recent advances made for binary granular gases by using…
