Evidence for the existence of an effective interfacial tension between miscible fluids: isobutyric acid-water and 1-butanol-water in a spinning-drop tensiometer

Emergence of Capillary Waves in Miscible Coflowing Fluids

We show that capillary waves can exist at the boundary between miscible coflowing fluids. We unveil that the interplay between transient interfacial stresses and confinement drives the progressive transition from the well-known inertial regime, characterized by a frequency independent wave number, k∼ω^{0}, to a capillary wave scaling, k∼ω^{2/3}, unexpected for miscible fluids. This allows us to measure the effective interfacial tension between miscible fluids and its rapid decay on timescales never probed so far, which we rationalize with a model going beyond square-gradient theories. Our work potentially opens a new avenue to measure transient interfacial tensions at the millisecond scale in a controlled manner.

Unraveling the interplay of temperature with molecular aggregation and miscibility in TEA-water mixtures

In the phase diagram of binary liquid mixtures, a miscibility gap is found with the concomitant liquid-liquid phase separation, wherein temperature is a key parameter in modulating the phase behavior. This includes critical temperatures such as the lower critical solution temperature (LCST) and upper critical solution temperature (UCST). Using a comprehensive approach including molecular dynamics (MD) simulation, graph theoretical analysis and spatial inhomogeneity measurement in an LCST-type mixture, we attempt to establish the relationship between the molecular aggregation pattern and phase behavior in TEA-water mixtures. At lower temperatures of binary liquid mixtures, TEA molecules tend to aggregate while simultaneously interacting with water forming a homogeneous solution. As the temperature increases, these TEA aggregates tend to self-associate by minimizing the interaction with water, which facilitates formation of two distinct liquid phases in the binary liquid. The spatial distribution analysis also reveals that the TEA aggregates compatible with water promote uniform distribution of water molecules, maintaining a homogeneous solution, while the water-incompatible ones generate isolation of water H-bond aggregates, leading to liquid-liquid phase separation in the binary system. This current study on temperature-induced molecular aggregation behavior is anticipated to contribute to a critical understanding of the phase behavior in binary liquid mixtures, including UCST, LCST, and reentrant phase behavior.

Trade Off between Hydrodynamic and Thermodynamic Forces at the Liquid-Liquid Interface

Viscous fingering (VF) instability has been investigated in the case of a partially miscible binary system by nonlinear numerical simulations. Partially miscible fluid systems offer the possibility of phase separation coupled with VF instability. The thermodynamics of such systems are governed by the Margules parameter (interaction parameter) as well as the fluid concentrations. Kinetics of the decomposition is also influenced by dynamical parameters such as the viscosity of the fluid, which incidentally also affects the hydrodynamic forces. Here, we explore the effects of concentration and Margules parameter in order to ascertain the trade-offs incurred between hydrodynamic and thermodynamic effects at the interface as well as the thermodynamics of the bulk. Based on the Gibb's free energy versus concentration curve, we select concentrations (i) outside spinodal and binodal regions, (ii) within binodal but outside the spinodal, and (iii) within the spinodal curve. We solve the modified Cahn-Hilliard-Hele-Shaw equation employing the COMSOL Multiphysics software. Applying high-resolution numerical simulations, we show a strong dependence of the thermodynamic forces on the concentration of the mixtures. Rapid phase separation and hence a faster rate of droplet formation have been found when the concentration lies inside the spinodal region. Further, we have investigated the correlation between the fractal dimension and dynamics of the system. The spatiotemporal studies presented in this work clearly illustrate the competition between hydrodynamic and thermodynamic forces and provide insights on the kinetics of decomposition and growth of interfacial instabilities.

Anomalous patterns of Saffman-Taylor fingering instability during a metastable phase separation

Phase separation is important in biology, biochemistry, industry, and other areas and is divided into two types: a spinodal decomposition type and a nucleation and growth type. The spinodal decomposition type phase separation occurs under the thermodynamically unstable conditions, and the nucleation and growth type phase separation occurs under thermodynamically metastable conditions. On the other hand, when a less viscous fluid displaces a more viscous one in porous media, the interface of the two fluids becomes hydrodynamically unstable and forms a finger-like pattern. The coupling of the hydrodynamic instability with the thermodynamic instability has been studied. It is reported that the hydrodynamic instability under thermodynamically unstable conditions, where spinodal decomposition type phase separation occurs, creates multiple moving droplets with a radius of 3-4 mm because of the spontaneous convection induced by the Korteweg force, which is driven by a compositional gradient during phase separation. However, the hydrodynamic instability under metastable conditions, where the phase separation of nucleation and growth type occurs, is still unrevealed. In this study, we applied fingering instability (hydrodynamic instability) under the metastable conditions, where the patterns are changed from fingering or droplets to anomalous patterns such as tip-widening or needle-like (top-pointed) fingering patterns when the initial concentration is metastable, which is considered near a binodal curve. These patterns are ubiquitous in nature, similar to dendrite crystals (snowflakes) or our body's cells. Thus, the patterns created can be controlled through hydrodynamic conditions such as the injection flow and thermodynamic conditions such as spinodal decomposition (thermodynamically unstable conditions) and metastable conditions.

Nonequilibrium Capillary Pressure of a Miscible Meniscus

We examine the dynamics of a miscible displacement in a capillary, calculating the nonequilibrium capillary pressure of a moving (and slowly diffusing) miscible meniscus. During the displacement, the capillary pressure varies with time following stretching and smearing of a miscible interface. The capillary pressure remains different from zero for a long time (on a diffusion time scale), slowing the displacement. This capillary pressure is however completely ignored by all theories currently available for practical modeling of miscible displacements in capillaries and porous matrices.

Controlled Formation of All-Aqueous Janus Droplets by Liquid-Liquid Phase Separation of an Aqueous Three-Phase System

Janus droplets have been demonstrated in a wide range of applications, ranging from drug delivery, to biomedical imaging, to bacterial detection. However, existing fabrication strategies often involve nonaqueous solvents, such as organic solvent or oil, which largely limits their use in fields that require a high degree of biocompatibility. Here, we present a method to achieve all-aqueous Janus droplets by liquid-liquid phase separation of an aqueous three-phase system (A3PS). An aqueous droplet containing two initially miscible polymers is first injected into an aqueous solution of another concentrated polymer, and then it spontaneously phase-separates into a Janus droplet due to the diffusive mass exchange between the drop and bulk phases during equilibration. To achieve continuous generation of the Janus droplets, the A3PS is further integrated with microfluidics and electrospray. The size and shape of the phase-separated Janus droplets can be easily controlled by tuning the operation parameters, such as the flow rate and/or the initial composition of the drop phases. Dumbbell-shaped and snowman-shaped Janus droplets with average sizes between 100 and 400 μm can be generated by both coflow microfluidics and electrospray. In particular, the phase-separated Janus droplets can simultaneously load two different liposomes into each compartment, which are promising carriers for combination drugs. The obtained Janus droplets are superior templates for biocompatible materials, which can serve as building blocks such as high-order droplet patterns for constructing advanced biomaterials.

Phase-Dependent Surfactant Transport on the Microscale: Interfacial Tension and Droplet Coalescence

Liquid-liquid emulsion systems are usually stabilized by additives, known as surfactants, which can be observed in various environments and applications such as oily bilgewater, water-entrained diesel fuel, oil production, food processing, cosmetics, and pharmaceuticals. One important factor that stabilizes emulsions is the lowered interfacial tension (IFT) between the fluid phases due to surfactants, inhibiting the coalescence. Many studies have investigated the surfactant transport behavior that leads to corresponding time-dependent lowering of the IFT. For example, the rate of IFT decay depends on the phase in which the surfactant is added (dispersed vs continuous) due in part to differences in the near-surface depletion depth. Other key factors, such as the viscosity ratio between the dispersed and continuous phases and Marangoni stress, will also have an impact on surfactant transport and therefore the coalescence and emulsion stability. In this feature article, the measurement techniques for dynamic IFT are first reviewed due to their importance in characterizing surfactant transport, with a specific focus on macroscale versus microscale techniques. Next, equilibrium isotherm models as well as dynamic diffusion and kinetic equations are discussed to characterize the surfactant and the time scale of the surfactant transport. Furthermore, recent studies are highlighted showing the different IFT decay rates and its long-time equilibrium value depending on the phase into which the surfactant is added, particularly on the microscale. Finally, recent experiments using a hydrodynamic Stokes trap to investigate the impact of interfacial surfactant transport, or "mobility", and the phase containing the surfactant on film drainage and droplet coalescence will be presented.

Spinning elastic beads: a route for simultaneous measurements of the shear modulus and the interfacial energy of soft materials

Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a spinning drop tensiometer. We determine the equilibrium shapes of the beads from the competition between the centrifugal force and the restoring elastic and surface forces. Considering the beads as neo-Hookean up to large deformations, we show that their elastic modulus and interfacial energy constant can be simultaneously deduced from their equilibrium shape. Also, our results provide further support to the scenario in which interfacial energy and interfacial tension coincide for amorphous polymer gels.

Phase Inversions Observed in Thermoresponsive Pickering Emulsions Stabilized by Surface Functionalized Colloidal Silica

In this study, the emulsification performance of functionalized colloidal silica is explored with the aim to achieve phase inversion of particle-stabilized (Pickering) emulsion systems. An increased understanding of inversion conditions can facilitate surfactant-free emulsion fabrication and expand its use in industrial applications. Phase inversion was achieved by adjusting the temperature but without changing the composition of the emulsion formulation. Silica nanoparticles modified with hydrophobic propyl groups and hydrophilic methyl poly(ethylene)glycol (mPEG) groups are used as emulsifiers, enabling control of the wettability of the particles and exploration of phase inversion phenomena, the latter due to the thermoresponsiveness of the attached PEG chains. The phase inversion conditions as well as the reversibility of the emulsion systems were examined at varying electrolyte concentrations and pH values of the suspensions. Transitional phase inversions, from oil-in-water and water-in-oil and back, were observed in functionalized silica particle-stabilized butanol emulsions at distinct temperatures. The phase inversion temperature was affected by electrolyte concentration and pH conditions due to salting-out effects, PEG-silica interactions, and the effects of the particle surface charge. Investigations of phase inversion conditions, temperature, and hysteresis effects in Pickering emulsions can improve the theoretical understanding of these phenomena and facilitate the implementation of low-energy emulsion preparation.

Spinning Drop Dynamics in Miscible and Immiscible Environments

We report on the extensional dynamics of spinning drops in miscible and immiscible background fluids following a rotational speed jump. Two radically different behaviors are observed. Drops in immiscible environments relax exponentially to their equilibrium shape, with a relaxation time that does not depend on the centrifugal force. We find an excellent quantitative agreement with the relaxation time predicted for quasi-spherical drops by Stone and Bush (Q. Appl. Math. 1996, 54, 551), while other models proposed in the literature fail to capture our data. By contrast, drops immersed in a miscible background fluid do not relax to a steady shape: they elongate indefinitely, their length following a power-law l(t)∼t2/5 in very good agreement with the dynamics predicted by Lister and Stone (J. Fluid Mech. 1996, 317, 275) for inviscid drops. Our results strongly suggest that low compositional gradients in miscible fluids do not give rise to an effective interfacial tension measurable by spinning drop tensiometry.

Kelvin-Helmholtz and Holmboe instabilities of a diffusive interface between miscible phases

The stability of a shear flow imposed along a diffusive interface that separates two miscible liquids (a heavier liquid lies underneath) is studied using direct numerical simulations. The phase-field approach is employed for description of a thermo- and hydrodynamic evolution of a heterogeneous binary mixture. The approach takes into account the dynamic interfacial stresses at a miscible interface and uses the extended Fick's law for setting the diffusion transport (the diffusion flux is proportional to the gradient of chemical potential). The shear flow is unstable to two kinds of instabilities: (1) the Kelvin-Helmholtz instability, with an immovable vortex formed in the middle of an interface (in the vertical direction) and (2) the Holmboe instability, with traveling waves along the interfacial boundary. The development of the Holmboe instability results in a stronger enhancement of molecular mixing between the mixture components. Earlier, the boundaries of these instabilities were determined using the linear stability analysis and employing the concept of a "frozen interface." In the current work, through the solution of full equations, we obtain the stability boundaries for several sets of governing parameters, showing a greater variety of the possible shapes of the stability diagrams. The Kelvin-Helmholtz instability always occurs at lower gravity effects (lower density contrasts), while the Holmboe instability occurs when gravity is stronger. We show that for some parameters these two instabilities are separated by a zone where the shear flow is stable, and this zone disappears for the other sets of parameters.

Rapid Determination of Interfacial Tensions in Nanopores: Experimental Nanofluidics and Theoretical Models

A rapid and accurate determination of interfacial tensions (IFTs) in nanopores is scientifically and practically significant, while most existing experimental measurements are restricted to the micrometer scale and theoretical calculations are relatively limited. In this study, six series of the IFT measurement tests for the binary CO₂-C₁₀, C₁-C₁₀, and N₂-C₁₀ mixtures are conducted at temperatures ( T) of 25.0 and 53.0 °C in a self-manufactured nanofluidic system. Moreover, a nanoscale-extended equation-of-state model considering the effects of the confinement, intermolecular interactions, and disjoining pressure and a semianalytical correlation are proposed to calculate the IFTs of the three mixtures in bulk phase and nanopores. Third, a new Tolman length formulation is developed for the IFT corrections in nanopores. Overall, the calculated IFTs from the two theoretical methods agree well with the measured results for most cases in nanopores. On the other hand, effects of the pore scale, temperature, pressure, and fluid composition on the IFTs of the three mixtures are effectively validated and specifically investigated. One suggestion comes from this work that the two theoretical methods for calculating the IFTs are better to be applied concurrently to minimize errors. Another important future work is to include more pore surface parameter (e.g., wettability) into the theoretical model.

Evolution and Disappearance of Solvent Drops on Miscible Polymer Subphases

Traditionally, an interface is defined as a boundary between immiscible phases. However, previous work has shown that even when two fluids are completely miscible, they maintain a detectable "effective interface" for long times. Miscible interfaces have been studied in various systems of two fluids with a single boundary between them. However, this work has not extended to the three-phase system of a fluid droplet placed on top of a miscible pool. We show that these three-phase systems obey the same wetting conditions as immiscible systems, and that their drop shapes obey the Augmented Young-Laplace Equation. Over time, the miscible interface diffuses and the shape of the drop evolves. We place 2-microliter drops of water atop miscible poly(acrylamide) solutions. The drop is completely wetted by the subphase, and then remains detectable beneath the surface for many minutes. An initial effective interfacial tension can be approximated to be on the order of 0.5 mN/m using the capillary number. Water and poly(acrylamide) are completely miscible in all concentrations, and yet, when viewed from the side, the drop maintains a capillary shape. Study of this behavior is important to the understanding of effective interfaces between miscible polymer phases, which are pervasive in nature.

Hydrodynamic instabilities in miscible fluids

Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural phenomena up to geological scales, to industrial and technological applications, where they represent the only way to control and promote mixing at low Reynolds numbers, well below the transition from laminar to turbulent flow. As for immiscible fluids, the onset of hydrodynamic instabilities in miscible fluids is directly related to the physics of their interfaces. The focus of this review is therefore on the general mechanisms driving the growth of disturbances at the boundary between miscible fluids, under a variety of forcing conditions. In the absence of a regularizing mechanism, these disturbances would grow indefinitely. For immiscible fluids, interfacial tension provides such a regularizing mechanism, because of the energy cost associated to the creation of new interface by a growing disturbance. For miscible fluids, however, the very existence of interfacial stresses that mimic an effective surface tension is debated. Other mechanisms, however, may also be relevant, such as viscous dissipation. We shall review the stabilizing mechanisms that control the most common hydrodynamic instabilities, highlighting those cases for which the lack of an effective interfacial tension poses deep conceptual problems in the mathematical formulation of a linear stability analysis. Finally, we provide a short overview on the ongoing research on the effective, out of equilibrium interfacial tension between miscible fluids.

Effect of pseudo-gravitational acceleration on the dissolution rate of miscible drops

The effect of pseudo-gravitational acceleration on the dissolution process of two phase miscible systems has been investigated at high acceleration values using a spinning drop tensiometer with three systems: 1-butanol/water, isobutyric acid/water, and triethylamine/water. We concluded that the dissolution process involves at least three different transport phenomena: diffusion, barodiffusion, and gravitational (buoyancy-driven) convection. The last two phenomena are significantly affected by the centrifugal acceleration acting at the interface between the two fluids, and the coupling with the geometry of the dissolving drop leads to a change of the mass flux during the course of the dissolution process.

Off-equilibrium surface tension in miscible fluids

The interfacial tension between immiscible fluids is responsible for a wealth of every-day phenomena, from the spherical shape of small drops and bubbles to the ability to walk on water of many insects. More than a century ago, physicist and mathematician D. Korteweg postulated the existence of an effective interface tension for miscible fluids, whenever a composition gradient exists, as encountered, e.g., in many flow geometries. In this mini-review, we discuss experimental work performed in the last decades that demonstrates the existence of a positive effective interface tension in a variety of systems, from molecular, near-critical liquids to complex fluids such as polymer solutions and colloidal suspensions. The various experimental strategies that have been deployed are discussed, together with their advantages and limitations. Finally, some of the key theoretical questions still open are outlined.

Self-Propelled Vesicles Induced by the Mixing of Two Polymeric Aqueous Solutions through a Vesicle Membrane Far from Equilibrium

This study describes the development of self-propelled vesicles using transient interfacial energy in an aqueous two-phase system composed of polyethylene glycol (PEG), dextran (DEX), and water. The transient interfacial energy was generated at the mixing boundary between the PEG and DEX solutions when the two miscible liquids were in contact with each other far from equilibrium. Vesicles encapsulating 20 wt % DEX solution traveled spontaneously when the PEG concentration in the environmental media was >15 wt %. The motility of the vesicles varied with the permeability of the vesicle membrane. The permeability increased significantly when the concentration of PEG was >15 wt %. PEG had a profound effect not only on mass transfer through the membrane but also on the motility of the vesicles.

On the phase-field modelling of a miscible liquid/liquid boundary

Mixing of miscible liquids is essential for numerous processes in industry and nature. Mixing, i.e. interpenetration of molecules through the liquid/liquid boundary, occurs via interfacial diffusion. Mixing can also involve externally or internally driven hydrodynamic flows, and can lead to deformation or disintegration of the liquid/liquid boundary. At the moment, the mixing dynamics remains poorly understood. The classical Fick's law, generally accepted for description of the diffusion process, does not explain the experimental observations, in particular, the recent experiments with dissolution of a liquid solute by a liquid solvent within a horizontal capillary (Stevar and Vorobev, 2012). We present the results of the numerical study aimed at development of an advanced model for the dissolution dynamics of liquid/liquid binary mixtures. The model is based on the phase-field (Cahn-Hilliard) approach that is used as a physics-based model for the thermo- and hydrodynamic evolution of binary mixtures. Within this approach, the diffusion flux is defined through the gradient of chemical potential, and, in particular, includes the effect of barodiffusion. The dynamic interfacial stresses at the miscible interface are also taken into account. The simulations showed that such an approach can accurately reproduce the shape of the solute/solvent boundary, and some aspects of the diffusion dynamics. Nevertheless, all experimentally-observed features of the diffusion motion of the solute/solvent boundary, were not reproduced.

Bulk and interfacial stresses in suspensions of soft and hard colloids

We explore the influence of particle softness and internal structure on both the bulk and interfacial rheological properties of colloidal suspensions. We probe bulk stresses by conventional rheology, by measuring the flow curves, shear stress versus strain rate, for suspensions of soft, deformable microgel particles and suspensions of near hard-sphere-like silica particles. A similar behaviour is seen for both kinds of particles in suspensions at concentrations up to the random close packing volume fraction, in agreement with recent theoretical predictions for sub-micron colloids. Transient interfacial stresses are measured by analyzing the patterns formed by the interface between the suspensions and their solvent, due to a generalized Saffman-Taylor hydrodynamic instability. At odds with the bulk behaviour, we find that microgels and hard particle suspensions exhibit vastly different interfacial stress properties. We propose that this surprising behaviour results mainly from the difference in particle internal structure (polymeric network for microgels versus compact solid for the silica particles), rather than softness alone.

Effect of Péclet number on miscible rectilinear displacement in a Hele-Shaw cell

The influence of fluid dispersion on the Saffman-Taylor instability in miscible fluids has been investigated in both the linear and the nonlinear regimes. The convective characteristic scales are used for the dimensionless formulation that incorporates the Péclet number (Pe) into the governing equations as a measure for the fluid dispersion. A linear stability analysis (LSA) is performed in a similarity transformation domain using the quasi-steady-state approximation. LSA results confirm that a flow with a large Pe has a higher growth rate than a flow with a small Pe. The critical Péclet number (Pec) for the onset of instability for all possible wave numbers and also a power-law relation of the onset time and most unstable wave number with Pe are observed. Unlike the radial source flow, Pec is found to vary with t0. A Fourier spectral method is used for direct numerical simulations (DNS) of the fully nonlinear system. The power-law dependence of the onset of instability ton on Pe is obtained from the DNS and found to be inversely proportional to Pe and it is in good agreement with that obtained from the LSA. The influence of the anisotropic dispersion is analyzed in both the linear and the nonlinear regimes. The results obtained confirm that for a weak transverse dispersion merging happens slowly and hence the small wave perturbations become unstable. We also observ that the onset of instability sets in early when the transverse dispersion is weak and varies with the anisotropic dispersion coefficient, ε, as ∼√[ε], in compliance with the LSA. The combined effect of the Korteweg stress and Pe in the linear regime is pursued. It is observed that, depending on various flow parameters, a fluid system with a larger Pe exhibits a lower instantaneous growth rate than a system with a smaller Pe, which is contrary to the results when such stresses are absent.

Conduction-only transport phenomena in compressible bivelocity fluids: diffuse interfaces and Korteweg stresses

"Diffuse interface" theories for single-component fluids—dating back to van der Waals, Korteweg, Cahn-Hilliard, and many others—are currently based upon an ad hoc combination of thermodynamic principles (built largely upon Helmholtz's free-energy potential) and so-called “nonclassical” continuum-thermomechanical principles (built largely upon Newtonian mechanics), with the latter originating with the pioneering work of Dunn and Serrin [Arch. Ration. Mech. Anal. 88, 95 (1985)]. By introducing into the equation governing the transport of energy the notion of an interstitial work-flux contribution, above and beyond the usual Fourier heat-flux contribution, namely, jq = -k∇T, to the energy flux, Dunn and Serrin provided a rational continuum-thermomechanical basis for the presence of Korteweg stresses in the equation governing the transport of linear momentum in compressible fluids. Nevertheless, by their failing to recognize the existence and fundamental need for an independent volume transport equation [Brenner, Physica A 349, 11 (2005)]—especially for the roles played therein by the diffuse volume flux j v and the rate of production of volume πν at a point of the fluid continuum—we argue that diffuse interface theories for fluids stand today as being both ad hoc and incomplete owing to their failure to recognize the need for an independent volume transport equation for the case of compressible fluids. In contrast, we point out that bivelocity hydrodynamics, as it already exists [Brenner, Phys. Rev. E 86, 016307 (2012)], provides a rational, non-ad hoc, and comprehensive theory of diffuse interfaces, not only for single-component fluids, but also for certain classes of crystalline solids [Danielewski and Wierzba, J. Phase Equilib. Diffus. 26, 573 (2005)]. Furthermore, we provide not only what we believe to be the correct constitutive equation for the Korteweg stress in the class of fluids that are constitutively Newtonian in their rheological response to imposed stresses but, equally importantly, we establish the explicit functional forms of Korteweg's phenomenological thermocapillary coefficients appearing therein.

Off-equilibrium surface tension in colloidal suspensions

We study the fingering instability of the interface between two miscible fluids, a colloidal suspension and its own solvent. The temporal evolution of the interface in a Hele-Shaw cell is found to be governed by the competition between the nonlinear viscosity of the suspension and an off-equilibrium, effective surface tension Γe. By studying suspensions in a wide range of volume fractions, ΦC, we show that Γe∼ΦC2, in agreement with Korteweg's theory for miscible fluids. The surface tension exhibits an anomalous increase with particle size, which we account for using entropy arguments.

All-aqueous multiphase microfluidics

Immiscible aqueous phases, formed by dissolving incompatible solutes in water, have been used in green chemical synthesis, molecular extraction and mimicking of cellular cytoplasm. Recently, a microfluidic approach has been introduced to generate all-aqueous emulsions and jets based on these immiscible aqueous phases; due to their biocompatibility, these all-aqueous structures have shown great promises as templates for fabricating biomaterials. The physico-chemical nature of interfaces between two immiscible aqueous phases leads to unique interfacial properties, such as an ultra-low interfacial tension. Strategies to manipulate components and direct their assembly at these interfaces needs to be explored. In this paper, we review progress on the topic over the past few years, with a focus on the fabrication and stabilization of all-aqueous structures in a multiphase microfluidic platform. We also discuss future efforts needed from the perspectives of fluidic physics, materials engineering, and biology for fulfilling potential applications ranging from materials fabrication to biomedical engineering.

Linear stability analysis of a horizontal phase boundary separating two miscible liquids

The evolution of small disturbances to a horizontal interface separating two miscible liquids is examined. The aim is to investigate how the interfacial mass transfer affects development of the Rayleigh-Taylor instability and propagation and damping of the gravity-capillary waves. The phase-field approach is employed to model the evolution of a miscible multiphase system. Within this approach, the interface is represented as a transitional layer of small but nonzero thickness. The thermodynamics is defined by the Landau free energy function. Initially, the liquid-liquid binary system is assumed to be out of its thermodynamic equilibrium, and hence, the system undergoes a slow transition to its thermodynamic equilibrium. The linear stability of such a slowly diffusing interface with respect to normal hydro- and thermodynamic perturbations is numerically studied. As a result, we show that the eigenvalue spectra for a sharp immiscible interface can be successfully reproduced for long-wave disturbances, with wavelengths exceeding the interface thickness. We also find that thin interfaces are thermodynamically stable, while thicker interfaces, with the thicknesses exceeding an equilibrium value, are thermodynamically unstable. The thermodynamic instability can make the configuration with a heavier liquid lying underneath unstable. We also find that the interfacial mass transfer introduces additional dissipation, reducing the growth rate of the Rayleigh-Taylor instability and increasing the dissipation of the gravity waves. Moreover, mutual action of diffusive and viscous effects completely suppresses development of the modes with shorter wavelengths.

Spectral properties of thermal fluctuations on simple liquid surfaces below shot-noise levels

We study the spectral properties of thermal fluctuations on simple liquid surfaces, sometimes called ripplons. Analytical properties of the spectral function are investigated and are shown to be composed of regions with simple analytic behavior with respect to the frequency or the wave number. The derived expressions are compared to spectral measurements performed orders of magnitude below shot-noise levels, which is achieved using a novel noise reduction method. The agreement between the theory of thermal surface fluctuations and the experiment is found to be excellent, elucidating the spectral properties of the surface fluctuations. The measurement method requires relatively only a small sample both spatially (few μm) and temporally (~20 s). The method also requires relatively weak light power (~0.5 mW) so that it has a broad range of applicability, including local measurements, investigations of time-dependent phenomena, and noninvasive measurements.

Diversified nanoparticle assembly pathways: materials architecture control beyond the amphiphilicity paradigm

The functional versatility of a chemical system is ultimately dictated by the availability of distinctly accessible architectures. The generation of a diverse array of assembled constructs from a single type of nanoscale building block is a promising yet largely elusive goal. We report herein the utility of a monolayer-modified nanoparticle for the creation of a broad range of architectures. The versatile modes of assembly complement the conventionally used, amphiphilicity-driven strategy. We demonstrate that one can vary the nanoparticle assembly pathways within the confines of solvent media through the modulation of interactions and partitioning of nanoparticles. Merging of the molecular-scale design and higher-ordered arrangement enables diversified assembly through the manipulation of experimental parameters such as solvent, pH, affinity molecule, and temperature. Microfluidics provides an effective channel to control the monodispersity and size on all the architectures attainable in the bulk solution phase. These observations could be further explored for an understanding of diversified matter organization and order generation beyond the amphiphilicity paradigm.

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

Transient surface tension in miscible liquids

Evidence of the existence of a transient surface tension between two miscible fluid phases is given. This is done by making use of a density matched free of gravity perturbations, binary liquid of isobutyric acid and water, which presents a miscibility gap and is studied by light scattering. The experiment is performed very near the critical point of the binary liquid, where the diffusion of phases is extremely slow. The surface tension is deduced from the evolution of the structure factor obtained from low angle light scattering. The latter evolution is successfully analyzed in terms of a local equilibrium diffusive approach that makes explicit how the surface tension decreases with time.

Quantitative experimental study on the transition between fast and delayed coalescence of sessile droplets with different but completely miscible liquids

Quantitative experimental data on the coalescence behavior of sessile droplets with different but completely miscible liquids are presented. The liquids consist of various aqueous mixtures of different nonvolatile diols and carbon acids with surface tensions ranging from 33 to 68 mN/m, contact angles between 9 degrees and 20 degrees, and viscosities from 1 to 12 cP. Two distinctly different coalescence behaviors, a delayed and a fast regime, are found. The transition between the two behaviors is remarkably sharp. It is found that the coalescence mode depends predominantly on the differences in the surface tensions of the two droplets. If the surface tension difference exceeds approximately 3 mN/m, the coalescence is delayed. If it is less, droplet fusion occurs fast. Within the investigated parameter space, the transition seems independent from droplet size, absolute values of the surface tensions, and viscosity. Certain aspects of the experimental findings are explained with the simple hydrodynamic model presented in a recent publication.

Controlled pattern formation in thin liquid layers

We examine the fully nonlinear behavior of a thin liquid film on a hydrophobic/hydrophilic solid support in three dimensions using a phase field model. For flat homogeneous substrates, the stability of thin liquid layers is investigated under the action of gravity. The coarsening process at the solid boundary can be controlled on inhomogeneous substrates. On substrates chemically patterned in an adequate way with hydrophobic and hydrophilic spots, one can obtain stable, regular liquid droplets and even design liquid structures (PACS numbers: 47.54.-r, 68.18.Jk, and 05.70.Np).

Radial viscous fingering in miscible Hele-Shaw flows: a numerical study

A modified version of the usual viscous fingering problem in a radial Hele-Shaw cell with immiscible fluids is studied by intensive numerical simulations. We consider the situation in which the fluids involved are miscible, so that the diffusing interface separating them can be driven unstable through the injection or suction of the inner fluid. The system is allowed to rotate in such a way that centrifugal and Coriolis forces come into play, imposing important changes on the morphology of the arising patterns. In order to bridge from miscible to immiscible pattern forming structures, we add the surface tensionlike effects due to Korteweg stresses. Our numerical experiments reveal a variety of interesting fingering behaviors, which depend on the interplay between injection (or suction), diffusive, rotational, and Korteweg stress effects. Whenever possible the features of the simulated miscible fronts are contrasted to existing experiments and other theoretical or numerical studies, usually resulting in close agreements. A number of additional complex morphologies, whose experimental realization is still not available, are predicted and discussed.

Evidence for the existence of an effective interfacial tension between miscible fluids. 2. Dodecyl acrylate-poly(dodecyl acrylate) in a spinning drop tensiometer

We studied drops of dodecyl acrylate in poly(dodecyl acrylate) (molecular weight of 25,000) in a spinning drop tensiometer to determine whether an effective interfacial tension (EIT) existed between these two miscible fluids. We found convincing evidence. We estimated the mechanical relaxation time from an immiscible analogue (1-propanol and poly(dodecyl acrylate)) and showed that the dodecyl acrylate drops maintained quasi-steady diameters long after this relaxation period. Drops continuously grew in length and became more diffuse, but the width of the transition zone did not grow with t(1/2) as expected from Fick's law although this system had been shown to follow Fick's law in a static configuration (Antrim, D.; Bunton, P.; Lewis, L. L.; Zoltowski, B. D.; Pojman, J. A. J. Phys. Chem. B 2005, 109, 11842-11849). The EIT was determined from Vonnegut's equation, EIT = (Deltarho)omega(2)r(3)/4; both the inner and outer diameters were measured, yielding values of 0.002 and 0.02 mN m(-1), respectively. The EIT was found to be independent of the rotation rate above 6000 rpm and independent of the initial drop volume. The EIT was found to decrease with temperature and increase with the difference in concentration between the monomer drop and polymer-monomer fluid. The square gradient parameter, k, was determined from EIT = k(Deltac(2)/delta), where Deltac is the difference in mole fraction and delta is the width of the transition zone. The square gradient parameter was on the order of 10(-9) N. The square gradient parameter was found to decrease with temperature, to be independent of concentration, and to increase with the molecular weight of the polymer.