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We investigate theoretically the surface tension between two immiscible liquids containing antagonistic and regular salts. The mean-field model includes the electrostatic energy and the Gibbs transfer energy of the ions. We find the Donnan potential difference between the liquids and solve the Poisson-Boltzmann equation to calculate the potential and ion density profiles. When the liquids contain only a regular salt, the surface tension increases when compared to the no-salt case; in contrast, the surface tension is reduced when they contain only an antagonistic salt. When both salts are present, the surface tension can either further decrease or increase depending on the preferential solvation of the ions, in agreement with published experimental observations., (© 2023. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.)

We present a model to describe ion-induced nucleation in fluids. Nucleation is induced by a charged molecular aggregate, a large ion, a charged colloid, or an aerosol particle. This model generalizes the Thomson model to polar environments. Solving the Poisson-Boltzmann equation, we find the potential profiles around the charged core and calculate the energy. Our results are analytical in the Debye-Hückel limit and numerical otherwise. From the Gibbs free energy curve vs. nucleus size, we find the metastable and stable states and the energy barrier between them, for varying saturation values, core's charge, and amount of salt. The nucleation barrier decreases with increasing core charge or Debye length. We calculate the phase lines in the phase diagram of supersaturation and core charge. We find regions of one phase, electro-prewetting, spontaneous nucleation, ion-induced nucleation, and classical-like nucleation., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

We look at the influence of external fields on systems described by generic free energy functional of the order parameter. The external force may have arbitrary spatial dependence, and the order parameter coupling may be nonlinear. The treatment generalizes seemingly disparate works, such as pure fluids, liquid and polymer mixtures, lipid monolayers, and colloidal suspensions in electric fields, fluids, and nematics in gravity, solutions in an ultracentrifuge, and liquid mixtures in laser radiation. The phase lines and thermodynamic behavior are calculated at the mean-field level. We find a "surface" critical point that can be shifted to higher or lower temperatures than the bulk critical point. Below this point, the transition from a "gas" phase to a "liquid" phase is first-order, while above it, the transition is second-order. The second-order line is affected by the spatial dependence of the force, while the first-order line is universal. Moreover, the susceptibility may diverge at a finite location r. Several analytical expressions are given in the limit where a Landau expansion of the free energy is valid.

During the COVID-19 pandemic authorities have been striving to obtain reliable predictions for the spreading dynamics of the disease. We recently developed a multi-"sub-populations" (multi-compartments: susceptible, exposed, pre-symptomatic, infectious, recovered) model, that accounts for the spatial in-homogeneous spreading of the infection and shown, for a variety of examples, how the epidemic curves are highly sensitive to location of epicenters, non-uniform population density, and local restrictions. In the present work we test our model against real-life data from South Carolina during the period May 22 to July 22 (2020). During this period, minimal restrictions have been employed, which allowed us to assume that the local basic reproduction number is constant in time. We account for the non-uniform population density in South Carolina using data from NASA's Socioeconomic Data and Applications Center (SEDAC), and predict the evolution of infection heat-maps during the studied period. Comparing the predicted heat-maps with those observed, we find high qualitative resemblance. Moreover, the Pearson's correlation coefficient is relatively high thus validating our model against real-world data. We conclude that the model accounts for the major effects controlling spatial in-homogeneous spreading of the disease. Inclusion of additional sub-populations (compartments), in the spirit of several recently developed models for COVID-19, can be easily performed within our mathematical framework., Competing Interests: The authors have declared that no competing interests exist.

We theoretically investigate the nucleation of liquid droplets from vapor in the presence of a charged spherical particle. Due to field gradients, sufficiently close to the critical point of the vapor-gas system, the charge destabilizes the vapor phase and initiates a phase transition. The fluid's free energy is described by the van der Waals expression augmented by electrostatic energy and a square-gradient term. We calculate the equilibrium density profile at arbitrary temperatures, particle charges, and vapor densities. In contrast to classical nucleation theory, here, both liquid and vapor phases are different from the bulk phases because they are spatially nonuniform. In addition, the theory applies to both sharp and diffuse interfaces and calculates the surface tension self-consistently. We find the composition profiles and integrate them to get the adsorption near the particle. We find that the adsorption changes discontinuously at a first-order phase transition line. This line becomes a second-order phase transition at high enough temperatures. We describe the transition point numerically and provide approximate analytical expressions for it. Similarly to prewetting, the adsorption diverges at the binodal phase boundary. We construct a phase diagram indicating changes in the binodal, spinodal, and critical temperature. It is shown that the field gradient enlarges the range of temperature and vapor density where liquid can nucleate.

We look at the wetting of a pure fluid in contact with a charged flat surface. In the bulk, the fluid is a classical van der Waals fluid containing dissociated ions. The presence of wall and ions leads to strong dielectrophoretic and electrophoretic forces that increase the fluid's density at the wall. We calculate the fluid's profiles analytically and numerically and obtain the energy integrals. The critical surface potential for prewetting is obtained. In the phase diagrams, the line of first-order transition meets a second-order transition line at a critical point whose temperature can be higher or lower than the bulk critical temperature. The results are relevant to droplet nucleation around charged particles in the atmosphere and could possibly explain deviations from expected nucleation rates.

We suggest a novel mathematical framework for the in-homogeneous spatial spreading of an infectious disease in human population, with particular attention to COVID-19. Common epidemiological models, e.g., the well-known susceptible-exposed-infectious-recovered (SEIR) model, implicitly assume uniform (random) encounters between the infectious and susceptible sub-populations, resulting in homogeneous spatial distributions. However, in human population, especially under different levels of mobility restrictions, this assumption is likely to fail. Splitting the geographic region under study into areal nodes, and assuming infection kinetics within nodes and between nearest-neighbor nodes, we arrive into a continuous, "reaction-diffusion", spatial model. To account for COVID-19, the model includes five different sub-populations, in which the infectious sub-population is split into pre-symptomatic and symptomatic. Our model accounts for the spreading evolution of infectious population domains from initial epicenters, leading to different regimes of sub-exponential (e.g., power-law) growth. Importantly, we also account for the variable geographic density of the population, that can strongly enhance or suppress infection spreading. For instance, we show how weakly infected regions surrounding a densely populated area can cause rapid migration of the infection towards the populated area. Predicted infection "heat-maps" show remarkable similarity to publicly available heat-maps, e.g., from South Carolina. We further demonstrate how localized lockdown/quarantine conditions can slow down the spreading of disease from epicenters. Application of our model in different countries can provide a useful predictive tool for the authorities, in particular, for planning strong lockdown measures in localized areas-such as those underway in a few countries., Competing Interests: The authors have declared that no competing interests exist.

We examine the ordering of the Lower Consolute Solution Temperatures (LCSTs) for a set of dimethylpyridines. Density functional theory (DFT) is used. The equilibrium geometries and binding energies of dimers, each comprised of a pair of dimethylpyridines in a sandwich conformation and one H 2 O molecule at a pivotal site between the nitrogens (the 2:1 dimer), are calculated. It was shown previously that dimer formation in the water-rich zone of the phase diagram has a crucial role in dimethylpyridine demixing. In the resulting dimer diffusion, large hydrophobic clusters of mostly organic content, which expel water and promote phase separation, are assembled. In this description, phase separation requires the formation of 2:1 dimers, but it is the cleavage of hydrogen bonds of the neighboring H 2 O molecules, which stimulates the diffusion and the subsequent separation dynamics at the LCST. In the present study, we investigate this model and calculate the interaction strength of the external hydrogen bonds. This is obtained as the difference in electronic energy between the 2:1 dimer and the dimer augmented by one or two H 2 O molecules. The results are compared to the known LCST hierarchy in five dimethylpyridines (DMP): 2,6-DMP > 2,4-DMP > 2,5-DMP > 3,4-DMP > 3,5-DMP. The complexes are derived using high level Kohn-Sham DFT including dispersion terms. The hydrophobic-hydrophilic properties are accounted for by the solvation model, employed for the mixed medium of 60%-water and 40%-organic content. This is simulated by combination of model descriptors of water and DMP in the parameterization scheme of the polarizable continuum model. The calculation results agree with the experimental evidence.

We use a modified Poisson-Boltzmann formalism to examine immiscible electrolytes containing dissolved antagonistic ions with arbitrary preferential solubilities. We solve the nonlinear equation and obtain an analytical expression for the potential profile, ion densities, and surface tension. Our model takes into account the dependence of the Debye lengths in the two liquids on the preferential solvation. In the limit of point-like ions, the surface tension scales with the average ion density n0 as the classical n01/2 power law. At larger densities ion crowding at the interface leads to a crossover to smaller exponents. The dependence of the surface tension on the Gibbs transfer energy is non-monotonic and exhibits a maximum or a minimum. We further look at a liquid bilayer confined in a parallel-plate capacitor and subject to an external potential. The ion distribution depends on whether the external potential has the same or opposite sign as the Donnan potential. Lastly, we calculate the surface tension of a liquid-liquid interface that has a sinusoidal height modulation and find that surface modulations increase the energy.

We examine the translation and rotation of an uncharged spheroidal colloid in polar solvents (water) near a charged flat surface. We solve the nonlinear Poisson-Boltzmann equation outside of the colloid in two dimensions for all tilt angles θ with respect to the surface normal. The colloid's size is assumed to be comparable to the Debye's length and hence field gradients are essential. The Maxwell stress tensor, including the ideal gas pressure of ions, is integrated over the colloid's surface to give the total force and torque on the colloid. From the torque we calculate the effective angular potential U eff (θ). The classical behavior where the colloid tends to align in the direction perpendicular to the surface (parallel to the field, θ=0) is retrieved at large colloid-surface distances or small surface potentials. We find a surprising transition whereby at small separations or large potentials the colloid aligns parallel to the surface (θ=90°). Moreover, this colloid orientation is amplified at a finite value of the aspect ratio. This transition may have important consequences to flow of colloidal suspensions or as a tool to switch layering of such suspensions near a surface., (Copyright © 2019 Elsevier Inc. All rights reserved.)

We investigate theoretically the kinetics of chemical reactions in polar solvents in the vicinity of charged porous membranes. When the pore charge (or potential) exceeds a critical value, the pores undergo a filling transition that can be first or second order depending on the ambient temperature, mixture composition, and other parameters. This filling transition leads to a dramatic acceleration or slowing down of the reaction. Such control of reaction kinetics by an external potential may be useful in applications where catalysts are absent or when fast spatiotemporal response is required.

Phase separation in substituted pyridines in water is usually described as an interplay between temperature-driven breakage of hydrogen bonds and the associating interaction of the van der Waals force. In previous quantum-chemical studies, the strength of hydrogen bonding between one water and one pyridine molecules (the 1:1 complex) was assigned a pivotal role. It was accepted that the disassembly of the 1:1 complex at a critical temperature leads to phase separation and formation of the miscibility gap. Yet, for over two decades, notable empirical data and theoretical arguments were presented against that view, thus revealing the need in a revised quantum-mechanical description. In the present study, pyridine-water and 2,6-dimethylpyridine-water systems at different complexation stages are calculated using high level Kohn-Sham theory. The hydrophobic-hydrophilic properties are accounted for by the polarizable continuum solvation model. Inclusion of solvation in free energy of formation calculations reveals that 1:1 complexes are abundant in the organically rich solvents but higher level oligomers (i.e., 2:1 dimers with two pyridines and one water molecule) are the only feasible stable products in the more polar media. At the critical temperature, the dissolution of the external hydrogen bonds between the 2:1 dimer and the surrounding water molecules induces the demixing process. The 1:1 complex acts as a precursor in the formation of the dimers but is not directly involved in the demixing mechanism. The existence of the miscibility gap in one pyridine-water system and the lack of it in another is explained by the ability of the former to maintain stable dimerization. Free energy of formation of several reaction paths producing the 2:1 dimers is calculated and critically analyzed.

When immiscible liquids are subject to electric fields interfacial forces arise due to a difference in the permittivity or the conductance of the liquids, and these forces lead to shape change in droplets or to interfacial instabilities. In this topical review we discuss recent advances in the theory and experiments of liquids in electric fields with an emphasis on liquids which are initially miscible and demix under the influence of an external field. In purely dielectric liquids demixing occurs if the electrode geometry leads to sufficiently large field gradients. In polar liquids field gradients are prevalent due to screening by dissociated ions irrespective of the electrode geometry. We examine the conditions for these 'electro prewetting' transitions and highlight few possible systems where they might be important, such as in stabilization of colloids and in gating of pores in membranes.

We examine theoretically a new idea for spatial and temporal control of chemical reactions. When chemical reactions take place in a mixture of solvents, an external electric field can alter the local mixture composition, thereby accelerating or decelerating the rate of reaction. The spatial distribution of electric field strength can be non-trivial and depends on the arrangement of the electrodes producing it. In the absence of electric field, the mixture is homogeneous and the reaction takes place uniformly in the reactor volume. When an electric field is applied, the solvents separate and the reactants are concentrated in the same phase or separate to different phases, depending on their relative miscibility in the solvents, and this can have a large effect on the kinetics of the reaction. This method could provide an alternative way to control runaway reactions and to increase the reaction rate without using catalysts.

We investigate the dynamics of liquid-liquid phase separation confined in a charged concentric cylindrical geometry. Two main time scales characterize the non-equilibrium interface behavior: (1) the lag time t(L) for forming an interface, and (2) the relaxation time to equilibrium. We find that t(L) increases as parameters (temperature, bulk composition, and surface charge) approach the electrostatic spinodal line in the phase diagram. Close to this line, t(L) is proportional to a renormalized bulk concentration with an exponent of -1.16 ± 0.03. The relaxation of the interface to equilibrium can be divided into three phases: early, intermediate (power-law), and late (exponential). During power-law relaxation, the location of the rescaled interface is proportional to time with an exponent of -0.94 ± 0.04. Exponential relaxation occurs as a consequence of finite-size effects, and the associated time constant decreases with decreasing system size (with a power-law scaling), decreasing concentration, and increasing surface charge. The time constant also decreases with increasing (decreasing) temperature when the concentration is below (above) the critical concentration.

We study the shift in the critical temperature T(c) in binary mixtures in strong electric fields. In experiments we measure the nonlinear dielectric effect (NDE) in a mixture of nitrobenze and n-octane and calculate Piekara's factor. We find that the critical anomaly of Piekara's factor is a function of an electric field strength. We propose to explain this observation as a result of a downward shift of T(c), and this allows us to calculate (∂T(c)/∂E(2)) = (-22 ± 10) × 10(-16) (K m(2))/V(2). In the theoretical part we amend Landau and Lifshitz's formula and show that the downward shift of Tc can be estimated from a simple mean-field theory taking into account the linear and quadratic terms in an expansion of the constitutive relation ε(x) between the electric constant ε and mixture composition x.

Spatially non-uniform electric fields can phase separate initially homogeneous mixtures of liquids. Here, we investigate the dynamics of phase separation using a modified Cahn-Hilliard equation and find three kinetically distinct regimes in the phase diagram: (1) discontinuous and (2) continuous interface formation kinetics and (3) a metastable state. By considering all possible solutions of the free energy density, we are able to map the time behavior in the vicinity of the interface as a series of equilibrium interfaces "moving" in the parameter space of the equilibrium phase diagram. The kinetic phase diagram, consequently, contains an "emergence line" that delineates the experimental conditions where a non-equilibrium interface can be forbidden from forming close to a charged surface. When the interface can form on the charged surface, an abrupt transition occurs that produces electrical signatures which distinguish the discontinuous from the continuous transition region. The third kinetic regime describes non-spontaneous phase separation and potential metastable states, and is bounded by the "electrostatic spinodal" line. The equivalent kinetic regimes exist in closed systems and can be found by considering an effective concentration in an open system.

We present a mechanism for the stabilization of colloids in liquid mixtures without use of surfactants or polymers. When a suitable salt is added to a solvent mixture, the coupling of the colloid's surface chemistry and the preferential solvation of ions leads to a repulsive force between colloids that can overcome van der Waals attraction. This repulsive force is substantial in a large range of temperatures, mixture composition, and salt concentrations. The increased repulsion due to addition of salt occurs even for charged colloids. This mechanism may be useful in experimental situations where steric stabilization with surfactants or polymers is undesired.

We deduce the mixing-demixing phase diagram for binary liquid mixtures in an electric field for various electrode geometries and arbitrary constitutive relation for the dielectric constant. By focusing on the behavior of the liquid-liquid interface, we produce simple analytic expressions for the dependence of the interface location on experimental parameters. We also show that the phase diagram contains regions where liquid separation cannot occur under any applied field. The analytic expression for the boundary "electrostatic binodal" line reveals that the regions' size and shape depend strongly on the dielectric relation between the liquids. Moreover, we predict the existence of an "electrostatic spinodal" line that identifies conditions where the liquids are in a metastable state. We finally construct the phase diagram for closed systems by mapping solutions onto those of an open system via an effective liquid composition. For closed systems at a fixed temperature and mixture composition, liquid separation occurs in a finite "window" of surface potential (or charge density). Higher potentials or charge densities counterintuitively destroy the interface, leading to liquid mixing. These results give valuable guides for experiments by providing easily testable predictions for how liquids behave in nonuniform electric fields.

We investigate the structure and phase behavior of the Stockmayer fluid in the presence of nonuniform electric fields using molecular simulation. We find that an initially homogeneous vapor phase undergoes a local phase separation in a nonuniform field due to the combined effect of the field gradient and the fluid vapor-liquid equilibrium. This results in a high-density fluid condensing in the strong field region. The system polarization exhibits a strong field dependence due to the fluid condensation.

We calculate the interaction potential between two charged colloids immersed in an aqueous mixture containing salt near or above the critical temperature. We find an attractive interaction far from the coexistence curve due to the combination of preferential solvent adsorption at the colloids' surface and preferential ion solvation. We show that the ion-specific interaction strongly depends on the amount of salt added as well as on the mixture composition. The calculations are in good agreement with recent experiments. For a highly antagonistic salt of hydrophilic anions and hydrophobic cations, a repulsive interaction at an intermediate inter-colloid distance is predicted even though both the electrostatic and adsorption forces alone are attractive.

We investigate the vapor-liquid coexistence of polar and nonpolar fluids in the presence of a nonuniform electric field. We find that a large enough electric field can nucleate a gas bubble from the liquid phase or a liquid droplet from the vapor phase. The surface tension of the vapor-liquid interface is determined within squared-gradient theory. When the surface potential (charge) is controlled, the surface tension increases (decreases) compared to the zero-field interface. The effect of the electric field on the fluid phase diagram depends strongly on the constitutive relation for the dielectric constant. Finally, we show that gas bubbles can be nucleated far from the bounding surfaces.

We consider the effect of mobile ions on the applied potential needed to reorient a lamellar system of two different materials placed between two planar electrodes. The reorientation occurs from a configuration parallel to the electrodes favored by surface interactions to an orientation perpendicular to the electrodes favored by the electric field. The system consists of alternating A and B layers with different dielectric constants. The mobile ions are assumed to be insoluble in the B layers and hence confined to the A layers. We find that the ions reduce the needed voltage most strongly when they are constrained such that each A lamella is electrically neutral. In this case, a macroscopic separation of charge and its concomitant lowering of free energy, is attained only in the perpendicular orientation. When the ions are free to move between different A layers, such that charge neutrality is only required globally, their effect is smaller and depends upon the preferred surface interaction of the two materials. Under some conditions, the addition of ions can actually stabilize the parallel configuration. Our predictions are relevant to recent experiments conducted on lamellar phases of diblock copolymer films with ionic selective impurities.

We consider the influence of electric field gradients on the phase behavior of nonpolar binary mixtures. Small fields give rise to smooth composition profiles, whereas large enough fields lead to a phase-separation transition. The critical field for demixing as well as the equilibrium phase-separation interface are given as a function of the various system parameters. We show how the phase diagram in the temperature-composition plane is affected by electric fields, assuming a linear or nonlinear constitutive relations for the dielectric constant. Finally, we discuss the unusual case where the interface appears far from any bounding surface.

We study the thermodynamic behavior of nonpolar liquid mixtures in the vicinity of curved charged objects, such as electrodes or charged colloids. There is a critical value of charge (or potential), above which a phase-separation transition occurs, and the interface between high- and low-dielectric constant components becomes sharp. Analytical and numerical composition profiles are given, and the equilibrium front location as a function of charge or voltage is found. We further employ a simple Cahn-Hilliard type equation to study the dynamics of phase separation in spatially nonuniform electric fields. We find an exponential temporal relaxation of the demixing front location. We give the dependence of the steady-state location and characteristic time on the charge, mixture composition and ambient temperature.

We calculate the meniscus location in tapered capillaries under the influence of pressure difference and dielectrophoretic forces with and without gravity. We find that the meniscus location can be a discontinuous function of the pressure difference or the applied voltage and that the meniscus can "jump" to one end or another of the capillary. Phase diagrams are given as a function of the pressure and voltage, depending on the geometrical parameters of the system. We further consider a revision of the dielectric rise under dielectrophoretic force in wedge capillaries and in the case of electrowetting, where the dielectrophoretic force is a small perturbation. Finally, we also find discontinuous liquid-gas interface location in the case of liquid penetration into closed volumes.

When a liquid mixture is subjected to external electric fields, ionic screening leads to field gradients. We point out that, if the mixture is initially in the homogeneous phase, this screening can bring about a robust phase-separation transition with two main features: (i) the phase separation is expected to occur in any electrode geometry, and (ii) the voltage required is typically of the order of 1 V and even less. We discuss several applications of the effect relevant to the field of microfluidics, focusing on the creation of a nanometer-scale lubrication layer in the phase separation process and the modification of the slip length.

We consider theoretically liquid rise against gravity in capillaries with height-dependent cross-sections. For a conical capillary made from a hydrophobic surface and dipped in a liquid reservoir, the equilibrium liquid height depends on the cone-opening angle alpha, the Young-Dupré contact angle theta, the cone radius at the reservoir's level R(0), and the capillary length kappa(-)(1). As alpha is increased from zero, the meniscus' position changes continuously until, when alpha attains a critical value, the meniscus jumps to the bottom of the capillary. For hydrophilic surfaces the meniscus jumps to the top. The same liquid height discontinuity can be achieved with electrowetting with no mechanical motion. Essentially the same behavior is found for two tilted surfaces. We further consider capillaries with periodic radius modulations and find that there are few competing minima for the meniscus location. A transition from one to another can be performed by the use of electrowetting. Finite pressure difference between the two sides of the liquids can be incorporated as well, resulting in complicated phase-diagrams in the alpha-theta plane. The phenomenon discussed here may find uses in microfluidic applications requiring the transport small amounts of water "quanta" (volume < 1 nL) in a regular fashion.

We point out that a spatially varying electric field can be used to cancel the effect of gravity in liquid mixtures by coupling to the different components' permittivities. Cancellation occurs if the system under consideration is small enough. For a simple "wedge" electrode geometry we show that the required system size and voltage are practical, and easily realizable in the laboratory. Thus this setup might be a simple alternative to other options such as the space shuttle, drop-tower, or magnetic levitation experiments.

Phase separation in liquid mixtures is mainly controlled by temperature and pressure, but can also be influenced by gravitational, magnetic or electric fields. However, the weak coupling between such fields and concentration fluctuations limits this effect to extreme conditions. For example, mixing induced by uniform electric fields is detectable only at temperatures that are within a few hundredths of degree or less of the phase transition temperature of the system being studied. Here we predict and demonstrate that electric fields can control the phase separation behaviour of mixtures of simple liquids under more practical conditions, provided that the fields are non-uniform. By applying a voltage of 100 V across unevenly spaced electrodes about 50 micro m apart, we can reversibly induce the demixing of paraffin and silicone oil at 1 K above the phase transition temperature of the mixture; when the field gradients are turned off, the mixture becomes homogeneous again. This direct control over phase separation behaviour depends on field intensity, with the electrode geometry determining the length-scale of the effect. We expect that this phenomenon will find a number of nanotechnological applications, particularly as it benefits from field gradients near small conducting objects.