New approach to the kinetics of heterogeneous unary nucleation on liquid aerosols of a binary solution

The formation of a droplet on a hygroscopic center may occur either in a barrierless way via Kohler activation or via nucleation by overcoming a free energy barrier. Unlike the former, the latter mechanism of this process has been studied very little and only in the framework of the classical nucleation theory based on the capillarity approximation whereby a nucleating droplet behaves like a bulk liquid. In this paper the authors apply another approach to the kinetics of heterogeneous nucleation on liquid binary aerosols, based on a first passage time analysis which avoids the concept of surface tension for tiny droplets involved in nucleation. Liquid aerosols of a binary solution containing a nonvolatile solute are considered. In addition to modeling aerosols formed through the deliquescence of solid soluble particles, the considered aerosols constitute a rough model of "processed" marine aerosols. The theoretical results are illustrated by numerical calculations for the condensation of water vapor on binary aqueous aerosols with nonvolatile nondissociating solute molecules using Lennard-Jones potentials for the molecular interactions.     

Model to describe light scattering by polymer film containing droplets with inhomogeneous anchoring of liquid crystal molecules at the polymer–droplet interface: asymmetry effect in the angular distribution of light

A model to describe light scattering by polymer film containing of monolayer of liquid crystal droplets with inhomogeneous anchoring of liquid crystal molecules at the polymer-droplet interface is developed. It is based on the interference approximation of the wave scattering theory. The director field distribution in the droplet volume is determined by solving the free energy density minimization problem using the relaxation method. The spatial distribution of droplets in the layer is described by the hard disks model. The amplitude scattering matrices of individual droplets are found in the anomalous diffraction approximation. The algorithm for numerical analysis of the characteristics of light scattered in a polymer film containing droplets at homogeneous and inhomogeneous surface anchoring is described in terms of the partial filling factors of the monolayer film. Electrically controllable symmetry breaking effect of angular distribution of light scattered by films containing droplets with inhomogeneous anchoring at the polymer-droplet interface is described and experimentally confirmed.     

Chemistry of Interfaces,M. J. Jaycock and G. D. Parfitt. Halstead Press,John Wiley and Sons,New York, 1981. 279 pp. $90. Paul Becher,Wilmington

A unique physical model is proposed for relating the dimensions and properties of droplets in aqueous diesel fuel invert mlcroemulsions to the measured water vapor pressures over such systems. The model assumes discrete droplets containing surfactant-sheathed liquid cores. A dynamic equilibrium condition is visualized wherein a closed mass transfer cycle e3tists, involving the movement of water molecules from the droplet interior, through the surfactant sheath into the continuous medium and vapor space above the pool. The flat-surface fugacity of the liquid water in the aqueous core would be reduced relative to that of normal water because of Increased intermolecular association stemming from high pressure in the aqueous core caused by surface tension forces. The possible presence of dissolved surfactant constituents would reduce this fugacity even further. The mass transfer cycle is assumed to be completed by the absorption of water vapor into transitory, flat surfaces of reduced fugacity, droplet core water exposed by collapsing droplets at the pool surface. These are assumed to be continually reforming into submerged microemulsion droplets as additional droplets collapse at the pool surface.

Analytical relationships based upon the described model allowed calculation of droplet core and sheath dimensions and droplet external interfacial tension. The efficacy of the proposed model is supported by the congruity of the thus derived values.     

Induced detachment of coalescing droplets on superhydrophobic surfaces

Coalescence of a falling droplet with a stationary sessile droplet on a superhydrophobic surface is investigated by a combined experimental and numerical study. In the experiments, the droplet diameter, the impact velocity, and the distance between the impacting droplets were controlled. The evolution of surface shape during the coalescence of two droplets on the superhydrophobic surface is captured using high speed imaging and compared with numerical results. A two-phase volume of fluid (VOF) method is used to determine the dynamics of droplet coalescence, shape evaluation, and contact line movement. The spread length of two coalesced droplets along their original center is also predicted by the model and compared well with the experimental results. The effect of different parameters such as impact velocity, center to center distance, and droplet size on contact time and restitution coefficient are studied and compared to the experimental results. Finally, the wetting and the self-cleaning properties of superhydrophobic surfaces have been investigated. It has been found that impinging water drops with very small amount of kinetic impact energy were able to thoroughly clean these surfaces.     

Influence of oil polarity on droplet growth in oil-in-water emulsions stabilized by a weakly adsorbing biopolymer or a nonionic surfactant

The influence of oil type (n-hexadecane, 1-decanol, n-decane), droplet composition (hexadecane:decanol), and emulsifier type (Tween 20, gum arabic) on droplet growth in oil-in-water emulsions was studied. Droplet size distributions of emulsions were measured over time (0-120 h) by laser diffraction and ultrasonic spectroscopy. Emulsions containing oil molecules of low polarity and low water solubility (hexadecane) were stable to droplet growth, irrespective of the emulsifier used to stabilize the droplets. Emulsions containing oil molecules of low polarity and relatively high water solubility (decane) were stable to coalescence, but unstable to Ostwald ripening, irrespective of emulsifier. Droplet growth in emulsions containing oil molecules of relatively high polarity and high water solubility (decanol) depended on emulsifier type. Decanol droplets stabilized by Tween 20 were stable to droplet growth in concentrated emulsions but unstable when the emulsions were diluted. Decanol droplets stabilized by gum arabic exhibited rapid and extensive droplet growth, probably due to a combination of Ostwald ripening and coalescence. We proposed that coalescence was caused by the relatively low interfacial tension at the decanol-water boundary, which meant that the gum arabic did not absorb strongly to the droplet surfaces and therefore did not prevent the droplets from coming into close proximity.     

On the closure conjectures for the Gibbsian approximation model of a binary droplet

Within the framework of Gibbsian thermodynamics, a binary droplet is regarded to consist of a uniform interior and dividing surface. The properties of the droplet interior are those of the bulk liquid solution, but the dividing surface is a fictitious phase whose chemical potentials cannot be rigorously determined. The state of the nucleus interior and free energy of nucleus formation can be found without knowing the surface chemical potentials, but the latter are still needed to determine the state of the whole nucleus (including the dividing surface) and develop the kinetics of nucleation. Thus it is necessary to recur to additional conjectures in order to build a complete, thermodynamic, and kinetic theory of nucleation within the framework of the Gibbsian approximation. Here we consider and analyze the problem of closing the Gibbsian approximation droplet model. We identify micro- and Gamma-closure conjectures concerning the surface chemical potentials and excess surface coverages, respectively, for the droplet surface of tension. With these two closure conjectures, the Gibbsian approximation model of a binary droplet becomes complete so that one can determine both the surface and internal characteristics of the whole nucleus and develop the kinetic theory, based on this model. Theoretical results are illustrated by numerical evaluations for binary nucleation in a water-methanol vapor mixture at T=298.15 K. Numerical results show a striking increase in the droplet surface tension with decreasing droplet size at constant overall droplet composition. A comparison of the Gibbsian approximation with density functional calculations for a model surfactant system indicate that the excess surface coverages from the Gibbsian approximation are accurate enough for large droplets and droplets that are not too concentrated with respect to the solute.     

Evaporation of two solution droplets and a droplet located near a flat liquid surface

The mutual influence of two moderate-sized droplets of a dilute nonvolatile substance solution on the processes of their evaporation or condensation is theoretically analyzed under the assumption of a uniform concentration distribution inside the droplets. The conditions for the applicability of this approach are revealed. The evaporation or condensation of a droplet near a flat liquid surface is considered as a limiting case. The fluxes of water molecules to and from the surface of aqueous glycerol solution droplets occurring in air are numerically estimated depending on the droplet radii, distances between their surfaces, and air humidity. Analogous estimates are obtained for an aqueous glycerol solution droplet growing near a flat water surface.     

On the applicability of Young–Laplace equation for nanoscale liquid drops

Debates continue on the applicability of the Young–Laplace equation for droplets, vapor bubbles and gas bubbles in nanoscale. It is more meaningful to find the error range of the Young–Laplace equation in nanoscale instead of making the judgement of its applicability. To do this, for seven liquid argon drops (containing 800, 1000, 1200, 1400, 1600, 1800, or 2000 particles, respectively) at T = 78 K we determined the radius of surface of tension R_s and the corresponding surface tension γ_s by molecular dynamics simulation based on the expressions of R_s and γ_s in terms of the pressure distribution for droplets. Compared with the two-phase pressure difference directly obtained by MD simulation, the results show that the absolute values of relative error of two-phase pressure difference given by the Young–Laplace equation are between 0.0008 and 0.027, and the surface tension of the argon droplet increases with increasing radius of surface of tension, which supports that the Tolman length of Lennard-Jones droplets is positive and that Lennard-Jones vapor bubbles is negative. Besides, the logic error in the deduction of the expressions of the radius and the surface tension of surface of tension, and in terms of the pressure distribution for liquid drops in a certain literature is corrected.     

A study of oil droplet coalescence

Oil droplets dispersed in water can be readily studied when they are coated with surfactants, which lower their interfacial tension and enhance their stability. Pure oil droplets are more difficult to study because of their high interfacial tension, which facilitates coalescence and the adsorption of contaminants. In this study, we have characterised the surface charging properties of a water insoluble oil, bromododecane, which has a density close to water. The small density difference allows us to study relatively large drops of this oil and to analyse its coalescence behaviour. The results obtained with this simple, surfactant-free, system suggest that an additional attractive force, such as the long range hydrophobic interaction, might be required to explain oil droplet coalescence behaviour.     

电喷雾离子源(ESI)中带电液滴的形成与碎裂模拟

基于电喷雾离子源(ESI)中液流的输运行为,构建了相应的物理模型,并利用Fluent软件对电喷雾离子源中带电液滴的形成与裂变过程进行模拟研究.分别考察了毛细管电压、离子源温度和溶液表面张力3个参数对源内液滴粒径分布的影响.模拟结果表明,较大的毛细管电压、较高的离子源温度和较低的表面张力条件下得到的液滴粒径较小,液滴碎裂效果较好.模拟结果与文献报道及经验公式结果一致.     

Line tension effects for liquid droplets on circular surface domains

We study the morphologies of single liquid droplets wetting a substrate in the presence of the line tension of the three-phase contact line. On a homogeneous substrate, the line tension leads to a discontinuous unbinding of the droplet if its volume is decreased below a critical value. For a droplet wetting a structured surface with a circular domain, a line tension contrast gives rise to discontinuous depinning transitions of the contact line from the domain boundary as the droplet volume is varied. We calculate the corresponding free energy bifurcation diagram analytically for axisymmetric droplet shapes. Numerical minimization of the droplet free energy shows that line tension contrasts can stabilize nonaxisymmetric droplet shapes, thus modifying the bifurcation diagram. These latter shapes should be accessible to experiments and can be used to reveal the presence of a line tension contrast.     

Surface tension of different sized single-component droplets,according to macroscopic data obtained using the lattice gas model and the critical droplet size during phase formation

Size dependences of the surface tension of spherical single-component droplets are calculated using equations of the lattice gas model for 19 compounds. Parameters of the model are found from experimental data on the surface tension of these compounds for a macroscopic planar surface. The chosen low-molecular compounds satisfy the law of corresponding states. To improve agreement with the experimental data, Lennard-Jones potential parameters are varied within 10% deviations. The surface tensions of different sized equilibrium droplets are calculated at elevated and lowered temperatures. It is found that the surface tension of droplets grows monotonically as the droplet size increases from zero to its bulk value. The droplet size R ₀ corresponding to zero surface tension corresponds to the critical size of the emergence of a new phase. The critical droplet sizes in the new phase of the considered compounds are estimated for the first time.     

Structure and dynamics of surfaces of thin films and water microdroplets

Systems containing 3456 water molecules in a periodic rectangular cell are studied by molecular dynamics simulation. The cell parameter along the z axis noticeably exceeds parameters along the x and y axes. Thin film with a thickness of about 30 Å is formed in a cell. Some molecules are transferred into the vapor phase; however, due to the periodicity along the z axis, they are poured into periodic images of the simulated layer above or below this layer. The width of the transition surface layer is about 6–7 Å in density upon passage from the liquid to vapor phases is generally related to the roughness of the surface rather than to a decrease in a local density. The self-diffusion coefficient of molecules in the surface layer is greatly larger than inside the film. Noticeable anisotropy in the diffusion motion of molecules in the surface layer is not revealed. As all of the cell parameters increase, the film is transformed into nearly spherical micro-droplet with a strongly roughed surface. The self-diffusion coefficient of surface molecules of microdroplet is also larger than for molecules inside the droplet.     

Evidence of Molecular Fragmentation inside the Charged Droplets Produced by Electrospray Process

The behavior of the analyte molecules inside the neutral core of the charged droplet produced by the electrospray (ES) process is not unambiguously known to date. We have identified interesting molecular transformations of two suitably chosen analytes inside the ES droplets. The highly stable Ni(II) complex of 1,8-dimethyl-1,3,6,8,10,13-hexaazacyclotetradecane (1) that consists of a positive charge at the metal center, and the allyl pendant armed tertiary amine containing macrocycle 3,4,5:12,13,14-dipyridine-2,6,11,15-tetramethyl-1,7,10,16-tetraallyl-1,4,7,10,13,16-hexaazacyclooctadeca-3,13-diene (M _4p ) have been studied by ESI mass spectrometry as the model analytes. We have shown that these two molecules are not representatively transferred from solution to gas phase by ESI; rather, they undergo fragmentation inside the charged droplets. The results indicated that a charged analyte such as 1 was possibly unstable inside the neutral core of the ES droplet and undergoes fragmentation due to the Coulombic repulsion imparted by the surface protons. Brownian motion of the neutral analyte such as M _4p inside the droplet, on the other hand, may lead to proton attachment on interaction with the charged surface causing destabilization that leads to fragmentation of M _4p and release of resonance stabilized allyl cations from the core of the droplet. Detailed solvent dependence and collision-induced dissociation (CID) studies provided compelling evidences that the fragmentation of the analytes indeed occurs inside the charged ES droplets. A viable model of molecular transformations inside the ES droplet was proposed based on these results to rationalize the behavior of the analyte molecules inside the charged ES droplets.     

Statics of polymer droplets on deformable surfaces

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different surface/drop compatibility and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness, and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupre? wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.     

Size-dependent surface tension and Tolman's length of droplets

A model for the size-dependent surface tension gammalv(D) of liquid droplets, free of any adjustable parameter, is presented in terms of the size-dependent surface energy gammasv(D). It is found that gammalv(D) drops monotonically with the size of the droplet in the nanometer region. Modeling predictions agree with computer simulations for sodium, aluminum, and water droplets. Meanwhile, the Tolman's equation is found to be valid for small particles, and the Tolman's length is always positive and becomes longer when the droplet size is decreased.     

Bias in the temperature of helium nanodroplets measured by an embedded rotor

The rovibrational spectra of molecules dissolved in liquid 4He nanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the ripplons of the droplet. This bias grows with both the total angular momentum of the droplet and with the moment of inertia of the solute molecule.     

Relating chromatographic retention and electrophoretic mobility to the ion distribution within electrosprayed droplets

Ions that are observed in a mass spectrum obtained with electrospray mass spectrometry can be assumed to originate preferentially from ions that have a high distribution to the surface of the charged droplets. In this study, a relation between chromatographic retention and electrophoretic mobility to the ion distribution (derived from measured signal intensities in mass spectra and electrospray current) within electrosprayed droplets for a series of tetraalkylammonium ions, ranging from tetramethyl to tetrapentyl, is presented. Chromatographic retention in a reversed-phase system was taken as a measure of the analyte’s surface activity, which was found to have a large influence on the ion distribution within electrosprayed droplets. In addition, different transport mechanisms such as electrophoretic migration and diffusion can influence the surface partitioning coefficient. The viscosity of the solvent system is affected by the methanol content and will influence both diffusion and ion mobility. However, as diffusion and ion mobility are proportional to each other, we have, in this study, chosen to focus on the ion mobility parameter. It was found that the influence of ion mobility relative to surface activity on the droplet surface partitioning of analyte ions decreases with increasing methanol content. This effect is most probably coupled to the decrease in droplet size caused by the decreased surface tension at increasing methanol content. The same observation was made upon increasing the ionic strength of the solvent system, which is also known to give rise to a decreased initial droplet size. The observed effect of ionic strength on the droplet surface partitioning of analyte ions could also be explained by the fact that at higher ionic strength, a larger number of ions are initially closer to the droplet surface and, thus, the contribution of ionic transport from the bulk liquid to the liquid/air surface interface (jet and droplet surface), attributable to migration or diffusion will decrease.     

Key thermodynamic characteristics of nucleation on charged and neutral cores of molecular sizes in terms of the gradient density functional theory

The gradient density functional theory and the Carnahan–Starling model formulated for describing the contribution of hard spheres have been used to calculate the profiles of condensate density in small critical droplets formed via homogeneous nucleation, as well as in stable and critical droplets formed via heterogeneous nucleation on solid charged and neutral condensation cores of molecular sizes. The calculations performed for water and argon at different values of condensate chemical potential have yielded the heights of the activation barriers for homoand heterogeneous nucleation as functions of vapor supersaturation at preset system temperatures. The interaction of condensate molecules with a solid core has been described by the resultant potential of molecular attractive forces. In the case of a charged core, the long-range Coulomb potential of electric forces has additionally been taken into account. Dielectric permittivities have been calculated as known functions of the local density of the fluid and temperature. The radius of the equimolecular droplet surface has been chosen as a variable describing the droplet size. Dependences of the chemical potential of condensate molecules in a droplet on its size have been plotted for water and argon with allowance for the action of capillary, electrostatic, and molecular forces. It has been shown that the role of the molecular force potential in heterogeneous nucleation increases with the size of condensation cores.