Effect of Ionic Strength of Dispersed Phase on Ostwald Ripening in Water-in-Oil Emulsions

Water-in-oil emulsions with a low electrolyte content in the internal phase are unstable with respect to Ostwald ripening. The main components of the total pressure acting on the surface of internal phase droplets are considered. The equilibrium values of the diameters of dispersed phase droplets are calculated. The dependences of the difference in the osmotic and Laplace pressures on the droplet size and electrolyte concentration in the droplets are obtained. It is shown that, at the electrolyte concentration below the critical value, the number of droplets in emulsion decreases. If the concentration is above the critical value, water diffuses from small to large droplets, but their number remains unchanged. The change in NaCl concentration in the droplets of internal phase of polydisperse emulsion during the Ostwald ripening is calculated. The results of calculations correlate with the experimental data on the stability of emulsions with respect to coalescence and sedimentation.     

Thermodynamics of Nucleation on the Particles of Salts-Strong Electrolytes: The Allowance for Ion Adsorption in the Droplet Surface Layer

The contributions dependent on ionic specificity (including those related to the differences in polarizabilities of cations and anions) to the surface tension and ion adsorption on the boundary between an aqueous strong electrolyte solution and the vapor-gas phase are taken into account. The role of these contributions in the thermodynamics of vapor condensation on salt particles completely dissolved in droplets that are emerged on these particles from the vapor is studied. Consistent domains of the applicability of the analytical theory suggesting the complete dissolution of a salt particle and the dissociation of substance comprising this particle into ions, as well as the ideal behavior of solution in a droplet and the linearization with respect to excess electric potentials near the droplet surface, are established in the approximation of a quasi-planar interface. Formulas are derived for the threshold values of the chemical potential of vapor molecules upon the barrierless condensation and for critical vapor supersaturations upon the barrier condensation on salt particles. In the explicit form, these formulas express the dependence of these values on the initial size of salt particles, physicochemical parameters of solution in droplets, and the charge of formed ions. Calculations for water condensation on NaCl, Na₂SO₄, and MgCl₂ particles are performed using these formulas.     

Master curves for elastic and plastic properties of highly concentrated emulsions

Critical comparison of dependences of elastic and plastic properties of highly concentrated emulsions (so-called “compressed” emulsions) on the concentration and droplet sizes is performed. The studied emulsions of water-in-oil type are so-called “liquid explosives.” They are characterized by different mean sizes and different droplet size distributions of the dispersed phase. Different average values (D _av, D ₃₂, and D ₄₃) are used as characteristics of droplet sizes. Experiments are carried out with emulsions of two concentrations. Aqueous phase (dispersed droplets) is presented by supercooled solutions of inorganic salt in water in a metastable state. The concentration limit of the existence of highly concentrated emulsions is determined by the condition of the closest packing of liquid droplets, which lies in the φ* = 0.77–0.80 range. In addition, there is a limiting value of the maximal size of droplets. This limiting value depends on the concentration and meets the requirement that droplets should be small enough for the solution to exist in a supercooled state. The elastic modulus and the yield stress of emulsions studied are proportional to the square of the reciprocal linear size of droplets, which contradicts some theoretical models, according to which these parameter should be proportional to the reciprocal size of droplets. Using the obtained experimental data, we constructed generalized dependences of the elastic modulus and the yield stress on the concentration and size of droplets. These characteristics are in good agreement with the experimental data.     

Dependence of the critical temperature on molecular parameters

At the critical temperature the surface tension between coexisting liquid and vapor phases must be zero, and the repulsive contributions associated with cavity formation must exactly counterbalance those from interactions of a molecule in the cavity and the bulk. An expression for the critical temperature of pure fluids in terms of the parameters of scaled particle theory (SPT) has been obtained, and the calculated critical temperatures are compared with experimental data for a range of pure fluids. These include noble and diatomic gases, short and medium length hydrocarbons, aromatic compounds, halogenated compounds, oxygen-containing compounds, and water. Considering the simplicity of this approach, a remarkably good correlation between calculated and experimental values is found for most of these fluids.     

Wetting phenomena on micro-grooved aluminum surfaces and modeling of the critical droplet size

The behavior of water droplets on aluminum surfaces with parallel grooves tens of microns in width and depth is considered, and a mechanistic model is developed for predicting the critical droplet size-droplets at incipient sliding due to gravity. The critical droplet size is nearly 50% smaller on micro-grooved surfaces than on the same surface without micro-grooves. The application of existing models fails to predict this behavior, and a new model based on empiricism is developed. The new model provides reasonable predictions of the critical droplet size for a given inclination angle, advancing contact angle, and maximum contact angle. When the grooves are aligned parallel to gravity, the maximum apparent contact angle does not occur at the advancing front but rather along the side of the droplet because of contact-line pinning. Droplets on these surfaces are elongated and possess a parallel-sided base contour shape. Novel data are provided for droplets in a Wenzel state, a Cassie-Baxter state, and combined state on micro-grooved surfaces, and the ability of the empirical model to handle these variations is explored. These findings may be important to a broad range of engineering applications.     

Comparison of deconvoluted plasma DSC curves on patients with solid tumors

Melting of crystalline compounds inside the nanopores of open-morphology porous systems was studied on a model system, consisted of 1-octadecene and silica gels with different pore sizes, by means of thermogravimetry, differential scanning calorimetry and powder X-ray diffraction. The parameters of silica gels porous structure (surface area, pore size and volume) were calculated using N₂ adsorption data. To describe the experimental results, a new thermodynamic model of crystallites melting inside the nanopores of irregular shape was established. This model allows an analytical prediction for the shift of phase transition temperature and melting enthalpy (latent heat of melting) due to the surface tension effects. To a first approximation, both parameters must linearly depend on the specific ratio of the total surface of pores to their total volume, and experimental studies have mostly confirmed this result for the melting of 1-octadecene confined inside the pores of a wide range of various silicas (with the pores of different sizes and geometry).

     

Displacement of liquid droplets on a surface by a shearing air flow

The motion of droplets on surfaces is crucial to the performance of a wide range of processes; this study examines the initiation of droplet motion through a shearing mechanism generated here by a controlled air flow. Systematic experiments are carried out for a range of fluids and well defined surfaces. A model is postulated that balances surface tension forces at the contact line and the drag force due to the air motion. Experiments reveal that the critical velocity at which droplet motion is initiated depends on the contact angle and the droplet size. Visualizations highlight three modes of motion: (I) the droplet retains a footprint similar to that at the point of motion; (II) a tail exists at the rear of the droplet; (III) a trail remains behind the droplet (that can shed smaller droplets). The predictions of droplet initiation velocity are good for type I motion, in accordance with the assumptions inherent within the model. This model confirms the dominant physics associated with the initiation of droplet motion and provides a useful predictive expression.     

New development in processing pendant droplet tensiometry data

A database linking the dimensionless volume of pendant droplets Vpen and the dimensionless volume of the spherical caps at the apex of the droplets Vcap has been constructed from the governing equations of pendant droplet tensiometry. The Bond number Bo that relates surface tension to gravitational body force appears as an independent parameter in this database. Computing Vpen and Vcap from the measured profile of a droplet and making use of the database allow the prevailing Bo to be determined and surface tension to be calculated. This new way of converting measured profiles into surface tension has a number of advantages, such as reliability and simplicity, compared to existing methods. These are demonstrated by applying the new method to a number of measured profile data taken from the literature.     

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.     

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.     

Jetting liquid marbles: study of the Taylor instability in immersed marbles

The behavior of liquid marbles encapsulated with various powders, immersed in oil, and exposed to a uniform DC field was investigated. At some critical value of the electric field, the Taylor instability of the marble shape took place, accompanied by the appearance of a cone and jetting a small droplet. The squared critical electric field was linear dependent on inverse of the size parameter of the marble. In some cases, the extrapolation of this linear dependence to the zero field gave the finite value of the spherical marble radius corresponding to the Rayleigh limit that meant that the marbles were charged. Lycopodium-coated marbles remained neutral under the action of a DC field, as well as a pure water droplet. Therefore, charging marbles is determined by their powder coverage. The data on effective surface tension at marble–oil interfaces were extracted from the above linear dependence for the uncharged marble. The effective surface tension was measured in parallel by the capillary rise method.     

Molecular dynamics study of structural and thermodynamic characteristics of nanodroplets of simple fluid

Equilibrium configurations of Lennard-Jones nanodroplets composed of 10–15000 spherically symmetric molecules placed in the center of a spherical container are studied at constant temperature by the molecular dynamics method. The distribution of local density is found and size dependences of density in the center of droplet, first coordination number, and energy surface tension coinciding for equimolecular dividing surface with specific excess free energy of droplet are studied. Radial distribution function is also determined. It is established that the passage of structural characteristics to their macroscopic values is observed for droplets containing as little as about 300 molecules, while, for energy surface tension, analogous passage for energy surface tension occurs for droplets containing 700–6000 molecules.     

Modeling of interface mobility in the description of flow-induced coalescence in immiscible polymer blends

A new semiempirical equation has been proposed for the rate of approach of highly flattened droplets, applicable in the whole range of the ratios, p, of viscosity of the dispersed droplets and matrix. The equation is utilized to calculate the probability, P _c, that the droplet collision induced by shear or extensional flow is followed by the droplet fusion for systems with Newtonian droplets and Newtonian or viscoelastic matrix. The comparison of the results of these calculations with available experimental data and with the calculation using the trajectory analysis shows that the proposed model of the matrix drainage provides more reasonable results than the broadly applied model of partially mobile interface.     

Detachment of liquid droplets from fibres--experimental and theoretical evaluation of detachment force due to interfacial tension effects

The detachment of barrel-shaped oil droplets from metal, glass and polymer fibres was examined using an atomic force microscope (AFM). The AFM was used to detach the droplets from the fibres while measuring the force-distance relationship. A novel fibre-droplet interfacial tension model was applied to predict the force required to draw the droplet away from its preferential axisymmetric position on the fibre, and also to predict the maximal force required to detach the droplet. The model assumes that the droplet retains a spherical shape during detachment, i.e., that droplet distortion is negligible. This assumption was found to be reasonably accurate for small radius oil droplets (<10 microm), however less accurate for larger droplets (>25 microm). However, it was found that the model produced a good agreement with the maximal detachment force measured experimentally--regardless of droplet size and degree of deformation--even though the model could not predict droplet extension beyond a length of one droplet radius.     

Influence of K24 on the structure of nematic liquid crystal droplets

A phenomenological free energy is used to describe the stable ordering of nematic liquid crystals confined to supramicron spherical cavities. In particular the effects of the saddle splay elastic constant, K₂₄, on the equilibrium structures and phase diagram of droplets with homeotropic surface anchoring are discussed. Some structures are illustrated by the corresponding simulated polarization microscope textures. Possibilities for an experimental determination of the saddle-splay elastic constant and surface anchoring strength by studying the radial-axial structural transition in such droplets are analysed. It is shown that the K₂₄ term in the elastic free energy stabilizes a deformed droplet structure even in the limit of the zero anchoring strength.     

Nucleation theory: Fisher's droplet picture and microscopic surface tension

Fisher's droplet picture is used to define a “microscopic” surface tension for small droplets. The nucleation rate is then calculated. Excellent agreement between experiments and our calculations has been found for H₂O, CH₃OH, C₂H₅OH, NH₃, C₆H₆, CHCl₃ and CCl₃F.     

A study of sulfur homogeneous nucleation from supersaturated vapor. Determination of surface tension of sulfur nanoparticles

Homogeneous nucleation in sulfur vapor is studied in a laminar-flow chamber. Concentration and size distribution of resulting aerosol particles are measured with a diffusion spectrometer of aerosols and a PK.GTA-0,3-002 photoelectric particle counter. The crystal structure of the formed particles is studied by X-ray diffraction analysis. The rate of sulfur evaporation from a boat and the profile of a deposit on the chamber wall along the axial coordinate are determined by gravimetry. Axial and radial temperature profiles are measured using a chromel-alumel thermocouple. The vapor concentration distribution in the chamber is found and the supersaturation is calculated from the solution of the mass-transfer problem. An experimental low-laborious method is developed for the supersaturation cutoff. This method enables one to rapidly deter-mine the position of the zone in which the nucleation proceeds at the highest rate. The position of the zone of nucleation found by this method is in good agreement with the results of calculations based on experimental data and theoretical calculation of the rate of nucleation by an exact formula that has been recently derived based on the works by Kusaka and Reiss, as well as the Frenkel liquid kinetics theory. The surface tension of critical sulfur nuclei resulting from the nucleation is calculated based on this formula and experimental data on the nucleation. It is established that, in a temperature range of 312–319 K, the critical nuclei have tension surface radius R _s ～ 10.6 Å and surface tension σ = 72.5 ± 1.1 dyn/cm. The surface tension of critical sulfur nuclei in this temperature range is constant and approximately 5% higher than that of a planar surface.     

Colloidosomes from the controlled interaction of submicrometer triglyceride droplets and hydrophilic silica nanoparticles

The self-assembly of hydrophilic silica nanoparticles at the surface of charged submicrometer triglyceride droplets has been investigated with the aim to optimize the preparation of stable colloidosomes. The droplet charge, oil phase volume fraction, droplet/nanoparticle ratio, and salt concentration play important roles in controlling nanoparticle interactions and are reflected in the colloidosome zeta potential, size, stability, and interfacial structure (visualized by freeze-fracture SEM). Silica nanoparticle interactions with negatively charged droplets are weak, and partially covered droplets are identified. Positively charged droplets are strongly coated by silica nanoparticles and undergo charge reversal at specific droplet to nanoparticle ratios and electrolyte concentrations. Droplets at volume fractions (varphi) <10 (-4) undergo time-dependent limited coalescence until nanoparticle coverage is complete. For varphi in the range 10 (-4) to 2.5 x 10 (-4) and at certain critical droplet to nanoparticle ratios, droplets undergo neutralization or charge reversal coupled with aggregation and precipitation; this occurs in a time-independent manner. Specific conditions have been identified where stable 1-3 mum colloidosomes can be phase separated from heterocoagulates of droplets and nanoparticles.     

Protein charge-state distributions in electrospray-ionization mass spectrometry do not appear to be limited by the surface tension of the solvent

According to a current model for protein electrospray, the charge-state distributions (CSDs) observed by electrospray-ionization mass spectrometry (ESI-MS) are controlled by the Rayleigh-limit charge of the droplets that generate the gas-phase protein ions. A testable prediction of this model is that the maximum charge state displayed by proteins in ESI-MS should respond to changes in the surface tension of the ESI droplets according to the Rayleigh equation. In this work, we subject this specific hypothesis to direct experimental testing. We show data obtained by time-of-flight (TOF) nano-ESI-MS with several different proteins in aqueous solutions containing 20-50% 1-propanol or 40% 1,2-propylene glycol. Both of these compounds have lower vapor pressure and lower surface tension than water. Propylene glycol also has a lower evaporation rate than water, providing an even more stringent test for surface tension effects in late ESI droplets. None of these cosolvents affects the CSDs of either folded or unfolded proteins as predicted by the Rayleigh-charge model. The only changes induced by 1-propanol can be ascribed to protein unfolding triggered above critical concentrations of the alcohol. Below such a threshold, no shift of the CSDs toward lower charge states is observed. The presence of 40% propylene glycol in the original protein solutions gives rise to CSDs that either are the same as those in the control samples or present much smaller changes than those calculated by the Rayleigh equation. Thus, the charge states of gas-phase protein ions produced by electrospray do not seem to be limited by the surface tension of the solvent. They rather appear to be quite protein-specific.