Growth and motion of heterogeneous water droplets in laminar flow diffusion chambers

The growth of heterogeneous water droplets containing nanoparticles is studied in two laminar flow diffusion chambers of different designs. It is shown that the efficiency of heterogeneous condensation is, to a substantial extent, governed by the processes of heat and mass transfer inside a chamber condenser. Integral parameter C(R) representing the probability that a nanoparticle with radius R is covered with a condensate film in a laminar flow chamber is calculated. It is established that, in air-water vapor mixtures, the radius of heterogeneous water droplets may amount to several micrometers and efficient condensation begins on spherical nanoparticles when their radii exceed 5 nm.     

Kinetics of the droplet formation at the early and intermediate stages of the spinodal decomposition in homopolymer blends

The kinetics of the droplet formation during the spinodal decomposition (SD) of the homopolymer blends has been studied by numerical integration of the Cahn‐Hilliard‐Cook equation. We have found that the droplet formation and growth occurs when the minority phase volume fraction, f_m , approaches the percolation threshold value, f_thr = 0.3 ± 0.01. The time for the formation of the disperse droplet morphology (coarsening time) depends only on the equilibrium minority phase volume fraction, f_m . f_m approaches its equilibrium value logarithmically at the late SD stages, and, therefore, the coarsening time decreases exponentially as the average volume fraction or the quench depth decrease. Since the temporal evolution of the total interfacial area does not depend on the quench conditions and blend morphology, the average droplet size and the droplet number density is determined by the coarsening time. Within the time scale studied, the droplet number density decreases with time as t ^{–0.63±0.03}; the average mean curvature decreases as t ^{–0.35±0.05}; the average Gaussian curvature decreases as t ^{–0.42±0.03}, and the average droplet compactness ˜V/S^3/2 where S is the surface area and V is the volume) approaches a spherical limit logarithmically with time. The droplets with larger area have lower compactness and in the low compactness limit their area is a parabolic function of compactness. The size and shape distribution functions have been also investigated.     

Stochastic diffusion interactions and coarsening in a system of droplets growing from a supersaturated gas mixture

In this work we study diffusion interactions among liquid droplets growing in stochastic population by condensation from supersaturated binary gas mixture. During the postnucleation transient regime collective growth of liquid droplets competing for the available water vapor decreases local supersaturation leading to the increase of critical radius and the onset of coarsening process. In coarsening regime the growth of larger droplets is prevailing noticeably broadening the droplet size-distribution function when the condensation process becomes more intensive than the supersaturation yield. Modifications in the kinetic equation are discussed and formulated for a stochastic population of liquid droplets when diffusional interactions among droplets become noteworthy. The kinetic equation for the droplet size-distribution function is solved together with field equations for the mass fraction of disperse liquid phase, mass fraction of water vapor component of moist air, and temperature during diffusion-dominated regime of droplet coarsening. The droplet size and mass distributions are found as functions of the liquid volume fraction, showing considerable broadening of droplet spectra. It is demonstrated that the effect of latent heat of condensation considerably changes coarsening process. The coarsening rate constant, the droplet density (number of droplets per unit volume), the screening length, the mean droplet size, and mass are determined as functions of the temperature, pressure, and liquid volume fraction.     

Director configurations in nematic droplets with tilted surface anchoring

The polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength W_s ~ 10^–6 (J m^?2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.     

Comparative study of monomer droplet nucleation in the seeded batch and semibatch miniemulsion polymerisation of styrene

Monomer droplet nucleation in the seeded miniemulsion polymerisation of styrene under monomer-flooded and monomer-starved conditions was studied. The miniemulsion feeds were added to the reactor either batchwise or semibatchwise. The droplets preserved longer under flooded conditions. As a result, the batch operation led to a larger number of particles (N_p) than the semibatch operation. For the miniemulsion droplets containing predissolved polymer, the final N_p was independent of the way that the feed was added to the reactor and was equivalent to the number of monomer droplets in the original miniemulsion feed. The size distribution of the final latexes, however, was influenced by the operation type. For the batch operation, the rate of polymerisation (R_p) with the miniemulsion feeds was higher than that with the conventional monomer emulsion feed because of the monomer droplet nucleation. But for the semibatch operation, the opposite was true because of R_p controlled by the rate of monomer diffusion from rather stable miniemulsion droplets to the growing polymer particles.     

Behavior of evaporating droplets at nonsoluble and soluble surfaces: Modeling with molecular resolution

Liquid droplets in equilibrium with vapor are simulated at solidlike surfaces using the cooperative motion algorithm (CMA). These droplets behave like real droplets, i.e., the densities of the coexistent liquid and vapor phases obey empirical relations such as rho l - rho v proportional, variant (1 - T/Tc)(1/3). Droplet evaporation was studied under various interaction conditions, i.e., nonsoluble and soluble substrates. In the last case, substrate particles migrate toward the liquid-vapor interface to minimize the droplet surface energy. This leads to the formation of a microwell surrounded by a ringlike deposit on the substrate surface. It is shown that the ring formation in the first stages of evaporation results in pinning of the droplet contact area.     

Kinetics of water sorption on a CaCl2-in-silica-gel-pores sorbent: The effects of the pellet size and temperature

Kinetics of water vapor sorption on the CaCl₂-in-KSK-pores composite (SWS-1L) have been studied at T = 33–69°C and vapor pressures of 8–70 mbar for pellet sizes of 2R _pel = 0.355–0.425, 0.71–0.85, and 1.2–1.4 mm. Sorption has been measured under isothermal conditions on a thermobalance by abruptly raising the vapor pressure in the measurement cell by a small value and then maintaining the new pressure. In the initial portion of the kinetic curves, the amount of sorbed water (Δm) increases in proportion to the sorption time (t) to the power 1/2. From the slope of the Δm versus t ^1/2 curve, it is possible to derive the sorption rate constant k _D = D _eff/R ² _pel and the effective diffusivity D _eff. The latter is independent of R _pel for 2R _pel ≥ 0.71 mm. The rate of water sorption on smaller (0.355-to 0.425-mm) pellets grows less rapidly, apparently because of the effect of the heat of sorption. The effective diffusivity is determined by the local slope of the water vapor sorption isotherm for SWS-1L. Applying an appropriate correction enables one to calculate the effective diffusivity for water vapor in the sorbent pores, which appears to be D _e = (0.35 ± 0.17) × 10^?6 m²/s. This value is approximately 10 times smaller than the Knudsen water diffusion coefficient calculated for a single cylindrical pore with a size equal to the average pore size of the composite. Two possible causes of this discrepancy are discussed, specifically, an increase in the pore tortuosity because of the presence of the salt and the interaction between water and the salt.     

Postnucleation droplet growth in supersaturated gas with arbitrary vapor concentration

This work concerns the reexamination and extension of the current theory of phase transition dynamics for liquid droplets growing on soluble aerosols from a supersaturated gas mixture for the general case of arbitrary value of vapor concentration. We found that the inconsistency in the common treatment of the vapor diffusion, due to an implicit assumption of the constancy of gas density in the vicinity of a droplet by neglecting its dependency on temperature and vapor concentration, leads to the obvious discrepancy in the Maxwell expression for the growth rate regarding droplets of near critical size. Restoring the correct treatment of the vapor diffusion in terms of the mass concentration of water vapor and taking into the consideration variations of gas density in the vicinity of a droplet in compliance with the equation of state of moist air, we have obtained a new expression for the droplet growth rate valid for an arbitrary value of vapor concentration. The limitations imposed by the molecular kinetic fluxes to postnucleation diffusional growth of small droplets with a large Knudsen number are also reevaluated to include previously neglected physical effects. In particular, the essential contribution of the vapor molecular energy flux into the total kinetic molecular heat flux as well as the temperature variations of mean thermal velocities of air and vapor molecules in the vicinity of the droplet interface have been taken into consideration. Surprisingly significant differences have been found in new expressions derived for the droplet growth rate and droplet temperature, even in the limit of small vapor concentration, if comparing with commonly used results. These findings could help with better interpretation of experimental measurements to infer more reliable data for the mass and thermal accommodations coefficients.     

Statistics of the Nucleation Process under the Conditions of Gradual Creation of the Metastable State in Vapor

Statistics of the nucleation process at the gradual creation of the metastable state in vapor under the conditions when sufficiently large number of droplets arises in a vapor–gas system by the end of nucleation stage is studied on the assumption of randomness of the droplet nucleation. The probability distribution for a given number of droplets created in the unit volume of the vapor–gas system by the end of the nucleation stage is constructed. The distribution has the Gaussian form with the dispersion depending on the regime of matter exchange between droplets and vapor. The mean number of nucleated droplets under given conditions coincides (with an accuracy of up to the first-order small values with respect to the relative fluctuations of this value) with the predictions of the theory dealing with the average nucleation rate.     

Visualization and characterization of SPG membrane emulsification

Shirasu-porous-glass (SPG) membrane emulsification is highly attractive for various fields of foods, cosmetics, and pharmaceuticals because this technique produces monodispersed emulsions. However, there are few reports on the observation of membrane emulsification at the membrane surface. In the present work, we aimed to visualize the membrane emulsification using a microscope high-speed camera system. The direct observation made it possible to measure the mean rate of droplet formation and the percentage of active pores. The mean rate of droplet formation ranged 0.3–12 s⁻¹ and the percentage of active pores ranged 0.3–0.5% under the dispersed-phase flux of 0.58×10⁻⁶–5.8×10⁻⁶ m³/(m² s). We also observed that the droplets were formed without continuous-phase flow and the droplets were also formed by shear force at the continuous-phase flow under different experimental conditions. The balance among the dispersed-phase flux and the continuous-phase flow velocity influenced droplet formation.     

Hydrodynamic interactions of evaporating droplet with droplet of nonvolatile substance

The hydrodynamic interactions of freely evaporating or growing droplet (suspended in gaseous medium) in the supersaturated vapor with the droplet of nonvolatile substance or spherical solid particle are theoretically studied with allowance for effects that are linear with respect to the Knudsen number. The process of interaction between the volatile droplet and the infinite plane surface of nonvolatile liquid or solid is considered as a limiting case. Numerical estimates of the velocities of the steady motion of evaporating droplets of water and castor oil are reported. For the droplet of water and spherical solid particle, the effect of the heat conductivity of the latter on the velocity of particle motion is considered. Analogous estimates are obtained for a water droplet that evaporates near the infinite solid surface of castor oil or solid. The effects of the droplet size and the heat conductivity of wall on the rate of the evaporation of water droplet are analyzed.     

A real-time AFM study on crystal nucleation and growth in nanodroplets of isotactic polypropylene

Isotactic polypropylene (iPP) nanodroplets were prepared by using the classical droplet method in this study. The formation of nanodroplets allowed the controlled observation of polymer nucleation as well as access to crystal growth at exceptionally high supercooling in iPP. Three cases including the heterogeneous nucleation and fast crystallization in iPP droplets, the formation of multiple independent homogeneous nuclei within a single droplet and a single nucleus within a single droplet were detected by using atomic force microscopy (AFM) during gradually cooling after remelting the nanodroplets. Moreover, it is found that when the volume of droplet is larger than the value of ca. 130000 nm3, the first case was observed. Otherwise, the latter two cases appeared. The temperature at which the onset of nucleation was observed in individual droplets was found to be mainly dependent on height of the droplets when the size scale of the droplet is comparable to the size of the critical nucleus in at least one dimension, which indicates the nucleation behavior under confinement.     

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.     

Nonstationary evolution of the size,composition, and temperature of microdroplets of nonideal two- and three-component aqueous solutions

Results of numerical solution have been presented for a set of equations describing the nonstationary and nonisothermal growth or evaporation of microdroplets consisting of ethanol and water, sulfuric acid and water, and sulfuric and nitric acids and water. Time dependences of droplet size, temperature, and composition have been determined at low concentrations of a condensable vapor, as compared with the concentration of a carrier gas in an ambient vapor–gas mixture. The calculations have been performed using different initial conditions and approximations for the dependences of saturation vapor pressures, activity coefficients, and partial heats of condensation of the components, as well as average volumes per molecule on droplet composition and temperature. By the examples of ethanol–water and sulfuric acid–water droplets, it has been shown that nonmonotonic variations in the droplet radius are possible. Regimes of nonmonotonic variations in the temperature of a droplet that precede the onset of its stationary growth or evaporation have been revealed for all systems under consideration.     

Continuous nanoparticle production by microfluidic-based emulsion, mixing and crystallization

BaSO₄ and 2,2′-dipyridylamine (DPA) nanoparticles were synthesized as reactive crystallization and anti-solvent recrystallization examples, respectively, of using the microfluidic-based emulsion and mixing approach as a new avenue of continuously producing inorganic and organic nanoparticles. BaSO₄ nanoparticles in the size range of 15-100 nm were reactively precipitated within the confinement of an aqueous droplet which was coalesced from two separate aqueous droplets containing BaCl₂ and (NH₄)₂SO₄ using a three T-junction micromixer configuration constructed with commercially available simple tubing and fitting supplies. Also, DPA nanoparticles of about 200 nm were crystallized by combining DPA+ethanol and water droplets using the same micromixer configuration.     

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.     

Thermodynamics of the gas-phase reactions in chemical vapor deposition of silicon carbide with methyltrichlorosilane precursor

The gas-phase reaction thermodynamics in the chemical vapor deposition system of preparing silicon carbide via methyltrichlorosilane pyrolysis is investigated with a relatively complete set of 226 species, in which the thermodynamic data of 163 species are evaluated in this work with accurate model chemistry G3(MP2) and G3//B3LYP calculations combined with standard statistical thermodynamics. The data include heat capacity (C _p,m ^θ ), entropy (S _m ^θ ), enthalpy of formation (Δ_f H _m ^θ ) and Gibbs free energy of formation (Δ_f G _m ^θ ). All the results are consistent with the available reliable experiments. Based on these thermodynamic data, the equilibrium concentration distribution of the 226 possible species in 300–2,000 K is evaluated with the chemical equilibrium principle under a typical experimental condition. It is shown that the theoretical results are in very good agreement with the experiments. We conclude that the present work is instructive for experiments with different conditions.     

Charging and Release Mechanisms of Flexible Macromolecules in Droplets

We study systematically the charging and release mechanisms of a flexible macromolecule, modeled by poly(ethylene glycol) (PEG), in a droplet by using molecular dynamics simulations. We compare how PEG is solvated and charged by sodium Na⁺ ions in a droplet of water (H₂O), acetonitrile (MeCN), and their mixtures. Initially, we examine the location and the conformation of the macromolecule in a droplet bearing no net charge. It is revealed that the presence of charge carriers do not affect the location of PEG in aqueous and MeCN droplets compared with that in the neutral droplets, but the location of the macromolecule and the droplet size do affect the PEG conformation. PEG is charged on the surface of a sodiated aqueous droplet that is found close to the Rayleigh limit. Its charging is coupled to the extrusion mechanism, where PEG segments leave the droplet once they coordinate a Na⁺ ion or in a correlated motion with Na⁺ ions. In contrast, as PEG resides in the interior of a MeCN droplet, it is sodiated inside the droplet. The compact macro-ion transitions through partially unwound states to an extended conformation, a process occurring during the final stage of desolvation and in the presence of only a handful of MeCN molecules. For charged H₂O/MeCN droplets, the sodiation of PEG is determined by the H₂O component, reflecting its slower evaporation and preference over MeCN for solvating Na⁺ ions. We use the simulation data to construct an analytical model that suggests that the droplet surface electric field may play a role in the macro-ion–droplet interactions that lead to the extrusion of the macro-ion. This study provides the first evidence of the effect of the surface electric field by using atomistic simulations.

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Graphical Abstract ?

     

Electro-optic effect,propagation loss,and switching speed in polymers containing nano-sized droplets of liquid crystal

Polymers containing droplets of liquid crystal smaller than 100 nm, which have good transparency and easily form films, were prepared under various conditions to evaluate their potential as electro-optic materials for waveguide-type devices. By varying the liquid crystal concentration and the strength of the UV irradiation causing photo-induced phase separation of the droplets, we were able to control the droplet size and density. We have clarified how the birefringence generated in an applied electric field, switching speed, and optical loss of light propagating in the film depend on droplet size and density. Polymer materials having a large electro-optic effect (δn = 0.001 at 8 V μm^-1), low propagation loss (~2.5 dB cm^-1), and fast response time (~10 μs) have been developed.