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.     

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.     

The effect of concentration of surfactant and electrolyte on the pit and droplet sizes nanoemulsions of <Emphasis Type="Italic">n</Emphasis>-dodecane in water

Nanoemulsions are transparent or semi-transparent systems mostly covering the size range of 50–200 nm. In the research, the production of nanoemulsion of n-dodecane in water was studied by phase inversion temperature method (PIT), and the effect of the changes in NaCl and surfactant concentration on PIT and droplet size of n-dodecane was studied. The changes in conductivity with temperature were measured for emulsions containing 20 wt % dodecane, 4 and 8 wt % Brij30, and NaCl of various concentrations in aqueous phase. The results showed a decrease in PIT with a rise in concentration of NaCl and also Brij30. There was a linear model fitted to the data. Analysis of variance (ANOVA) shows that, the significance value (p-value) is less than 0.05, and the effect of the changes in concentration of surfactant Brij30 on the decrease in PIT and droplet size was the more than that in concentration of NaCl in aqueous phase. The lowest mean droplet diameters were in the range of 8.6–14 nm.     

Diffusion and Relaxation Dynamics of Supercooled Polymer Melts

The dynamic properties of polymer melts are investigated in the range of normal liquid regime to the supercooled liquid regime. The polymer is modeled as a coarse-grained bead-spring model with chain length ranging from 5 to 160. The mean squared displacement and non-Gaussian parameter are used to describe the self diffusion of polymer beads. We find slow dynamics with decreasing temperature and increasing chain length. The time evolution of non-Gaussian parameters shows two peaks(or one peak one shoulder) in the α-relaxation time, τα, regime and sub-diffusion time regime, respectively, where the first primary peak indicates the dynamic heterogeneity stemmed from the motion of beads, and the secondary peak is the result of correlated motion along a polymer chain. Moreover, the relaxation of polymer beads shows clear two-step decay in supercooled melts and the dynamics shows growing heterogeneity with decreasing temperature. As chain length is increased, a peak of the dynamic susceptibility occurs, and the peak height,χ*4, increases and then reaches a plateau. The curves of the height of the first peak of α_2, α _2~*, versus τ and the curves of χ_4~*α versus τα follow two master curves for different chain lengths. Our results indicate the similarity of dynamic heterogeneity dominated by the motion of single bead even the chain length is different. It is interesting to find that the Stokes-Einstein(SE) relation between τα and diffusion coefficient D, D~τ-1 q, is highly length-scale dependent. The SE relation breaks down in both normal melts regime and supercooled regime at large magnitude of wave vectors, attributed to the non-Brownian motion arising from the chain connectivity and growing heterogeneity due to supercooling. However, the SE relation is reconstructed when the probing length scale is large(at small magnitude of wave vectors). Our results show a hierarchical physical picture of the supercooled polymeric dynamics.     

Times of metastable droplet relaxation to equilibrium states

Times of metastable droplet relaxation to their equilibrium state are calculated at saturated vapor pressures, depending on the droplet size. It is shown that for small droplets with radius R = 6 molecular diameters (or ~2 nm) the relaxation times are ~1 ns (which is comparable to the characteristic flight times of rarefied gas molecules). For large droplets with radius R ~ 800 molecular diameters, the relaxation times are as long as 10 μs. At a fixed droplet radius (6 ≤ R ≤ 800), the range of variation in relaxation time from the melting point to the critical temperature does not exceed one order of magnitude: the lower the temperature, the slower the relaxation process.     

Disperse systems based on chloracetophos in the low concentration range: self-organization,physicochemical properties and influence on representatives of higher plants and hydrobionts

A set of physicochemical methods was used to establish that aqueous solutions of chloracetophos fungicide and bactericide (1) in the range of calculated concentrations from 1?10^–18 to 1?10^–4 mol L^–1 are disperse systems in which a dispersed phase hundreds of nanometers in size is formed above and below a threshold concentration of 1?10^–9 mol L^–1. Upon dilution disperse systems 1 are capable of non-monotonic changing the physicochemical properties and changing the toxicity profile (inhibition–stimulation) when influencing the growth and development of unicellular algae Chlorella vulgaris. The formation of domains and nanoassociates is accompanied by the appearance in the UV spectrum of an absorption band at 210–300 nm with a maximum at ~220 nm (A₂₂₀). The interrelated concentration dependences of A₂₂₀, the size of the dispersed phase, and electrical conductivity indicates that the observed spectral features of systems 1 are caused by the properties of the domains and nanoassociates.     

The Effect of a Background Electrolyte on the Viscosity of Aqueous Dodecyltrimethylammonium Bromide Solutions

Conductometry and viscometry have been employed to study the effect of a background electrolyte (KBr) taken in concentrations of 0.03 and 0.1 M on the critical micelle concentration of dodecyltrimethylammonium bromide (С₁₂ТАB) and the dependence of relative viscosity η/η₀ of С₁₂ТАB micellar solutions on the overall surfactant concentration. It has been found that, as a first approximation, each of these dependences may be represented as the sum of two linear portions. Concentrations c* of С₁₂ТАB micellar solutions, which correspond to the inflections between the two linear portions in the concentration curves of relative viscosity, have been determined. The Einstein equation η/η₀ = 1 + 2.5p (p is the volume fraction of the dispersed phase and 2.5 is a theoretical parameter that takes into account the spherical shape of the particles) has been transformed into a form corresponding to the concentration dependence of the relative viscosity on the overall surfactant concentration to make it applicable to the consideration of low-concentration systems, which are uncomplicated by intermicellar interaction. In particular, the applicability of the above equation for estimating micelle radii has been studied. It has been shown that the (η/η₀–1) = f(c/с₀₁–1) concentration dependences represented in bilogarithmic coordinates (c is the overall С₁₂ТАB concentration and c₀₁ is the critical micelle concentration) are linear in the absence of a significant intermicellar interaction and have slopes equal to unity. This fact may be considered as a criterion for the applicability of the Einstein equation to micellar solutions.     

Molecular Dynamics Study on Carbon Dioxide Absorbed Potassium Glycinate Aqueous Solution

Molecular dynamics (MD) simulations have been performed to investigate the effects on structure, transport properties, and dynamical properties in the potassium glycinate aqueous solution caused by carbon dioxide (CO₂) absorption. The optimized structure and charges of constituents of the solution, such as the glycine zwitterion, have been determined by Gaussian09 using the density functional theory. The obtained pair distribution functions, g _ij (r)’s, show the significant distribution difference of bicarbonate ion, \({\text{HCO}}_{3}^{ - }\), around the glycine anion and glycine zwitterion. The shear viscosity and diffusion coefficient obtained by MD show different CO₂ concentration dependences. The frequency dependent diffusion coefficient D _i (ν) for N and C in glycine ions are mainly influenced by the cage effect of surrounding water molecules, whereas D _i (ν) for H show the characteristic vibration due to the structure difference of the glycine ions.     

Peculiarities of rheological properties and flow of highly concentrated emulsions: The role of concentration and droplet size

Results of a complete study of the rheological properties of highly concentrated emulsions of the w/o type with the content of the dispersed phase up to 96% are reported. The aqueous phase is a supersaturated solution of nitrates, where the water content does not exceed 20%. Dispersed droplets are characterized by a polyhedral shape and a broad size distribution. Highly concentrated emulsions exhibit the properties of rheopectic media. In steady-state regimes of shearing, these emulsions behave as viscoplastic materials with a clearly expressed yield stress. Highly concentrated emulsions are characterized by elasticity due to the compressed state of droplets. Shear storage modulus is constant in a wide range of frequencies that reflect solid-like behavior of such emulsions at small deformations. The storage (dynamic) modulus coincides with the elastic modulus measured in terms of the reversible deformations after the cessation of creep. Normal stresses appear in the shearing. In the low shear rate domain, normal stresses do not depend on shear rate, so that it can be assumed that they have nothing in common with normal stresses arising owing to the Weissenberg effect. These normal stresses can be attributed to Reynolds’ dilatancy (elastic dilatancy). Normal stresses sharply decrease beyond some threshold value of the shear rate and slightly increase only in a high shear rate domain. Observed anomalous flow curves and unusual changes of normal stresses with shear rate are explained by the two-step model of emulsion flow. Direct optical observations show that emulsions move by the mechanism of the rolling of larger droplets over smaller ones without noticeable changes of their shape at low shear rates, while strong distortions of the droplet shape is evident at high shear rates. The transition from one mechanism to the other is attributed to a certain critical value of the capillary number. The concentration dependence of the elastic modulus (as well as the yield stress) can be described by the Princen-Kiss model, but this model fails to predict the droplet size dependence of the elastic modulus. Numerous experiments demonstrated that the modulus and yield stress are proportional to the squared reciprocal size, while the Princen-Kiss model predicts their linear dependence on the reciprocal size. A new model based on dimensional arguments is proposed. This model correctly describes the influence of the main structural parameters on the rheological properties of highly concentrated emulsions. The boundaries of the domain of highly concentrated emulsions are estimated on the basis of the measurement of their elasticity and yield stress.     

Inclusion of the concentration dependence of the diffusion coefficient in the sand equation

The applications of the Sand equation in potentiometry of electrode and membrane systems for precise measurements of the transition time (τ) have been determined. An approach was suggested for choosing the diffusion coefficient of electrolyte (D) in the case when the concentration changes from its value in the agitated solution (where D = D_b) to the nearly zero value at the surface (D = D₀ corresponds to an infinitely dilute solution), D_b and D₀ being substantially different. The Nernst–Planck–Poisson nonstationary equations were numerically solved in a one-dimensional system including an ion-exchange membrane and two adjacent diffusion layers (for the electrode–solution system, the result is a particular case). An effective value D_ef was found, whose substitution in the Sand equation gave τ identical to that obtained by numerical solution. The neglect of the concentration dependence D(с) can lead to a nonadequate determination of the ion transport numbers in the membrane.     

Experimental and actual values of self-diffusion coefficients of liquids in porous media

Self-diffusion coefficients D* of liquids in porous media, as measured by the pulsed-field gradient NMR method, have been investigated as functions of the interval t ₁ between the first and the second radio-frequency pulses (the time of spin dephasing) in the “stimulated echo” pulsed procedure. Experimental D*(t ₁) dependences have been shown to be adequately described by the relations of the Fatkullin theory for moderate and short correlation times of spin motion in an internal random Gaussian magnetic field. Actual self-diffusion coefficients and some parameters of the porous media have been estimated.     

Experimental study of extraction fraction and mass transfer coefficient in a microchannel using butyl acetate/acetic acid/water chemical system

The droplet flow regime in microchannels can increase the mass transfer and chemical reactions considerably. In this work, the mass transfer of immiscible fluids of water as the solvent and butyl acetate containing 5 vol% of acetic acid as the feed is experimentally studied in a vertical flow inside a microchannel with the inner diameter of 8 mm. Effect of total flow velocity, Re number and volumetric flux ratio of two phases (Q_aq/Q_or) on the extraction fraction of acetic acid, mass transfer coefficient and droplet size were investigated. Based on the experiments, increasing the flux ratio can shift the flow regime from the plug to the droplet. Compared to the plug flow, the extraction fraction increased by 2–3 times in the droplet regime, depending on the total velocity, while the average diameter of the droplets decreased. Moreover, with the increase in the total velocity, the extraction fraction is reduced by 22%. However, in the case of the plug flow, the extraction fraction does not change appreciably with the increase in the total flow velocity. The mass transfer coefficient was found to increase monotonously with increasing Re number and an enhancement of 133% was achieved in the droplet flow regime.     

Percolation in the model of random successive adhesion of anisotropic particles

Numerical studies of random successive adsorption (the RSA model) of rectangular particles on a flat substrate are performed and the dependences of saturation concentration and the percolation threshold on the parameters of a model are determined. The dependences of saturation concentration φ _j∞ on the particle diameter-to-length ratio r and the parameter of orientational order S are found. Correlations between the ? _j∞(r) function and excluded surface area are discussed. It is revealed that for highly ordered systems (S ≈ 1), the saturation concentration φ _j∞ is equal to 0.557 ± 0.005 and is virtually independent of r. For partially ordered systems, the ? _j∞ value decreases with an increase in r and in the r → ∞, ? _j∞ → 0. Percolation transition and electrical connectivity for the systems studied can take place only under the assumption of the tunnel mechanism of conductivity through gaps with finite thicknesses. The minimum thickness of tunnel gaps, at which percolation can occur, rises with increasing r and decreasing S.     

Method for calculating the sizes of nucleation centers upon homogeneous crystallization from a supercooled liquid

An alternative approach to calculating critical sizes l_k of nucleation centers and work A_k of their formation upon crystallization from a supercooled melt by analyzing the variation in the Gibbs energy during the phase transformation is considered. Unlike the classical variant, it is proposed that the transformation entropy be associated not with melting temperature T_L but with temperature T < T_L at which the nucleation of crystals occurs. New equations for l_k and A_k are derived. Based on the results from calculating these quantities for a series of compounds, it is shown that this approach is unbiased and it is possible to eliminate known conflicts in analyzing these parameters in the classical interpretation.     

Growth and motion of heterogeneous water droplets in laminar diffusion chambers: 2. High nanoparticle concentrations

The heterogeneous condensation of water vapor on nanoparticles and the growth of formed droplets are numerically studied under conditions of laminar diffusion chamber (LDC) of a new type with a hot porous wall. The main attention is focused on the growth of heterogeneous droplets in the gas flow at high number densities of nanoparticles exceeding 10⁸ droplet/m³. Under these conditions, there is an interrelation between the growth of droplets and processes of heat and mass transfer in LDC due to vapor depletion and the release of latent heat of phase transition on growing droplets. The efficiency of the coverage of nanoparticles with water film is studied under LDC nonuniform conditions. It is shown that, at initial number densities of nanoparticles (N _d > 10¹¹ droplet/m³), heterogeneous droplets do not grow to optically detected sizes.     

Droplet Formation Study in Emulsification Process by KSM using a Novel In Situ Visualization System

The semi real-time observations of oil-in-water emulsification process in a Kenics static mixer were performed using a novel in situ visualization system. The homogenization processes and emulsion characteristics were analyzed using images taken periodically in fixed time intervals during the emulsification process. Morphological evolution of droplets was monitored and the mechanism of droplet formation was studied, both experimentally and theoretically. A wide range of dispersed phase concentration as well as surfactant concentration were used in the experiments and their impacts on emulsion characteristics were determined. Different droplet formation mechanisms occurred during the experimental results are presented. The relationship between droplet sizes, flow rate, surfactant concentration, and other impact factors was visually shown, and their role in controlling the emulsification process was revealed. The minimum droplet size obtained from the dispersed phase in emulsions was shown to be perfectly monitored and controlled by this technique.     

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.     

The use of recurrent equations in chromatography

Recurrent equations A(x + k) = aA(x) + b were shown to be applicable to the approximation not only of virtually arbitrary properties of organic compounds (A) in homologous series (A = n _C, k = 1 or 2) but also of the dependences of chromatographic retention parameters on the number of carbon atoms in homologue molecules (A = t _R). The same equations described the temperature dependences of retention times of arbitrary compounds under isothermal separation conditions in gas chromatography (x = T, k = ΔT = const) and the dependences of retention times on the concentration of an organic solvent as an eluent component (x = C, k = ΔC = const) under isocratic separation conditions in high performance liquid chromatography.     

Simulation of electrical percolation in disperse systems at a small difference between specific conductivities of components

The possibility of development of electrical percolation upon variations in the contents of components in a disperse system has been studied in terms of Bruggeman’s ideas of an effective medium and the continual model of the electrical conductivity of composite materials. The case of a small difference between the specific conductivities of a dispersed phase K_m and a dispersion medium K_d has been considered. It has been shown that the dependence of electrical conductivity K of a disperse system on volume fraction p of a wellconducting component may exhibit an inflection in the vicinity of the p* value, which depends on the K_m/K_d ratio. Different methods for determining the p* value have been described. At low ratios between the conductivities of a dispersed phase and a dispersion medium, the inflection is very weakly pronounced. However, the representation of the K(p) dependences in semilog coordinated substantially facilitates its identification.     

The assignment of signals in the EPR spectra of axially symmetrical quintet dinitrenes

Fine structure levels in an external magnetic field and angular dependences of resonance magnetic fields on the direction of an external magnetic field were calculated for two axially symmetrical quintet dinitrenes with the zero-field splitting parameters D _q = 0.260 cm^?1, E _q = 0.000 and D _q = 0.243 cm^?1, E _q = 0.003 cm^?1. The EPR spectra of such dinitrenes contained lines of only three xy transitions (xy ₁, xy ₂, and xy ₄), two Δm _s = ±2 transition lines between the W _?2 and W ₀ sublevels, and three additional lines from noncanonically oriented molecules whose magnetic axis Z made an angle of 12°–16° or 52°–54° with an external magnetic field.