Self-similar solution to the problem of vapor diffusion toward the droplet nucleated and growing in a vapor-gas medium

The problem of vapor diffusion toward a droplet nucleated and growing in the diffusion regime is exactly solved using the similarity theory. The surface motion of droplets is taken into account in the solution. The constructed nonstationary concentration field of vapor satisfies the diffusion equation, the boundary condition of equilibrium on the surface of growing droplet, and the initial homogeneous condition. According to the found solution, the radius of a droplet is proportional to the square root of the time of its growth. Far from the critical point, at a low ratio between the densities of excess vapor and a liquid droplet, the proportionality coefficient coincides with that resulting from an approximate solution. The balance between the numbers of molecules removed from vapor and those composing a growing droplet exactly corresponds to the obtained solution.     

Kinetics of binary condensation on the droplet growing in diffusion regime

A relaxation equation determining the regular tendency of the concentration of binary solution in the growing droplet to the stationary value, at which there is a self-similar solution to the problem of the condensation in a binary mixture, is derived. An analytical solution of the relaxation equation is obtained and it is demonstrated that the stationary value of concentration is achieved via the power law. The time interval that elapses from the emergence of the droplet until the diffusion regime of droplet growth and derived relaxation equation become effective is revealed. The stationary value of concentration is found for the model of ideal solution.     

Simulation of ion mass transfer processes with allowance for the concentration dependence of diffusion coefficients

The system of equations describing ion transport in a binary electrolyte z _a-z _c with allowance for the linear dependence of the diffusion coefficients on the concentration was analyzed in the framework of the phenomenological Nernst-Planck approach. The expressions are obtained that define concentration profiles of ions and conditions favorable for the limiting current caused by the achievement of the concentration of a saturated solution (in the case of the anodic reaction) and depletion of the near-electrode region in electroactive cations (in the case of the cathodic reaction). The revealed theoretical dependence of the limiting current on the volume concentration of the salt agrees with published experimental data. The voltammetric characteristics of the corresponding systems were calculated. The role of the migrational component of the ion flow is discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 638–642, April, 2006.     

Power laws for the establishment of a stationary concentration in a binary solution droplet growing in a vapor-gas medium

The kinetic laws are found for establishing a stationary concentration in solution droplets growing under diffusion and free-molecular regimes in a vapor-gas medium composed of two condensing vapors and a passive gas. Parameters of these laws are related to the thermodynamic and kinetic characteristics of condensing substances. Original Russian Text ? F.M. Kuni, A.A. Lezova, 2009, published in Kolloidnyi Zhurnal, 2009, Vol. 71, No. 4, pp. 563–565.     

The dependence of the osmotic coefficient on the composition of multicomponent solutions

The thermodynamic theory of binary aqueous solutions of electrolytes taking into account the electrostatic interaction of ions and their hydration and association was extended to multicomponent solutions. Equations for calculating the osmotic coefficient of multicomponent solutions from parameter estimates (hydration and association numbers under standard conditions) determined for the corresponding binary subsystems were substantiated. Interval parameter estimates were used to calculate the osmotic coefficients for several three-five-component aqueous solutions containing both nonelectrolytes and electrolytes. A comparison of the results with the literature data showed that cross interactions between components could be ignored for the multicomponent solutions studied.     

The effect of diffusion on nanoaerosol filtration through porous materials with allowance for desorption processes

The effects of the finite residence time of aerosol particles in the bound state and their detachment due to thermal fluctuations on the filtration efficiency of porous and fibrous materials have been investigated with allowance for longitudinal diffusion in a flow. It has been shown that the desorption of particles affects the filtration efficiency even at times shorter than residence time τ_d of the particles in the bound state, while, at t ? τ_d, filtration stops. Allowance for the diffusion of aerosol particles in the flow leads to a decrease in the filtration efficiency as compared with the calculations performed without taking into account the longitudinal diffusion.     

The pressure and composition dependence of mutual diffusion in the system helium-nitrogen at 300 K

Diffusion coefficients for the system helium-nitrogen have been measured as a function of pressure at 300 K from 1 to 12.5 atmospheres. These measurements include composition dependences at 1, 3, 5 and 7 atmospheres. The results show reasonable agreement with the Thorne-Enskog theory for moderately dense gases.     

Temperature and composition dependence of the Soret coefficient in Lennard-Jones mixtures presenting evaporation/condensation phase transition

The thermodiffusive behavior of a Lennard-Jones binary mixture has been studied by using nonequilibrium molecular dynamics. In particular, the dependence of the Soret coefficient, S(T), on the temperature and composition has been investigated, exploring a wide range of temperatures from 1000 K to the condensation temperature of the mixture. In a previous paper the dependence of S(T) on the temperature and the composition was studied for Lennard-Jones binary mixtures presenting mixing/demixing (consolute) phase transition, and the results allowed the formulation of a very simple expression with the computed values of S(T) in the one phase region outside the critical region closely fitted by the function [T - T(c)(x(1))](-1), with T(c)(x(1)) the demixing temperature of the mixture under study. The results of the present work show that the same expression of S(T) can be found for the one phase region outside the evaporation/condensation region but now with T(c) representing the condensation temperature of the mixture under study.     

A diffusion model of the development of concentration heterogeneities in a photopolymerizable environment with allowance for the limited compatibility of a monomer and a polymer

A diffusion model of the development of concentration heterogeneities of a photopolymerizable composite that takes into account the transition of the monomer-polymer system from the homophase state to the heterophase state with an increase in conversion is proposed. Numerical simulation shows that a significant increase in the amplitude of these heterogeneities is determined not only by the microsyneresis of the composite but also by the efficiency of their development in the homophase state at the initial stage of polymerization. The possibility of controlling the optical properties of the final polymeric material via initiation of the polymerization by radiation of different intensities in the regions of the homophase and heterophase states of the composite is discussed. The numerical-simulation results are experimentally verified.     

Capillary zone electrophoresis for the determination of average hydrodynamic velocity and diffusion coefficient

The determination of the average hydrodynamic velocity and diffusion coefficient by capillary zone electrophoresis is described. The present simple method only requires basic experimental data, such as peak area, peak height and migration time to complete the task of determining the diffusion coefficient and the average hydrodynamic velocity.     

Capillary zone electrophoresis for the determination of average hydrodynamic velocity and diffusion coefficient

The determination of the average hydrodynamic velocity and diffusion coefficient by capillary zone electrophoresis is described. The present simple method only requires basic experimental data, such as peak area, peak height and migration time to complete the task of determining the diffusion coefficient and the average hydrodynamic velocity. Received: 29 September 1998 / Revised: 14 May 1999 / Accepted: 19 May 1999     

Characterization of macromolecules in liquid solutions by thermal diffusion. I. Dependence of the soret coefficient on the nature of the dispersing medium

Experiments have been carried out on thermal diffusion of macromolecular particles dispersed in various liquids, with the object of checking some predictions of the radiation-pressure theory of Soret effect in liquids and of establishing a method of physical characterization of macromolecules in liquid solutions. The experimental results confirm the importance of the ratio G between thermal conductivity K and (phase) velocity v of high-frequency elastic waves of the materials composing the mixture in determining the thermodiffusive behavior of a liquid solution. We have shown that the migration of the macromolecular component takes place in the same direction in which thermal energy is flowing or opposite to it, depending on whether G of the dispersed particles is smaller or larger relative to the G of the liquid. Another aspect of the same phenomenon may be observed when macroscopic pieces of nonmetallic materials are suspended in a liquid, and heat is made to flow through this solid plunger and the surrounding liquid. The experiments performed with molecular solutions and with macroscopic plungers mutually complement and confirm each other. Anomalous results obtained in the case of solutions of polyvinylpyrrolidone in methanol are also discussed, and the possibility that this might be the consequence of the existence of a marked velocity dispersion in the high-frequency region of the spectrum of thermal waves in both water and methyl alcohol is indicated. Finally the possibility is hinted that thermal diffusion might have been responsible for the phenomena of molecular selection and evolution which ultimately led to the origin of life on our planet.     

A simple rule for describing the composition dependence of the aggregation number of mixed micelles

The mean aggregation numbers of mixed micelles composed of hydrocarbon surfactants (nonionic/nonionic and ionic/nonionic surfactants) have been determined by the intensity light-scattering method, in order to compare them with the values calculated by using the equations derived. The equations have been derived for representative micellar shapes (disk-like, rod-like, and spherical shapes) by making the assumptions that (i) the surface area of the hydrocarbon core of a mixed micelle is built up by independent contributions from each surfactant monomer, and (ii) the dimension of the hydrocarbon core is determined by the number of carbon atoms of a surfactant. The closest agreement of the observed aggregation numbers with the calculated ones has been obtained for the mixed micelle of an oblate ellipsoidal shape as a geometrical model for a disk-like micelle. This suggests that an oblate ellipsoidal shape may be more probable for a micelle formed at a moderate range of surfactant concentration than a prolate ellipsoidal (a rod-like) and a spherical shape if the assumptions (i) and (ii) hold. The equations presented here are useful, since they make it possible to calculate an accurate aggregation number of the mixed micelle of any composition from the aggregation numbers of the pure micelles of the components and the number of carbon atoms of component surfactants as long as there is no highly specific interaction between different surfactant components.     

The effects of pH and calcium on the diffusion coefficient of humic acid

Humic acid is a major component of natural organic matter in surface water and can cause serious fouling problems in membrane filtration processes for drinking water treatment. The transport of humic acid to the membrane surface and within membrane pores is related to its diffusivity. Thus, the diffusion coefficient of humic acid is an important mass transport parameter. Clark and Lucas [J. Membr. Sci. 143 (1998) 13–25] studied the diffusion and partitioning of humic acid into a porous ultrafiltration membrane and developed a model to predict how humic acid diffusivity changes under different pH and calcium concentration conditions. In this work, the diffusion coefficient of humic acid was directly measured and compared to the predictions of the Clark and Lucas model. The experiments were conducted in a two-chamber diffusion cell separated by a track-etched membrane. The results show that the diffusivity of humic acid increases with decreasing pH and increasing calcium concentration, which can be explained by the compaction of humic acid molecules at low pH and high ionic strength. The experimental measurements strongly support the predictions of the Clark and Lucas model.     

Influence of temperature and pressure on the effective diffusion coefficient in fine-pored catalysts

Conclusions For the investigated substances at low degrees of surface coverage and temperatures below 150°, a substantial fraction of the mass transport is comprised of the flux along the surface; at high temperatures (>150°), the basic type of transport is diffusion in the gas phase.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2419–2424, November, 1972.     

A data base for polymer chromatography: dependence of interaction parameters on mobile phase composition

In chromatography of polymers, retention is determined by the characteristic volumes of the column (pore volume and interstitial volume), the pore diameter, and the interaction parameter. While the influence of the pore diameter is predominant in size exclusion chromatography, the key parameters in liquid adsorption chromatography are the interaction parameter and the pore surface of the column. It is shown, that the retention behaviour of polymers in liquid adsorption chromatography (LAC) can be predicted very well using the accessible volume and pore surface of the column, which can be determined very easily, and the interaction parameters from a data base.     

Theory and mechanism of electron transfer in a condensed medium at high temperatures with allowance for change in vibrational frequencies

An expression for electron transfer rate has been obtained through the solution of a time wave equation by the variational method by defining the wave function as a linear combination of functions corresponding to electron localization on the donor and on the acceptor. A dependence of electron transfer on temperature, on the electronic and vibrational characteristics of the system has been derived. An activation energy temperature-variation effect has been obtained. It has been proved that many-electron transfers are impossible.     

A simple HPLC-MS method for the quantitative determination of the composition of bacterial medium chain-length polyhydroxyalkanoates

Bacterial poly(hydroxyalkanoates) (PHAs) vary in the composition of their monomeric units. Besides saturated side-chains, unsaturated ones can also be found. The latter leads to unwanted by-products (THF ester, secondary alcohols) during acidic cleavage of the polymer backbone in the conventional analytical assays. To prevent these problems, we developed a new method for the reductive depolymerization of medium chain-length PHAs, leading to monomeric diols that can be separated and quantified by HPLC/MS. Reduction is performed at room temperature with lithium aluminum hydride within 5-15 min. The new method is faster and simpler than the previous ones and is quantitative. The results are consistent with the ones obtained by quantitative (1)H NMR.