The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.     

Models of thermodiffusion in 1D

The goal of the paper is to study the Cauchy problem for 1D models of thermodiffusion. We explain qualitative properties of solutions. In particular, we show which part of the model has a dominant influence on well‐posedness, propagation of singularities, L^p ? L^q decay estimates on the conjugate line, and on the diffusion phenomenon. Copyright © 2013 John Wiley & Sons, Ltd.     

Comment on “Role of the velocity frame of reference in thermodiffusion in liquid mixtures” by M. Eslamian,C.G. Jiang and M.Z. Saghir

We analyze the material transport equations (MTE) derived by Eslamian and co-authors and address the criticism expressed regarding the approach formulated in our previous work. In doing so, we show that the MTE formulated by Eslamian and co-authors are valid only in closed stationary non-isothermal systems in combination with the restrictions on the Onsager coefficients formulated in our work which is criticized, and that for non-stationary systems the approach we took can be used.     

Two-Stage Seebeck Effect in Charged Colloidal Suspensions

We discuss the peculiarities of the Seebeck effect in stabilized electrolytes containing the colloidal particles. Its unusual feature is the two stage character, with the linear increase of differential thermopower as the function of colloidal particles concentration n⊙ during the first stage (“initial state”) and dramatic drop of it at small n⊙ during the second one (“steady state”). We show that the properties of the initial state are governed by the thermo-diffusion flows of the mobile ions of the stabilizing electrolyte medium itself and how the colloidal particles participate in the formation of the electric field in the bulk of the suspension. In its turn, we attribute the specifics of the steady state thermoelectric effect the massive colloidal particles undergoing slow thermal diffusion and the break down of their electro-neutrality in the vicinity of electrodes.     

Spontaneous electrochemical transport reactions in ionic and ionic-electronic salt melts: The production of diffusion coatings

Extensive material concerning the interaction of metals in ionic and ionic-electronic salt melts is presented. The mechanism and character of the phenomenon of the directed spontaneous transport of metals by their ions in salt melts are established. Examples of application of this phenomenon for depositing diffusion coatings on metals and alloys (by aluminum, beryllium, boron, zinc, titanium, chromium, silicon, and so on, as well as by two-component coatings) are presented.     

Thermodiffusion and Vaporization of Metal from Levitated Droplet V. Determination of Condensation Rate and Thermodiffusion Parameters of Mn, Fe, and Ni Vapours

In the present paper the experimental data of vaporization from levitated droplet for Mn, Co, Ni in the flow of argon obtained from the bibliography were evaluated by means of the new method published in the previous work [Czech. J. Phys. 50 (2000) 737]. The rate constants of condensation, thermodiffusion ratios, thermodiffusion coefficients and the corresponding temperature dependencies were determined together with other physical quantities for Mn vapour at the temperature 2000 K and for Fe, Ni at 2200 K. The rate constant of condensation and the thermodiffusion ratio are higher for Ni than for Fe. The value of thermodiffusion coefficient determined for Mn is rather high and the rate constant of condensation is higher than for Ni. The increase of vaporization resulting from condensation and thermodiffusion for Mn was only 2.7-times and for Fe and Ni (5.5-5.65)-times. The process of vaporization from a levitated droplet includes molecular diffusion and convective diffusion, molecular thermodiffusion with vapour condensation and condensation without thermodiffusion. The proportions of these processes were for Mn in the range (37-29) condensation dominated and its share was over 70 accurate experimental data and this is the reason why the evaluation of the Co vaporization was unsuccessful. The work also presents some proposals of experimental procedures leading to the data accuracy improvement.     

Numerical simulation of injection of a solvent into a production well under electromagnetic action

The results of a theoretical investigation of the possibility of using powerful radio-frequency (RF) electromagnetic (EM) radiation combined with solvent injection in high-viscosity oil fields for the purpose of intensifying oil recovery are given. A mathematical model of the three-stage stimulation of a high-viscosity oil pool is proposed. The model takes into account the cross-flow heat and mass transfer effects initiated by the movement of a multicomponent system through a porous medium under the action of an EM field. A comparative analysis of the results of calculations of the proposed combined method and its components (EM treatment of the reservoir bottomhole zone without solvent injection and “cold” displacement of oil by a solvent) is carried out.     

Quasi-stability and upper semicontinuity for coupled parabolic equations with memory

This current study deals with the long-time dynamics of a nonlinear system of coupled parabolic equations with memory. The system describes the thermodiffusion phenomenon where the fluxes of mass diffusion and heat depend on the past history of the chemical potential and the temperature gradients, respectively, according to Gurtin-Pipkin's law. Inspired by the works of Chueshov and Lasiecka on the property of quasi-stability of dynamic systems, we prove this property for the problem considered in this study. This property allows us to analyze certain properties of global and exponential attractors in a more efficient and practical way. This approach is applied for the first time for coupled parabolic equations. We analyze the continuity of global attractors with respect to a pair of parameters in a residual dense set and their upper semicontinuity in a complete metric space. Finally, we analyze the upper semicontinuity of global attractors with respect to small perturbations of the damping terms.     

Connection between thermophoresis and thermodiffusion in a liquid binary mixture

In a liquid suspension, thermophoresis is the motion of a suspended particle under a temperature gradient. In a liquid binary mixture, thermodiffusion is the generation of a composition gradient upon application of a temperature gradient. A quantitative connection is established between the two phenomena without making assumptions about their mechanisms. It is shown that Galilean invariance and the choice of a Galilean reference frame play a key role in that connection. The results are not restricted to very dilute suspensions or mixtures.