Evaporation in mixture of vapor and gas mixture

Abstract

The evaporation problem in vapor and gas mixture is investigated by the methods of molecular-kinetic theory and fluid dynamics. Solution results are obtained for the case when investigation domain length is several thousands mean free paths of molecules. In this statement two types of evaporation problem solutions are obtained. In the first type gas is completely pushed up by vapor from the region near the evaporation interface surface. In this, “shelf” (straight step) in dependence of vapor density on coordinate takes place. In the second type such “shelf” is not formatted. Transition from one type solution to another is found.

Introduction

It is well known that the intensity of transfer processes at evaporation and condensation depends strongly on the presence of a non-condensable gas in vapor and gas mixture. This effect is confirmed by different calculations [1], [2] and experimental research data [3], [4]. For example in [2] the condensation process on interface surface is studied for one-dimensional statement when vapor flowed from semi-infinite space through the binary vapor and gas mixture. In this paper it was concluded that condensation is possible in principle only if the quantity of gas in system is smaller in some limited value. Thus non-condensable component can lock up the interface surface and condensation stops completely. A similar behavior was noted early by Aoki and co-authors in [1] on the study of vapors flows caused by evaporation and condensation on two parallel plane surfaces in the presence of a non-condensable gas.

Sometimes the role of non-condensable gas can be very important. For example: in [3] experimental study of the condensation of mercury the small enough pressures were realised. In [4] the concentration of background gas pressure was in five times smaller than that in the previous paper. In these conditions the corresponding mass flux densities at condensation processes differ from each other by 15–20%.

The evaporation and condensation problems for pure vapor and in semi-infinite statement have been studied by different authors [5], [6], [7], [8], [9], [10], [11]. For example in [5] the solutions of one-dimensional weak evaporation and condensation problems in a semi-infinite space were reported. The authors of this paper obtained the following expression for the intensity of evaporation and condensation processes:

$$j=\frac{\beta }{1-0.4\beta }\left({\rho }_s\sqrt{\frac{{\mathit{RT}}_s}{2\pi }}-{\rho }_{\infty }\sqrt{\frac{{\mathit{RT}}_{\infty }}{2\pi }}\right)\text{,}$$

where β – evaporation (condensation) coefficient. This expression can be used in the case when vapor flow Mach number is much smaller the unit (weak evaporation). Weak condensation problem from space contained vapor and gas mixture on the base of kinetic theory was investigated in [6].

In [7], [8], [9], [10] strong evaporation and condensation of pure vapor have been studied. For the case when intensity evaporation and condensation can be arbitrary the following expression for evaporation intensity at β = 1 is presented in [9]:

$$j=0.6\sqrt{2{\mathit{RT}}_s}({\rho }_s-{\rho }_{\infty })\sqrt{\frac{{\rho }_{\infty }}{{\rho }_s}}$$

The problem becomes more difficult in the case when investigation domain is occupied by a mixture of vapor and non-condensable component. The results of problem solution in this case are presented in [11] for some sets of component masses and concentrations relation. These results were received as evolution of [9] approach.

In the present article, we have used method of joint solution of the Boltzmann kinetic equations (BKEs) system and system of Navier and Stokes equations (NSEs). In this approach the study of mixture flows near surfaces is based on the BKEs system. Mixture flow outside these regions is described by fluid dynamic equations (NSEs).