Diffusion of a gaseous admixture in a semitransparent solid body due to electromagnetic radiation in the infrared range

Abstract

We propose a mathematical model for quantitative description of the diffusion process of a gaseous admixture in a solid body (a solid solution) due to electromagnetic radiation in the infrared range. We write out the original relations that describe the diffusion of the admixture in a layer subject to electromagnetic radiation in the heated body.Mass transfer in a multi-component solid body (or a solid solution) may be caused not only by a nonuniform distribution of the concentration of the individual components over the volume, but also by processes of a different physical character, especially electromagnetic, thermal, and mechanical actions. In the continuous models of solid solutions known in the literature the coupling of electromagnetic and diffusion processes is taken into account by adding constituent connections that describe either the coupling between the parameters that characterize the process [17,18] or the thermodynamic fluxes caused by ponderomotor forces (or mass forces equivalent to them) acting on the individual components [1, 13]--the so-called "forced" diffusion. With the first approach it is necessary to determine experimentally the new "electromagnetic/diffusion" characteristics, and with the second it is necessary to determine the forces that act on the individual components of the body, which may differ in their electric or magnetic properties. In the literature the second approach has been applied only to study diffusion in a binary ion solution caused by a stationary electric field [13].The purpose of the present paper is to study diffusion in a semitransparent solid body due to electromagnetic radiation in the infrared range.Our point of departure is the continuous model of a solid solution, in which the balance equation of mechanics and the first and second laws of thermodynamics are written in the context of the single continuum approach for the single continuum of the center of mass of its components. In constructing the constituent connections we apply the assumption of local equilibrium and the methods of nonequilibrium thermodynamics [7,8]. Then by the Euler (field) approach to describing the physical proc~esses being studied in the body the mass-balance law for the k-th component of an n-component solution when there are no chemical reactions in the body has the form [7,8] From nonequilibrium thermodynamics, using the condition of linearity of the constituent connections between the thermodynamic flows and the forces (Onsager's principle) taking account of the connection of the diffusion and thermal processes and the presence of solid forces acting on the body, we obtain the following expression for the total flux of mass of the k-th component [1]: j, = j~r) + j~, + j~/).Here j~r), j~), j/) are the mass fluxes connected with heat transfer (thermodiffusion), the nonuniform distribution of concentrations of the k-th component in the solution, and the action of solid forces on it (the "forced" diffusion), which have the form