Mathematical model on surface reaction diffusion in the presence of front chemical reaction

Abstract

a b s t r a c tThe article discusses a mathematical model of solid-phase diffusion over substance surface accompanied a frontal chemical reaction. The purpose of our article is to describe the concentration distribution and surface reacted layer growth. The model is a system parabolic equations, complicated with the presence of mobile front. It takes account of diffusive fluxes redistribution, sublimation from the surface, chemical reaction reversibility. The asymptotic approximation of the obtained nonlinear problem is constructed. Numerical solution was also carried out. Both numerical and analytical solutions conform to each other in a wide range of parameter changes, whereas observed differences are explained. It was obtained that the reaction front at the substrate surface grows as the fourth root of time in the assumed absence of evaporation and reaction reversibility. In the presence of evaporation the logarithmic distribution law ln(t) is obtained. The theoretical possibility of sharp deceleration and stop of reaction product layer growth is obtained.

Reactive metal-organic interfaces studied with hard x-ray photoelectron spectroscopy: controlled formation of metalloporphyrin interphase layers during metal vapor deposition onto porphyrin films

“…(4) The concentration profiles that are expected in our experiments are described with a complementary error function ('erfc'), a type of function that is frequently encountered in the analysis of concentration profiles in reaction-diffusion systems [20][21][22][23][24][25][26][38][39][40] and theoretically predicted for this class of system [20]. Accordingly, the following equation was used to parameterize the curves (see figure 2(a)):…”

“…It should be emphasized that the formation of the closed metal film is the only limiting factor for the diffusion of the metal in the organic layer (unless there is a reaction and the reaction products create a barrier for diffusion). Without this self-limiting effect, the diffusion (and reaction) of the metal would likely continue indefinitely, creating a metalation reaction front that would propagate into the organic bulk material [20], creating a conceptually well understood instance of a reaction-diffusion system [20][21][22][23][24][25][26].…”

Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions

“…The investigation of a mathematical model has broad implications for a great number of important applications, such as chemical diffusions [1,2], heat conduction problems, [3][4][5], population dynamics [6], thermoelasticity [7], medical science, electrochemistry [8], engineering, and control theory. This necessitates the analysis of two-dimensional parabolic partial differential equations with nonlocal boundary conditions [9][10][11].…”

Analytical and Numerical Investigation of two-dimensional Heat Transfer with Periodic Boundary Conditions

“…The investigation of mathematical model for a great number of important applications such as chemical diffusions [1,2] application in the heat conduction problems, application of heat conduction problems [3][4][5], population dynamics [6], thermoelasticity [7], medical science, electrochemistry [8], engineering, and control theory require the analysis of the analyses of two-dimensional parabolic partial differential equations with nonlocal boundary conditions [9][10][11].…”