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DOI 10.21662
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Demin V.A., Demina T.V., Zinurova V.E. Penetration of a Silicon Vapor through Residual Gaseous Medium during Siliconizing of a Carbon Composite Material. Multiphase Systems. 19 (2024) 3. 103–111 (in Russian).
2024. Vol. 19. Issue 3, Pp. 103–111
URL: http://mfs.uimech.org/mfs2024.3.015,en
DOI: 10.21662/mfs2024.3.015
Penetration of a Silicon Vapor through Residual Gaseous Medium during Siliconizing of a Carbon Composite Material
V.A. Demin∗,∗∗, T.V. Demina∗,∗∗∗, V.E. Zinurova∗,∗∗∗
∗Perm State National Research University, Perm, Russia
∗∗Perm National Research Polytechnic University, Perm, Russia
∗∗∗Institute of Continuous Media Mechanics, Perm, Russia

Abstract

A new physical and mathematical approach is proposed for the description of a silicon vapor high-temperature transfer from the melt mirror to the surface of absorbing carbon porous medium in an atmosphere of residual gas under moderate vacuum conditions. The general hydrodynamic equations are simplified as much as possible and lead to the model, which is intended for further numerical implementation in the course of simulation the non-stationary three-dimensional process of high-temperature siliconizing of porous carbon products of arbitrary shape and under the condition of complex distribution of silicon sources and sinks. The physical and mathematical model of transport consists of only one non-linear differential equation in partial derivatives for the silicon vapor concentration in the atmosphere of argon or any other residual gas. The main achievement consists of obtaining two stationary analytical solutions for plane and cylindrical geometry in one-dimensional formulation of the problem, which explain the anomalously large silicon vapor flux into the porous material in full-scale experiments. The exact solutions for the studied gas mixtures are expressed in terms of the well-known verified values of material parameters. The high degree of the model usability is supported by numerical simulation in a non-steady two-dimensional case. It has shown that despite the low saturation density of gaseous silicon, the vapor-liquid phase process of high-temperature siliconizing of the carbon material is physically possible in a reasonable time.

Keywords

high temperature processes,
rare gaseous medium,
transfer of silicon vapor,
diffusive and convective transport

The authors acknowledge financial support by the Ministry of Science and Higher Education of the Russian Federation (theme №124021600038-9)

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