Towards modeling thermochemical erosion

A quasisteady multidimensional Stefan problem is treated by means of similarity, asymptotic methods, and numerical analysis. The continuous removal of a solid 'erodee' is effected by gradual consumption of a solid 'eroder'. In the process under study, the erodee melts and the (liquid) melt diffuses to the eroder, where an exothermic, indefinitely rapid, diffusion-controlled surface reaction occurs. The products of reaction convey some of the chemically-generated heat to the surface of the erodee, so that further melting may occur, and the process may proceed. The analysis seeks to estimate the quasisteady rates of consumption of the erodee and the eroder, for the (convenient) self-similar case of confocal parabolas defining the edges of the melt layer. The analysis is simplified by observing that the flow is of lubrication-theory type: creeping, primarily unidirectional motion owing to the thinness of the melt layer between the erodee and eroder, with diffusion predominantly perpendicular to the principal motion. The analysis is completed by consideration of the force balance on the eroder.