Influence of mass diffusion on the stability of thermophoretic growth of a solid from the vapor phase
The stability of solid planar growth from a binary vapor phase with a condensing species dilute in a carrier gas is studied when the ratio of depositing to carrier species molecular masses is quite large and the main diffusive transport mechanism is thermophoresis (thermal diffusion). Direct Fick/Brownian transport is important only in a thin layer (of relative thickness given by the inverse of the Schmidt number Sc >> 1) adjacent to the solid-vapor interface. Then, only disturbances with a large wavenumber k are affected by Brownian diffusion and a linear stability analysis is performed in the limit k = O(Sc). The resulting dispersion relation shows that there exist three different regions: i) for small wavenumber disturbances the planar front is unstable when the ratio of fluid to deposit thermal conductivities is less than unity, ii) for very large wavenumbers interfacial tension effects damp out all disturbances, and iii) in the intermediate range of wavenumbers the amplification rate depends on the degree of constitutional supersaturation.