Theory of surface deposition from boundary layers containing condensable vapor and particles
J.C. Neu (Department of Mathematics, UC Berkeley, USA), A. Carpio (Departamento de Matemática Aplicada, U. Complutense de Madrid, Spain) and L.L. Bonilla (G. Millán Institute, Universidad Carlos III, Leganés, Spain)
Heterogeneous condensation of vapors mixed with a carrier gas in a stagnation point boundary layer flow near a cold wall is considered in the presence of solid particles much larger than the mean free path of vapor particles. The supersaturated vapor condenses on the particles by diffusion and the particles are thermophoretically attracted to the wall. We assume that the heat of vaporization is large, so there is a condensation layer whose distance from the wall and width depend on the parameters of the problem. We present three asymptotic theories of the condensation layer: The simplified equilibrium model in which the vapor is in local equilibrium with the condensate after it enters the dew surface, a condensation layer theory based on matched asymptotic expansions, and finally, a nother based on nonlinear multiple scales.
We calculate the shift in the dew point due to the flow, the vapor density profile, and the deposition rates at the wall according to these three analyses, and compare them to direct numerical solution of the full equations.