Theory of surface deposition from boundary layers containing condensable vapour and particles

TL;DR

This paper develops an asymptotic theory for surface deposition from boundary layers with condensable vapour and particles, analyzing the effects of parameters like wall temperature and scavenging rate on condensation and deposition.

Contribution

It introduces the $ ext{delta}$-CL theory and the 0-CL and multiple scales theories to accurately model vapour condensation and particle deposition in boundary layers, extending previous models.

Findings

The $ ext{delta}$-CL theory accurately predicts vapour and droplet profiles and deposition rates.

The 0-CL theory improves predictions near the maximum dew point temperature.

Multiple scales theory effectively models large and moderate scavenging rates.

Abstract

Heterogeneous condensation of vapours mixed with a carrier gas in the 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 vapour particles. The supersaturated vapour condenses on the particles by diffusion and particles and droplets are thermophoretically attracted to the wall. Assuming that the heat of vaporization is much larger than the Boltzmann constant times the temperature far from the wall, vapour condensation occurs in a {\em condensation layer} (CL). The CL width and characteristics depend on the parameters of the problem, and a parameter $R$ yielding the rate of vapour scavenging by solid particles is particularly important. Assuming that the CL is so narrow that temperature, particle density and velocity do not change appreciably inside it, an asymptotic theory is found, the $\delta$-CL theory, that approximates very well the vapour and droplet profiles, the dew point shift and the deposition rates at the wall for wide ranges of the wall temperature $\tilde{T}_{w}$ and the scavenging parameter $R$. This theory breaks down for $\tilde{T}_{w}$ very close to the maximum temperature yielding non-zero droplet deposition rate, $\tilde{T}_{w,M}$. For large $R$, we can either assume that the width of the CL is zero (0-CL theory, then the vapour density reaches local equilibrium with the condensate immediately after it enters the dew surface), or use a nonlinear multiple scales theory. The 0-CL theory corrects the $\delta$-CL theory for $\tilde{T}_w$ very close to $\tilde{T}_{w,M}$ and any $R$, whereas the multiple scales theory is appropriate for large and moderate $R$.