  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 $R$.
