Particle growth by condensation. When a suspended spherical particle of radius $R$ passes

through an environment where a condensable vapor is present, the vapor deposits on the

particle by diffusion, as depicted below.

a$.$ Develop a shell balance in the exterior region of the particle and obtain the

concentration profile for the vapor. Assume that all the vapor that reaches the

particle deposits ${?}^1$ and forms a film, therefore at the particle radius, $r=R,C=0.$

Also assume that the amount of the vapor far away from the particle, $C_0,$ does not

change much throughout the process ${?}^2.$ You should get ${?}^3$ :

$C=C_0(1-\frac{R}{r})$

What is the second $BC?$