It is proposed to measure diffusivity coefficient $D_{AB}$ from the knowledge of evaporation rate.

A droplet of liquid $A$ of radius $R$ is suspended in a stagnant gas $B.$ The temperature and

pressure are kept constant.

$($a$)$ Assume that the gas $B$ is stagnant, reduce the Fick's law

$N_{Ar}=-c{D}_{AB}\frac{d{x}_A}{dr}+x_A(N_{Ar}+N_{Br})$

$($b$)$ Find the rate of evaporation of A from the spherical droplet.

You can start by Writing a shell balance around the droplet in the stagnant film to find

the molar flux of $A$ in the $r$ direction. Note that the mole fraction of A outside the film

will be negligible.$($State the assumptions, List the boundary conditions needed to solve

etc..$)$

$($c$)$ Assuming the droplet as the system, write a mass balance on $A.$ Integrate the mass

balance to find an expression for the time it takes to reduce the radius of the droplet

from $r=R$ at $t=0$ to $r=R_1$ at $t=t_1$ by evaporation.

$($d$)$ Suppose if an experimental data of time vs$.$ radius of sphere is available, how will you

compute diffusivity $D_{AB}$