Suppose that a spherical liquid droplet of radius $R(t)$ is growing in a supersaturated vapor. Assume that

the gas density ${}_G$ and liquid density ${}_L$ are each constant, and let the origin correspond to the center of

the droplet.

$($a$)$ Show that the liquid inside the droplet is at rest. $[$Hint: Choose a stationary control volume of constant

radius, which at a given instant is slightly smaller than $R(t).]$

$($b$)$ Evaluate the scalar mass flux into the droplet $($i$.$e$.,$ crossing the vapor$-$liquid interface$).$

$($c$)$ Evaluate the mass flux vector in the vapor at a fixed position just outside the droplet. In what direction

does the flux vector point?