Diffusion of ink in the rotating flow

$($a$)$ Consider you have a cylindrical ink $($Figure shows the top view of the cylinder filled with

liquid$)$ at the center of the large cylinder. The ink can diffuse outward to the wall by the

chemical potential with the diffusion coefficient $D.$ How long does it take for the ink to reach

the wall? $(10$ pts$)$

$($b$)$ Now we start to rotate the outer wall of cylinder with the angular velocity of $.$ Derive a

governing equation to describe the concentration profile at the steady state. Then, how long

does it take for the ink to reach the wall? $(15pts)$