Moving Mesh and Variable Knudsen Diffusion Coefficient during CVD

Dear Forum Members,

I am trying to simulate oxide deposition inside a 100 nm pore by using a 2D axisymmetric model. The model is similar to a heterogeneous catalysis problem and the only modification is that I am tracking the boundary movement using ALE. Uptil now, I am using a constant diffusion coefficient to model the transport of reactant inside the pore. But since I am in the high Knudsen number regime, the diffusion coefficient changes with time as the pore closes. Basically, it is a function of the pore radius at that instant and varies with 'z'. I haven't found a way to define a suitable variable that will represent the position of the pore surface and have been stuck on this problem for days.

I have been thinking of integrating (point integration) the mesh velocity with time and then obtain mesh growth from this. After subtracting this contribution from the initial pore radius I can obtain the instantaneous pore radius and then relate it to the diffusion coeff. Although I can do this for a cut point, how do I specify this integral on all points along the height of the pore (as pore radius will vary with z due to non-conformality) ?

Thank you in advance
Sanket Kelkar