Diffusion of a particle between two immiscible liquids

I am trying to find a model, or construct my own to describe the diffusion of a particle between layers of immiscible fluids with different densities.

The particle size is much larger than the sizes of molecules of both liquids, so Brownian motion assumption holds for the entire system. The particle is uncharged as well.

At a first glance, I believe the important factors are surface tension of the liquids, angle of incidence, and the energy of the particle. I might be wrong, but I think the overall solution should have a Snell-Law like structure, which is a direct consequence of the least action principle.

Is there an established model for this? Is there a concept like total internal reflection, where the particle bounces back from the boundary? Does the particle lose energy to overcome the surface tension of both fluids?

Alternatively, how well does "skipping stone" physics help us?

I assumed brownian motion is more related to physics than chemistry, but please let me know if I need to look for an answer in Chemistry SE.

Thanks!