# Mechanical effects of convective flow in steady-state stagnant film diffusion

When analysing diffusion problems in the context of the simplified film model, two limiting cases are ussually introduced during the solution of the differential chemical species mass balance equation. Those cases are the so-called equimolecular counter-diffusion (which implies a purely diffusional movement of species) and the stagnant film diffusion (in which the net flux of every but one species is null).

In the latter case, the solution of the equation gives rise to a convective term (i.e. bulk flow of the fluid) which contributes to the overall flux of the species being transferred, and opposes the diffusional flux of the stagnant species. Furthermore, this convective term implies that a net macroscopic (i.e. mass average) velocity field is established across the film.

I wonder how is this field mechanically established on the film -given the widely recognized limitations of the model- because the mass average velocity field obtained from the solution of the mass-balance equation is constant through it (an example is derived in this paper by Brouwers and Chesters: http://doc.utwente.nl/20661/1/Journal5New2.pdf). Solving the momentum balance equation with the characteristic boundary conditions of the model won't do the job, because the constant component of the velocity field in the direction perpendicular to the film boundary will lead to a non-informing pressure profile (constant too, assuming nearly-inviscid flow). What puzzles me is the transition between the velocity profile far away from the film (i.e. the turbulent, chaotic velocity of the fluid) which has a null average velocity component in the direction normal to the film, and the constant, net component of velocity in that direction inside the film which arises from the mass-balance resolution.

I suppose the pressure profile should be distorted in some way, but I couldn't figure it out by myself.

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