Solubilization front

[edelperi]

Dear All,

Modeling solubilization of a body in a fluid (i.e., a spheric shaped salt granule in water) needs to move the solubilization front as the body dissolves. Mass conservation obeys the change rate in volume of the body equals the species flux across the boundary.

I would very much appreciate a candidate solution to this case of moving boundary.

Thank you very much.

Eugenio

P.S. I'm using ElmerSolver v 5.5.0

[raback]

Hi

Generally you can model free surface problems with Lagrangian (moving mesh) or Eulerian (fixed mesh) methods. If your change in geometry is modest the Lagrangian approach should be favoured, otherwise you need to use some Eulerian method.

In Elmer the Lagrangian method would involve some equation (AdvectionDiffusionSolver) for the transport of the dissolved material, simple model to estimate the change in shape from the surface flux, and a solver to extend the mesh deformation (MeshUpdateSolver).

The Eulerian method in Elmer is level set. I think it could be applied here as well allthough I have some doubts on the accuracy.

Is your solubility limited by diffusion or surface reaction rate?

-Peter

[edelperi]

Dear Peter,

Thank you very much for your comments. Regarding your question about the limiting step, I'm trying to use both models to evaluate the hypothesis about the limiting step. I think is easier to start with the diffusion limited model and the Lagrangian approach, using 2D axisymmetric geometry, and spheric soluble body.

I will try it.

Thanks a lot

Eugenio

[raback]

Hi Eugenio

Yes, I also think that starting with diffusion limited transport and Lagrangian approach would be the natural choice.

I suggest that you get the optimally accurate nodal fluxes by setting for the diffusion equation "Calculate loads = True". Now we may assume that there is no tangential velocity component at the interface. Hence you could use MeshUpdateSolver and use the normal tangential coordinates. With these choices the nodal loads for the "Mesh Update 1 Load" would be just a constant times the computed "Concentration Loads". Or scaling time approapriately just

Mesh Update 1 Load = Equals Concentration Loads

or something in that style. I don't remember whether MeshUpdateSolver is additive and there may be some tweaks to do. The main message here is that you would probably get optimal accuracy and simplest implementation by working directly with the nodal quantities when coupling these equations.

-Peter