# Adding wall friction to a 3D model - Stokes equation

Maybe that is not the best place for the following question, if such, let me know and sorry.

I would like to model the flow of expanding bentonite in a fracture following the given reference. In order to take into account the swelling pressure, they modified the Stokes equation (momentum equation) by adding the swelling pressure explicitly (equation 4-6 of reference): $$$$\frac{\partial \bf{u}}{\partial t} -\nabla \cdot \bf{\tau} + \nabla (p+p_{sw}) = 0 \\$$$$

After that they add the static friction at the wall (equation 4-7 in reference): $$$$\frac{\partial \bf{u}}{\partial t} -\nabla \cdot \bf{\tau} + \nabla (p+p_{sw}(1-2\mu)) = 0 \\$$$$

the friction coefficient is $$$$\mu$$$$ I wonder if such assumption in a 3D model would be correct. I assume that if I solve the system with the last equation, the nodes that are not close to the wall are also going to take into account the friction coefficient. I think it has more sense to add the Friction force into the wall as a boundary condition. I thought to use a navier slip condition.

Does it make sense what I am saying, or I am wrong.

Thanks

Best Regards

Dani

Ref:

Pont, A., Coene, E., & Idiart, A. (2020). Bentonite erosion project. Svensk kärnbränslehantering AB [Swedish Nuclear Fuel and Waste Management Company]}