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Ink absorption in Paper as a porous media flow

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Hello everyone, I would like to set up a macroscopic model of a microscopic flow of ink in a paper sheet domain. I am mostly intereste in modelling the absorption rate as a function of the porosity but it may be necessary to include the effect of the surface tension. What interface do you advice me to use for such kind of model ? I have a clear idea of: Paper thickness (t): 0.1 mm Paper width (w): 0.6 mm Ink density (ρ): 1071.9 [kg/m3] Ink dynamic viscosity (ν): 0.004875 [Pa S]

I know I can use the darcy' law or the creeping (stokes) flow. It is not really clear if I need to decide which one of the two approach I need to use or if I can them in the same model.

Do you know how I can define and simulatate the absorption rate once defined a range of porosity to set ?

Thank you for your time


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