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Capillary Filling — Phase Field Method

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I have a question regarding the Capillary Filling – Phase Field Method (https://www.comsol.com/model/capillary-filling-8212-phase-field-method-1878).

I noticed that when I plot the variable psi (chemical potential) the result is different when I plot the equal quantity of psi which is ” -pf.epsilon_pf^2(phipfrr + phipfzz + 1/rphipfr) + phipf*(phipf^2 – 1)”. Why does that happen?

Of course the correct chemical potential is equal_of_psi.jpg.

How does Cosmol take weak form of the capillary force in navier stokes equation (F_{st}=constant*)? Does integration by parts applied to the ?

Thanks for your time, Kostis


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