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Davius
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How could we estimate the number of molecules below which a fluid cannot be adequately modeled by the Navier-Stokes equations?

As is known, the Navier-Stokes equations are an approximation in the continuum mechanics to model an aggregate of independent molecules, which, although they can move freely, interact strongly with each other. The Navier-Stokes equations are enormously successful in modeling everything from atmospheric phenomena to producing practical engineering solutions, but in all these cases there is a number of molecules much larger than $10^{25}$ molecules. For sure $10^4$ water molecules together and interacting do not exhibit liquid behavior, but something different, while $10^{18}$ would have liquid behavior.

Davius
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