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The pitch drop experiment, for example, shows bitumen as a liquid, even though it appears to be a solid, and then there is the "glass: solid or liquid" debate. Is there a numerical value in viscosity that defines the boundary between a solid and a liquid?
Or is there another numerical identifier that separates the two?

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No.

The elasticity of the solids is a liquid kind of character. The non newtonian fluids provide a solid kind of character.

As everything is just electromagnetism, you can split your thoughts down the an single atom level, and play it with magnets on real scale. You can push your hands between magnets, and you can make them flow.

In the wikipedia article about Cold welding Richard Feynman explains this well;

The reason for this unexpected behavior is that when the atoms in contact are all of the same kind, there is no way for the atoms to “know” that they are in different pieces of copper. When there are other atoms, in the oxides and greases and more complicated thin surface layers of contaminants in between, the atoms “know” when they are not on the same part. — Richard Feynman, The Feynman Lectures, 12–2 Friction

If you bend a steel the atoms are changing their positions just like they do in a fluid. There is no way to define exactly which is the exact difference between solid and fluid, which would be exactly valid for all materials. You can't barely do it to even a single material; You think that water freezes at 0 °C? Think again, as you might have it liquid down to -48 °C - at Standard pressure!

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  • $\begingroup$ Bummer. Would be nice if They just said "everything above 10^9 Pa.s is solid". Or some other sensible arbitrary value. It's such a common distinction we make in every day life and no one has really defined it $\endgroup$ – Roman Nov 22 '15 at 21:14
  • $\begingroup$ Though I do see problems with that approach by modelling the mantle flow for example. Blech $\endgroup$ – Roman Nov 22 '15 at 21:16
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    $\begingroup$ @Roman All the "flow problems" are mainly there because the physics of turbulence are not known. I think even there you shouldn't make too much difference between fluids and solids, but it's another story. $\endgroup$ – Jokela Nov 22 '15 at 21:26

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