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When does the macroscopic continuum description of a medium like a fluid break down? Say I'm interested in a scattering process of some particles with momentum p and energy E off a fluid of temperature T, volume V, and pressure p: when should I consider the single fluid particles rather than the collective modes? For a solid with a lattice, there is a natural cutoff, but is there for a fluid? |
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When you consider scales of time and distance beyond the Hydrodynamic regime given by the hydrodynamic time $\tau_H$ and the hydrodynamic length $l_H$. For instance in an ordinary gas under ordinary conditions the mean free path for the particles is much shorter than $l_H$ and the hydrodynamic description characterizes the behaviour of the gas. But for an ordinary gas under a shock wave or for a plasma at very high temperatures the mean free path becomes very long, of the order of meters and you need to go beyond a hydrodynamic description. |
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From the particle physics point of view... As a general rule, when the length scale associated with the interaction drops much below the inter-molecular distance in the liquid you can treat the interaction as a point like interaction between two particles. Possible there are special cases when you could generate coherent effects even at those energies, but these will exception not the rule. |
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