# particles scattering on fluids: breakdown of the effective continuum description

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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## 2 Answers

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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 how are these hydrodynamic time and length defined? beside, the mean free path I guess it refers to a particle of the fluid, rather than to other type of particles scattering off the fluid. – argopulos Nov 3 '12 at 14:40 Yes, the mean free path refers to fluid particles. You need to consider the fluid molecular parameters to know if a hydrodynamic description of the fluid is enough or not. The hydrodynamic length is defined as $l_H \approx \max(|\nabla f| / f)$ in kinetic theory. The corresponding time scale satisfies $l_H = V \tau_H$ where $V$ is a typical particle velocity, say the thermal velocity. – juanrga Nov 4 '12 at 12:30

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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