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I am familiar with the Kinetic Theory of a gas, where atoms or molecules are in relatively high-speed, random motion, and the bulk properties of the gas are determined by aggregations of these particles - eg. averaging the particle velocities to determine bulk velocity.

I am curious of if, and how, this model applies to fluids, where the particles are much closer together, and intuitively shouldn't have nearly as much space to fly around and past each other. Can this theory still be applied, or is it no longer valid?

EDIT: Further reading shows that the kinetic theory is based on the Boltzmann equation, which assumes only binary collisions between particles (dilute). Can the Boltzmann equation be used to model liquids also? If so, does the binary collision assumption affect things?

Qmechanic
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zplizzi
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    Perhaps one could compare the mean free path from kinetic theory vs the average particle spacing in the liquid vs the effective range of the inter-atomic forces... – Jon Custer Jul 14 '15 at 21:17
  • It is through moments of the Boltzmann equation that the hydrodynamic equations can be derived, cf. this Wikipedia post and also this unanswered Physics.SE question – Kyle Kanos Jul 15 '15 at 02:17
  • In addition to @Jon's nice suggestion one might compare the thermal energy of the particles to escape energy from the edge of the bulk (i.e. energy needed to overcome surface tension, which results from those same inter-atomic forces Jon was talking about). But I am not aware of any spherical-cow models that work well with liquids the was traditional kinetic theory works for dilute gasses. – dmckee --- ex-moderator kitten Jul 15 '15 at 16:03

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Max Born and Herbert S. Green developed a kinetic theory of liquids in the late 1940s. However, as they say in the introduction to their first paper on the topic, the kinetic theory of liquids cannot use the simplifying conditions of the kinetic theory of gases (low density) or solids (spatial order). As a result, their theory is much more difficult than either, and I do not know if it is used in practice.

Erlend Magnus Viggen
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