What is a Fluid?
Contents
What is a Fluid?¶
1. Characterization¶
I highly recommend the introductory chapter of Batchelor’s book [Batchelor, 2000] `for an in-depth discussion of this issue.
A continuous medium with material at every point.¶
This is of course a mathematical abstraction. A fluid is comprised of individual molecules and at sufficiently short distances the continuum approximation breaks down. In practice fluid mechanics is a coarse-grained description of materials.
The assumption is that if we coarse-grain over a large enough volume, the material can be effectively described by a set of quantities which vary smoothly in space and time, eg: 1. velocity: \({\vec v}({\vec x},t)\) 2. density: \(\rho({\vec x},t)\) (we will often take this to be constant) 3. temperature: \(T({\vec x},t)\) 4. For ocean water, salinity (salt content): \(S({\vec x},t)\) 5. For the atmosphere, specific humidity \(q = \rho_{vapor}/\rho\). and so on.
Density, temperature, and so on are themodynamic quantities that we typically define in equilibrium. A dynamic fluid will not be in equilibrium and in many interesting examples it is constantly being driven out of equilibrium. As an example, the solar heating of the atmosphere varies from the equator to th poles, varies with time over the seasons and over longer times as the Earth’s roational axis and orbital characteristics change. In this class we will be assuming that the fluid is in local thermal equilibrium, such that thermodynamic quantities make sense but vary in space and time.
Deformation under shear¶
Fluids always deform under shear stress: essentially, a gradient of force across some planar surface. There may be friction, corresponding to a force between two layers sliding on top of each other, but there is no restoring force.
2. Examples¶
Note that for our purposes, a fluid could be a liquid, a gas, a plasma, and so on. Examples of fluids:
Planetary fluids: oceans, atmospheres, ice sheets, magma
Astrophysics and cosmology: protons and electrons in the early universe, solar interiors, accretion disks, protoplanetary disks, near-horizon geometry of black holes (spacetime as an effective fluid)
Condensed matter physics: superfluids, quantum hall fluids
Biological media (blood, mucous,…)
Plasma in heavy ion collisions
In other words this subject is everywhere: biological physics, soft and hard condensed matter physics, nuclear physics, astrophysics, cosmology, earth science, and so on.