What is a fluid?

How does a fluid (liquid or gas) differ from a solid? We can answer this question either in terms of microscopic properties or in terms of macroscopic properties.

• Solids:
  • often have microscopic long-range order; the atoms or molecules form a regular lattice (rubber and plastic are notable exceptions);
  • tend to form faceted crystals if grown under the right conditions;
  • hurt when you kick them; they have a non-zero "shear modulus".
• Liquids:
  • have microscopic short-range order, but no long-range order;
  • flow under the influence of gravity;
  • have zero shear modulus, so they flow aside when you kick them (not too hard);
  • have a fixed volume at low pressure and are usually hard to compresss.
• Gases:
  • have very little short-range order (ideal gases have none);
  • have zero shear modulus and you can easily move through them;
  • expand to occupy the available volume and are highly compressible.

The shear modulus is a material property which tells us how a substance responds to shear forces, which change the shape of the substance without changing the volume. This is illustrated in Fig. 2.1.
  

Figure 2.1: Shear forces acting on a fluid element.

A solid tries to resist static shear distortions, while a fluid does not. However, a sufficiently large stress will cause a solid to break (if it is brittle), or to take a very different shape, perhaps permanently (if it is ductile, like a hot steel rod). Conversely, some liquids are highly viscous and change shape only slowly. Glasses are liquids that increase their viscosity enormously as they cool, but can behave like brittle solids under high stress. Obviously, rigid solids and freely flowing liquids are just extreme cases.
The behavior under time-varying stress is more subtle, and inertia plays a role. For instance, a nearly incompressible and non-viscous liquid, like water, will not part under impact if it has no time to flow aside (as anyone who has done a belly-flop can attest).

• Phases of matter
• Hydrodynamic variables