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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.

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).

V. Celli, UVa
Mon Aug 11 22:46:35 EDT 1997