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In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (flow) under an applied shear stress, or external force.^[1] They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them.

Although the term fluid generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of solid vary as well, and depending on field, some substances can have both fluid and solid properties.^[2] Non-Newtonian fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied.^[3] Substances with a very high viscosity such as pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases.^[4] A fluid in medicine or biology refers to any liquid constituent of the body (body fluid),^[5][6] whereas "liquid" is not used in this sense. Sometimes liquids given for fluid replacement, either by drinking or by injection, are also called fluids^[7] (e.g. "drink plenty of fluids"). In hydraulics, fluid is a term which refers to liquids with certain properties, and is broader than (hydraulic) oils.^[8]

Physics

Fluids display properties such as:

• lack of resistance to permanent deformation, resisting only relative rates of deformation in a dissipative, frictional manner, and
• the ability to flow (also described as the ability to take on the shape of the container).

These properties are typically a function of their inability to support a shear stress in static equilibrium. In contrast, solids respond to shear either with a spring-like restoring force, which means that deformations are reversible, or they require a certain initial stress before they deform (see plasticity).

Solids respond with restoring forces to both shear stresses and to normal stresses—both compressive and tensile. In contrast, ideal fluids only respond with restoring forces to normal stresses, called pressure: fluids can be subjected to both compressive stress, corresponding to positive pressure, and to tensile stress, corresponding to negative pressure. Both solids and liquids also have tensile strengths, which when exceeded in solids makes irreversible deformation and fracture, and in liquids causes the onset of cavitation.

Both solids and liquids have free surfaces, which cost some amount of free energy to form. In the case of solids, the amount of free energy to form a given unit of surface area is called surface energy, whereas for liquids the same quantity is called surface tension. The ability of liquids to flow results in different behaviour in response to surface tension than in solids, although in equilibrium both will try to minimise their surface energy: liquids tend to form rounded droplets, whereas pure solids tend to form crystals. Gases do not have free surfaces, and freely diffuse.

Modelling

In a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state.

The behavior of fluids can be described by the Navier–Stokes equations—a set of partial differential equations which are based on:

• continuity (conservation of mass),
• conservation of linear momentum,
• conservation of angular momentum,
• conservation of energy.

The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.

See also

• Matter
• Liquid
• Gas
• Supercritical fluid

References

• Bird, Robert Byron; Stewart, Warren E.; Lightfoot, Edward N. (2007). Transport Phenomena. New York: Wiley, Revised Second Edition. p. 912. ISBN 978-0-471-41077-5.