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In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas, and to some extent, plastic solids. Fluids are substances that have zero shear modulus, or, in simpler terms, a fluid is a substance which cannot resist any shear force applied to it.

Although the term "fluid" includes both the liquid and gas phases, in common usage, "fluid" is often used as a synonym for "liquid", with no implication that gas could also be present. For example, "brake fluid" is hydraulic oil and will not perform its required incompressible function if there is gas in it. This colloquial usage of the term is also common in medicine and in nutrition ("take plenty of fluids").

Liquids form a free surface (that is, a surface not created by the container) while gases do not. The distinction between solids and fluid is not entirely obvious. The distinction is made by evaluating the viscosity of the substance. Silly Putty can be considered to behave like a solid or a fluid, depending on the time period over which it is observed. It is best described as a viscoelastic fluid. There are many examples of substances proving difficult to classify. A particularly interesting one is pitch, as demonstrated in the pitch drop experiment currently running at the University of Queensland.

## Physics

Fluids display properties such as:

• not resisting 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 with a spring-like restoring force, which means that small deformations, whether shear or normal, are reversible.

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. Gases do not have tensile strength, and freely expand in response to changes in pressure.

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 very 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.

Depending on the relationship between shear stress, and the rate of strain and its derivatives, fluids can be characterized as one of the following:

• Newtonian fluids: where stress is directly proportional to rate of strain
• Non-Newtonian fluids: where stress is not proportional to rate of strain, its higher powers and derivatives.

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

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