# Fluid

In physics, a fluid is a liquid or gas that continually deforms (flows) under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them.

Although the term "fluid" includes both the liquid and gas phases, in common usage, "fluid" is often used synonymously with "liquid". This usage of the term is also common in medicine and in nutrition ("drink plenty of fluids").

Liquids form a free surface (that is, a surface not created by the container) while gases do not. Viscoelastic fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Also substances with a very high viscosity such as pitch appear to behave like a solid (see pitch drop experiment).

## 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:

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

### Classification of fluids

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.

Newtonian fluids follow Newton's law of viscosity and may be called viscous fluids.

Fluids may be classified by their compressibility:

• Compressible fluid: A fluid that causes volume reduction or density change when pressure is applied to the fluid or when the fluid becomes supersonic.
• Incompressible fluid: A fluid that does not vary in volume with changes in pressure or flow velocity (i.e., ρ=constant) such as water or oil.

Newtonian and incompressible fluids do not actually exist, but are assumed to be for theoretical settlement. Virtual fluids that completely ignore the effects of viscosity and compressibility are called perfect fluids.