Viscosity

Viscosity
A simulation of liquids with different viscosities. The liquid on the left has lower viscosity than the liquid on the right.
Common symbols	η, μ
Derivations from other quantities	μ = G·t
Dimension	${\displaystyle {\mathsf {M}}{\mathsf {L}}^{-1}{\mathsf {T}}^{-1}}$

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Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another.^[1] For liquids, it corresponds to the informal concept of thickness; for example, syrup has a higher viscosity than water.^[2] Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square meter, or pascal-seconds.^[1]

Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion.^[1] For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's center line than near its walls.^[3] Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity.

In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is negligible in certain cases. For example, the viscosity of a Newtonian fluid does not vary significantly with the rate of deformation.

Zero viscosity (no resistance to shear stress) is observed only at very low temperatures in superfluids; otherwise, the second law of thermodynamics requires all fluids to have positive viscosity.^[4][5] A fluid that has zero viscosity (non-viscous) is called ideal or inviscid.

For non-Newtonian fluid's viscosity, there are pseudoplastic, plastic, and dilatant flows that are time-independent, and there are thixotropic and rheopectic flows that are time-dependent.