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	${\displaystyle {\mathsf {M}}{\mathsf {L}}^{-1}{\mathsf {T}}^{-1}}$

Part of a series on
Continuum mechanics
${\displaystyle J=-D{\frac {d\varphi }{dx}}}$ Fick's laws of diffusion
Laws Conservations Mass Momentum Energy Inequalities Clausius–Duhem (entropy)
Solid mechanics Deformation Elasticity linear Plasticity Hooke's law Stress Strain Finite strain Infinitesimal strain Compatibility Bending Contact mechanics frictional Material failure theory Fracture mechanics
Fluid mechanics Fluids Statics · Dynamics Archimedes' principle · Bernoulli's principle Navier–Stokes equations Poiseuille equation · Pascal's law Viscosity (Newtonian · non-Newtonian) Buoyancy · Mixing · Pressure Liquids Adhesion Capillary action Chromatography Cohesion (chemistry) Surface tension Gases Atmosphere Boyle's law Charles's law Combined gas law Fick's law Gay-Lussac's law Graham's law Plasma
Rheology Viscoelasticity Rheometry Rheometer Smart fluids Electrorheological Magnetorheological Ferrofluids
Scientists Bernoulli Boyle Cauchy Charles Euler Fick Gay-Lussac Graham Hooke Newton Navier Noll Pascal Stokes Truesdell
v t e

The viscosity of a fluid is a measure of its resistance to deformation at a given rate.^[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.