Viscosity

Newton's law of viscosity is not a fundamental law of nature, but rather a constitutive equation (like Hooke's law, Fick's law, and Ohm's law) which serves to define the viscosity ${\displaystyle \mu }$. Its form is motivated by experiments which show that for a wide range of fluids, ${\displaystyle \mu }$ is independent of strain rate. Such fluids are called Newtonian. Gases, water, and many common liquids can be considered Newtonian in ordinary conditions and contexts. However, there are many non-Newtonian fluids that significantly deviate from this behavior. For example:


Trouton's ratio is the ratio of extensional viscosity to shear viscosity. For a Newtonian fluid, the Trouton ratio is 3.^[21][22] Shear-thinning liquids are very commonly, but misleadingly, described as thixotropic.^[23]


Viscosity may also depend on the fluid's physical state (temperature and pressure) and other, external, factors. For gases and other compressible fluids, it depends on temperature and varies very slowly with pressure. The viscosity of some fluids may depend on other factors. A magnetorheological fluid, for example, becomes thicker when subjected to a magnetic field, possibly to the point of behaving like a solid.

Units[edit]

The SI unit of dynamic viscosity is the newton-second per square meter (N·s/m²), also frequently expressed in the equivalent forms pascal-second (Pa·s), kilogram per meter per second (kg·m⁻¹·s⁻¹) and poiseuille (Pl). The CGS unit is the poise (P, or g·cm⁻¹·s⁻¹ = 0.1 Pa·s),^[28] named after Jean Léonard Marie Poiseuille. It is commonly expressed, particularly in ASTM standards, as centipoise (cP). The centipoise is convenient because the viscosity of water at 20 °C is about 1 cP, and one centipoise is equal to the SI millipascal second (mPa·s).


The SI unit of kinematic viscosity is square meter per second (m²/s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm²·s⁻¹ = 0.0001 m²·s⁻¹), named after Sir George Gabriel Stokes.^[29] In U.S. usage, stoke is sometimes used as the singular form. The submultiple centistokes (cSt) is often used instead, 1 cSt = 1 mm²·s⁻¹ = 10⁻⁶ m²·s⁻¹. 1 cSt is 1 cP divided by 1000 kg/m^3, close to the density of water. The kinematic viscosity of water at 20 °C is about 1 cSt.


The most frequently used systems of US customary, or Imperial, units are the British Gravitational (BG) and English Engineering (EE). In the BG system, dynamic viscosity has units of pound-seconds per square foot (lb·s/ft²), and in the EE system it has units of pound-force-seconds per square foot (lbf·s/ft²). The pound and pound-force are equivalent; the two systems differ only in how force and mass are defined. In the BG system the pound is a basic unit from which the unit of mass (the slug) is defined by Newton's Second Law, whereas in the EE system the units of force and mass (the pound-force and pound-mass respectively) are defined independently through the Second Law using the proportionality constant g_c.


Kinematic viscosity has units of square feet per second (ft²/s) in both the BG and EE systems.


Nonstandard units include the reyn (lbf·s/in²), a British unit of dynamic viscosity.^[30] In the automotive industry the viscosity index is used to describe the change of viscosity with temperature.


The reciprocal of viscosity is fluidity, usually symbolized by ${\displaystyle \phi =1/\mu }$ or ${\displaystyle F=1/\mu }$, depending on the convention used, measured in reciprocal poise (P⁻¹, or cm·s·g⁻¹), sometimes called the rhe. Fluidity is seldom used in engineering practice.


At one time the petroleum industry relied on measuring kinematic viscosity by means of the Saybolt viscometer, and expressing kinematic viscosity in units of Saybolt universal seconds (SUS).^[31] Other abbreviations such as SSU (Saybolt seconds universal) or SUV (Saybolt universal viscosity) are sometimes used. Kinematic viscosity in centistokes can be converted from SUS according to the arithmetic and the reference table provided in ASTM D 2161.