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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]
This constitutive equation is also called the Newton law of viscosity. The total stress tensor σ {\displaystyle {\boldsymbol {\sigma }}} can always be decomposed as the sum of the isotropic stress tensor and the deviatoric stress tensor ( σ ′ {\displaystyle {\boldsymbol {\sigma }}'} ):
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For kinematic viscosity, the SI unit is m^2/s. In engineering, the unit is usually Stoke or centiStoke, with 1 Stoke = 0.0001 m^2/s, and 1 centiStoke = 0.01 Stoke. For liquid, the dynamic viscosity is usually in the range of 0.001 to 1 Pascal-second, or 1 to 1000 centiPoise. The density is usually on the order of 1000 kg/m^3, i.e. that of water.
A fluid is flowing between and in contact with two horizontal surfaces of contact area A. A differential shell of height Δy is utilized (see diagram below). Diagram of the shell balance process in fluid mechanics. The top surface is moving at velocity U and the bottom surface is stationary. Density of fluid = ρ; Viscosity of fluid = μ
A Newtonian fluid is a power-law fluid with a behaviour index of 1, where the shear stress is directly proportional to the shear rate: = These fluids have a constant viscosity, μ, across all shear rates and include many of the most common fluids, such as water, most aqueous solutions, oils, corn syrup, glycerine, air and other gases.
To map the viscosity as a function of all these variables require a large sequence of experiments that generates an even larger set of numbers called measured data, observed data or observations. Prior to, or at the same time as, the experiments is a material property model (or short material model) proposed to describe or explain the observations.
where τ zx is the flux of x-directed momentum in the z-direction, ν is μ/ρ, the momentum diffusivity, z is the distance of transport or diffusion, ρ is the density, and μ is the dynamic viscosity. Newton's law of viscosity is the simplest relationship between the flux of momentum and the velocity gradient.