Generalized Newtonian fluid
Encyclopedia
A generalized Newtonian fluid is an idealized fluid
for which the shear stress
, τ, is a function of shear rate at the particular time, but not dependent upon the history of deformation.
where:
∂u/∂y is the shear rate or the velocity
gradient
perpendicular to the plane of shear (SI unit s−1).
The quantity
represents an apparent or effective viscosity
as a function of the shear rate (SI unit Pa⋅s).
The most commonly used types of generalized Newtonian fluids are:
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
for which the shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
, τ, is a function of shear rate at the particular time, but not dependent upon the history of deformation.
where:
∂u/∂y is the shear rate or the velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
perpendicular to the plane of shear (SI unit s−1).
The quantity
represents an apparent or effective viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
as a function of the shear rate (SI unit Pa⋅s).
The most commonly used types of generalized Newtonian fluids are:
- Power-law fluidPower-law fluidA Power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid for which the shear stress, τ, is given by\tau = K \left^n where:...
- Cross fluid
- Carreau fluid
- Second-order fluidSecond-order fluidAn incompressible second-order fluid is the retarded-motion expansion terms through second order. The retarded motion expansion is one constitutive model to describe non-Newtonian fluids....