Cross fluid
Encyclopedia
A Cross fluid is a type of generalized Newtonian fluid
whose viscosity
depends upon shear rate according to the following equation:
where
is viscosity
as a function of shear rate,
, 
and n are coefficients.
At low shear rate (
), cross fluids behave as Newtonian fluid
s and at high shear rate (
) as power-law fluid
s.
Generalized Newtonian fluid
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.\tau = F\left where:...
whose 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...
depends upon shear rate according to the following equation:
where
is viscosityViscosity
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 shear rate,
, and n are coefficients.At low shear rate (
), cross fluids behave as Newtonian fluidNewtonian fluid
A Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.-Definition:...
s and at high shear rate (
) as power-law fluidPower-law fluid
A 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:...
s.
See also
- Navier-Stokes equationsNavier-Stokes equationsIn physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous...
- FluidFluidIn 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....
- Carreau fluid
- 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:...
- Generalized Newtonian fluidGeneralized Newtonian fluidA 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.\tau = F\left where:...