A non-Newtonian fluid has a stress--strain-rate relation with nonlinear, time-dependent, history-dependent, or microstructure-dependent behavior.
A generalized Newtonian fluid has instantaneous scalar constitutive law , with viscosity depending on the current shear rate but carrying no memory.
A yield-stress fluid behaves as a rigid material below a critical shear stress and flows once that stress is exceeded.
A Herschel–Bulkley fluid is unyielded for and obeys after yield. The parameters and are its consistency and power-law index.
Where the stress in a yield-stress fluid remains below the yield stress, the shear rate vanishes and the material moves as an undeformed plug bounded by yielded layers.
A slump test releases a known volume of material and infers its yield stress from the dimensions of the final gravity-supported deposit.
A power-law fluid has shear stress . It is shear thinning for , Newtonian for , and shear thickening for .
Viscoelasticity combines viscous dissipation with elastic storage and relaxation of deformation.
The conformation tensor describes the average stretch and orientation of polymer molecules. Its equilibrium value is the identity tensor under a common normalization.
An objective time derivative transforms covariantly under time-dependent rigid changes of observer, so constitutive predictions do not depend on the observer's rotation.
The Oldroyd-B model combines a Newtonian solvent with infinitely extensible Hookean polymer dumbbells. It predicts constant shear viscosity, a positive first normal-stress difference, and an extensional catastrophe at a finite extension rate.
The FENE-P model replaces infinitely extensible Hookean polymers by finitely extensible nonlinear elastic springs with a mean-field closure. Finite extensibility regularizes the Oldroyd-B extensional catastrophe and produces shear thinning.
The Oldroyd-A model is the lower-convected counterpart of the Oldroyd-B model: its polymeric stress evolves using a lower-convected derivative.
The uniaxial extensional viscosity is the tensile normal-stress difference divided by the imposed extension rate.
The Trouton ratio is extensional viscosity divided by shear viscosity. It approaches three for an incompressible Newtonian fluid in uniaxial extension.
Suspension rheology relates particle concentration, particle pressure, shear stress, deformation rate, and fluid migration in a mixture of particles and a liquid.
Jamming is the loss of the ability of a dense disordered material to flow as its particle fraction or applied confinement reaches a critical state.
Shear-induced dilation is the tendency of a dense granular or suspended-particle packing to increase its volume under shear. In a saturated confined system it requires pore-fluid migration and can delay stress adjustment.
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A non-Newtonian fluid is a type of fluid whose viscosity changes with the applied shear rate or shear stress, unlike Newtonian fluids, which have a constant viscosity regardless of the applied forces. In simpler terms, the behavior of non-Newtonian fluids can vary depending on how they are being acted upon.