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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.
The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...
In rheology, shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain. It is sometimes considered synonymous for pseudo- plastic behaviour, [ 1 ] [ 2 ] and is usually defined as excluding time-dependent effects, such as thixotropy .
The Herschel–Bulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a complicated, non-linear way. Three parameters characterize this relationship: the consistency k , the flow index n , and the yield shear stress τ 0 {\displaystyle \tau _{0}} .
Rheology (/ r iː ˈ ɒ l ə dʒ i /; from Greek ῥέω (rhéō) 'flow' and -λoγία (-logia) 'study of') is the study of the flow of matter, primarily in a fluid (liquid or gas) state but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force.
The power law model is used to display the behavior of Newtonian and non-Newtonian fluids and measures shear stress as a function of strain rate. The relationship between shear stress, strain rate and the velocity gradient for the power law model are: τ x y = − m | γ ˙ | n − 1 d v x d y , {\displaystyle \tau _{xy}=-m\left|{\dot {\gamma ...
The chemical potential μ is, by definition, the energy of adding an extra electron to the fluid. This energy may be decomposed into a kinetic energy T part and the potential energy − eφ part. Since the chemical potential is kept constant, Δ μ = Δ T − e Δ ϕ = 0. {\displaystyle \Delta \mu =\Delta T-e\Delta \phi =0.}
Rheometry (from Greek ῥέος (rheos) 'stream') generically refers to the experimental techniques used to determine the rheological properties of materials, [1] that is the qualitative and quantitative relationships between stresses and strains and their derivatives.