Power law (liquid)

In the material laws of rheology ( flow laws ), non-linear approximation approaches according to power laws are often made in order to be able to describe the behavior of non-Newtonian liquids .

Shear stress-shear rate diagram:
1: dilatant fluid
2: Newtonian fluid
3: shear-thinning (pseudoplastic) fluid
4: Bingham plastic fluid
5: Casson plastic fluid

The general law of power , also called the Herschel-Bulkley relation , is:

${\displaystyle \tau =\tau _{o}+k\cdot {\dot {\gamma }}^{n}}$ with the yield point . ${\displaystyle \tau _{o}}$

With the parameters one obtains the two-parameter flow law according to Ostwald and de Waele : ${\displaystyle \tau _{o}=0}$

${\displaystyle \tau =k\cdot {\dot {\gamma }}^{n}}$,

there are:

• ${\displaystyle \tau }$: Shear stress (see stress (mechanics) )
• k : consistency
• ${\displaystyle {\dot {\gamma }}}$: Shear rate
• n : flow exponent or flow index.

The flow exponent n characterizes the deviation from Newtonian behavior:

• n <1: pseudoplastic (shear thinning) and pseudoplastic ( plasticity )
• n = 1: Newtonian
• n > 1: dilatant (shear thickening).

See also

• Flow curve