Herschel-Bulkley fluid (constitutive equation)


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}} \tau _{0}. The consistency is a simple constant of proportionality, while the flow index measures the degree to which the fluid is shear-thinning or shear-thickening. Ordinary paint is one example of a shear-thinning fluid, while oobleck provides one realization of a shear-thickening fluid. Finally, the yield stress quantifies the amount of stress that the fluid may experience before it yields and begins to flow.

This non-Newtonian fluid model was introduced by Winslow Herschel and Ronald Bulkley in 1926.

Related formulas


τshear stress (dimensionless)
τ0yield stress (dimensionless)
kconsistency index (dimensionless)
γshear rate (dimensionless)
nn (dimensionless)