What is a Herschel-Bulkley fluid?

A Herschel-Bulkley fluid is a generalized mathematical model used to describe non-Newtonian fluids that exhibit yield stress alongside shear-thinning or shear-thickening behavior. Introduced in 1926 by Winslow Herschel and Ronald Bulkley, the model relates fluid strain to stress using three specific parameters: consistency, flow index, and yield shear stress. It effectively extends simpler models like the Bingham plastic model to better represent complex substances such as toothpaste and blood.

What we know

• The Herschel-Bulkley fluid model is a generalized model of a non-Newtonian fluid where strain and stress are related in a non-linear way. [1, 2]
• The relationship is characterized by three parameters: the consistency k, the flow index n, and the yield shear stress. [2]
• The model was introduced by Winslow Herschel and Ronald Bulkley in 1926. [2]
• The Herschel-Bulkley model extends the Bingham plastic model to include shear-thinning or shear-thickening behaviors. [3]

Where to go next

• whoWho were Winslow Herschel and Ronald Bulkley?
• compared withHow does the Bingham plastic model compare?
• a case in pointWhat materials act like Herschel-Bulkley fluids?
• the bigger pictureWhat is rheology?
• how it workedHow do power-law fluids relate to non-Newtonian mechanics?
• an unexpected connectionHow does Heraclitus inspire the study of fluid deformation?The formal study of fluid flow and soft solids, known as rheology, was named using a term inspired by the ancient Greek philosopher Heraclitus and his aphorism that everything flows.

Sources

• [1]Herschel–Bulkley fluid (Wikidata Q10862968) · CC0 1.0
• [2]Herschel–Bulkley fluid · CC BY-SA 4.0
• [3]Rheology · CC BY-SA 4.0
• [4]Non-Newtonian fluid · CC BY-SA 4.0
• [5]Power-law fluid · CC BY-SA 4.0