dHerschelBulkley

dHerschelBulkley is a mathematical model used to describe the flow behavior of certain non-Newtonian fluids. These fluids, unlike Newtonian fluids such as water, do not have a constant viscosity. Instead, their viscosity changes depending on the shear rate applied to them. The dHerschelBulkley model is a specific type of constitutive equation that accounts for this variable viscosity.

The model is characterized by three parameters. The first is the yield stress, which is the minimum stress that must be applied before the fluid begins to flow. Below this yield stress, the fluid behaves like a solid. Once the yield stress is exceeded, the fluid starts to flow. The second parameter is the consistency index, which describes how readily the fluid flows after the yield stress is overcome. The third parameter is the flow behavior index, which determines whether the fluid is shear-thinning (viscosity decreases with increasing shear rate), shear-thickening (viscosity increases with increasing shear rate), or Newtonian (viscosity is constant).

The dHerschelBulkley model is particularly useful for describing the behavior of fluids like toothpaste, ketchup, and certain drilling muds. These substances exhibit a yield stress, meaning they can hold their shape until a certain force is applied, after which they flow. The model's ability to incorporate both a yield stress and shear-dependent viscosity makes it a valuable tool in various engineering and scientific applications where the accurate prediction of fluid flow is important. It is an extension of simpler models like the Bingham plastic model and the power-law model, offering a more comprehensive description for a wider range of complex fluid behaviors.