Bingham plastic

[1] It is used as a common mathematical model of mud flow in drilling engineering, and in the handling of slurries.

Figure 1 shows a graph of the behaviour of an ordinary viscous (or Newtonian) fluid in red, for example in a pipe.

However, the Bingham plastic again does not exhibit any shear rate (no flow and thus no velocity) until a certain stress is achieved.

For the Newtonian fluid the slope of this line is the viscosity, which is the only parameter needed to describe its flow.

The physical reason for this behaviour is that the liquid contains particles (such as clay) or large molecules (such as polymers) which have some kind of interaction, creating a weak solid structure, formerly known as a false body, and a certain amount of stress is required to break this structure.

Once the friction factor has been calculated the pressure drop can be easily determined for a given flow by the Darcy–Weisbach equation: where: An exact description of friction loss for Bingham plastics in fully developed laminar pipe flow was first published by Buckingham.

The Swamee–Aggarwal equation is used to solve directly for the Darcy–Weisbach friction factor f for laminar flow of Bingham plastic fluids.

The Swamee–Aggarwal equation is given by: Danish et al. have provided an explicit procedure to calculate the friction factor f by using the Adomian decomposition method.

Mayonnaise is a Bingham plastic. The surface has ridges and peaks because Bingham plastics mimic solids under low shear stresses .
Figure 1. Bingham Plastic flow as described by Bingham
Figure 2. Bingham Plastic flow as described currently