# Bingham fluid

As Bingham fluids are special, according to Eugene C. Bingham named, non-Newtonian fluids referred. Their dynamic viscosity is a function of the shear rate (or shear gradient) and leads to a linear flow behavior:

${\ displaystyle \ tau = \ eta {\ frac {\ mathrm {d} v} {\ mathrm {d} y}} + \ tau _ {0}}$

With

${\ displaystyle \ tau}$: Shear stress
${\ displaystyle {\ frac {\ mathrm {d} v} {\ mathrm {d} y}}}$: Shear rate
${\ displaystyle \ eta}$: dynamic viscosity
${\ displaystyle \ tau _ {0}}$: Yield point

This means that a Bingham fluid only begins to flow from a minimum shear stress, the yield point . Below it it behaves like a rigid solid. However, many materials also exhibit elastic material behavior; these materials are described in rheology by the Bingham model . ${\ displaystyle \ tau _ {0}}$

## Examples

Examples of Bingham fluids are ketchup , toothpaste , yeast dough and certain wall paints , but also blood . Technically used suspensions such as electro- and magnetorheological fluids as well as fresh concrete (concrete before hydration ) can also be described with a Bingham model. These fluids only go into a flow state when a certain shear stress is reached. This happens e.g. B. if you press the wall roll with paint on it on the wall and roll it off. At this moment the shear forces become so great that the paint changes into a flow state and wets the wall. As long as the paint is on the roller - largely without external force - it behaves like an elastic solid and does not drip off the roller.