A Bingham plastic is a
viscoplasticmaterial that behaves as a rigid body at low stresses but flows as a viscous fluidat high stress. It is named after Eugene C. Binghamwho proposed its mathematical form. [E.C. Bingham,(1916) "U.S. Bureau of Standards Bulletin", 13, 309-353 "An Investigation of the Laws of Plastic Flow"] .
It is used as a common
mathematical modelof mudflow in offshore engineering, and in the handling of slurries. A common example is toothpasteJ. F. Steffe (1996) "Rheological Methods in Food Process Engineering" 2nd ed ISBN 0-9632036-1-4] , which will not be extrudeduntil a certain hydrostatic pressureis used on the tube. It then is pushed out as a solid plug.
Figure 1 shows a graph of the behaviour of an ordinary viscous (or Newtonian) fluid in red, for example in a pipe. If the pressure at one end of a pipe is increased this produces a stress on the fluid tending to make it move (called the
shear stress) and the volumetric flow rate increases proportionally. However for a Bingham Plastic fluid (in blue), stress can be applied but it it will not flow until a certain value, the yield stress, is reached. Beyond this point the flow rate increases steadily with increasing shear stress. This is roughly the way in which Bingham presented his observation, in an experimental study of paints. [E. C. Bingham (1922) "Fluidity and Plasticity" McGraw-Hill (New York) page 219]
Figure 2 shows the way in which it is normally presented nowadays. The graph shows
shear stresson the vertical axis and shear rateon the horizontal one. (Volumetric flow rate depends on the size of the pipe, shear rate is a measure of how the velocity changes with distance. It is proportional to flow rate, but does not depend on pipe size.) As before, the Newtonian fluid flows and gives a shear rate for any finite value of shear stress. 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. By contrast the Bingham Plastic requires two parameters, the yield stress and the slope of the line, known as the plastic viscosity.
The physical reason for this behaviour is that the liquid contains particles (e.g. clay) or large molecules (e.g. 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 structure has been broken, the particles move with the liquid under viscous forces. If the stress is removed, the particles associate again.
The material is rigid for
shear stress"τ", less than a critical value . Once the critical shear stress (or "yield stress") is exceeded, the material flows as a Newtonian fluidwith incremental shear stress and shear rate, ∂"u"/∂"y", (as defined in the article on viscosity) related by:
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Bingham plastic liquid — klampiai plastiškas skystis statusas T sritis chemija apibrėžtis Skystis, kuris pradeda tekėti, kai tangentinis įtempis pasiekia takumo ribą. atitikmenys: angl. Bingham plastic liquid; viscoplastic fluid rus. вязкопластическая жидкость ryšiai:… … Chemijos terminų aiškinamasis žodynas
Bingham — may refer to:In people: *Bingham (surname)On the moon: *Bingham (crater), a lunar craterIn the United Kingdom: *Bingham, Nottinghamshire, a town *Bingham, Edinburgh, a suburbIn the United States: *Bingham, Illinois *Bingham, Maine, the town… … Wikipedia
plastic — 1. Capable of being formed or molded. 2. A material that can be shaped by pressure or heat to the form of a cavity or mold. [G. plastikos, relating to molding] Bingham p. a material that, in the idealized case, does not flow … Medical dictionary
Bingham — Eugene C., U.S. chemist, 1878–1945. See B. flow, B. model, B. plastic … Medical dictionary
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