Bingham plastic

A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who 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 model of mud flow 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 extruded until a certain hydrostatic pressure is 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 stress on the vertical axis and shear rate on 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 au_0. Once the critical shear stress (or "yield stress") is exceeded, the material flows as a Newtonian fluid with incremental shear stress and shear rate, ∂"u"/∂"y", (as defined in the article on viscosity) related by:

:frac {partial u} {partial y} = left{egin{matrix} 0 &, au < au_0 \ ( au - au_0)/ {mu} &, au ge au_0 end{matrix} ight.


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • 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

  • Fluide de Bingham — La mayonnaise est un fluide de Bingham. Les plis et crêtes à la surface montrent que sous de faibles contraintes de cisaillement, les fluides de Bingham sont des quasi solides. Le fluide de Bingham est un modèle théorique de milieu viscoplastique …   Wikipédia en Français

  • Eugene C. Bingham — Eugene Cook Bingham, born 7 December 1878, died 6 November 1945 [ New York Times , November 7, 1945, p 23 DR. EUGENE BINGHAM; Leading Rheologist Organized Society in 1929 Dies at 67 ] , was a professor and head of the Department of Chemistry at… …   Wikipedia

  • Viscoplasticity — Figure 1. Elements used in one dimensional models of viscoplastic materials. Viscoplasticity is a theory in continuum mechanics that describes the rate dependent inelastic behavior of solids. Rate dependence in this context means that the… …   Wikipedia

  • Non-Newtonian fluid — Continuum mechanics …   Wikipedia

  • Magnetorheological fluid — Continuum mechanics …   Wikipedia

  • Derivation of the Navier–Stokes equations — The intent of this article is to highlight the important points of the derivation of the Navier–Stokes equations as well as the application and formulation for different families of fluids. Contents 1 Basic assumptions 2 The material derivative 3 …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.