- Bingham plastic
A Bingham plastic is a
viscoplastic material that behaves as a rigid body at low stresses but flows as a viscousfluid at high stress. It is named afterEugene 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 ofmud flow in offshore engineering, and in the handling of slurries. A common example istoothpaste J. F. Steffe (1996) "Rheological Methods in Food Process Engineering" 2nd ed ISBN 0-9632036-1-4] , which will not beextruded until a certainhydrostatic pressure is used on the tube. It then is pushed out as a solid plug.Explanation
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, theyield 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]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.
Definition
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 aNewtonian fluid with incremental shear stress andshear rate , ∂"u"/∂"y", (as defined in the article onviscosity ) 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.
References
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