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##
Quasi-static Bingham fluid

Let
be a bounded domain in .
The flow of a Bingham fluid through
is described by the following system of equations:
Here
is the density of the applied outer forces. The tensor
satisfied the following constituent law:
If
then we claim
Furthermore let
and .
denotes the strain velocity and
the corresponding stress. Strain velocity can be expressed in terms of
the velocity field
where
is the vector field of displacements. We have
Note that
is the so-called tensor divergence, which iimage is a vector.
is the gradient for spatial variables. Boundary conditions are imposed
for
and .

Bingham fluids have a quasi-static viscoelastic material behaviour.
A good reference for this model is the book written by G. Astarita and
G. Marrucci (*Principles of Non-Newtonian Fluid Mechanics*, McGraw-Hill,
London 1974). If
then we have the case of the so-called *Norton fluid*. In the last
time energy minimising concepts become important. Note that the energy
can be given by the functional

**A late reference:** M. Fuchs, J.F. Grotowski and Reuling J. (1996),
*On variational models for Quasi-static Bingham Fluids* MMAS, 19,
991-1015.

**Nächste Seite:**Magnetohydrodynamic
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collected and worked out by Wolfgang Sprößig, TU-Bergakademie
Freiberg