Nächste Seite:Magnetohydrodynamic equationsAufwärts:Models of Mathematical PhysicsVorherige Seite:Extensible beam with attached

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 equationsAufwärts:Models of Mathematical PhysicsVorherige Seite:Extensible beam with attached
collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg