On steady flows of incompressible fluids with implicit power-law-like rheology

2009 ◽  
Vol 2 (2) ◽  
Author(s):  
Miroslav Bulíček ◽  
Piotr Gwiazda ◽  
Josef Málek ◽  
Agnieszka Świerczewska-Gwiazda
Keyword(s):  
Power Law ◽  
Incompressible Fluids ◽  
Steady Flows ◽  
Implicit Power

Variational study of steady flows stability in incompressible fluids

2000 ◽  
Vol 286 (3-4) ◽  
pp. 435-446
Author(s):  
Rafael González ◽  
A.C. Sicardi-Schifino ◽  
L.G. Sarasua
Keyword(s):  
Incompressible Fluids ◽  
Steady Flows ◽  
Variational Study

Exact solutions for two-dimensional steady flows of a power-law liquid on an incline

2005 ◽  
Vol 17 (1) ◽  
pp. 013102 ◽  
Author(s):  
Carlos Alberto Perazzo ◽  
Julio Gratton
Keyword(s):  
Exact Solutions ◽  
Power Law ◽  
Steady Flows ◽  
Two Dimensional

On steady flows of fluids with pressure– and shear–dependent viscosities

2005 ◽  
Vol 461 (2055) ◽  
pp. 651-670 ◽  
Author(s):  
M. Franta ◽  
J. Málek ◽  
K. R. Rajagopal
Keyword(s):  
Shear Rate ◽  
Weak Solutions ◽  
Velocity Gradient ◽  
Dirichlet Boundary ◽  
Incompressible Fluids ◽  
Dirichlet Boundary Conditions ◽  
Steady Flows ◽  
Existence Of Weak Solutions ◽  
Wide Range ◽  
Homogeneous Dirichlet Boundary Conditions

There are many technologically important problems such as elastohydrodynamics which involve the flows of a fluid over a wide range of pressures. While the density of the fluid remains essentially constant during these flows whereby the fluid can be approximated as being incompressible, the viscosity varies significantly by several orders of magnitude. It is also possible that the viscosity of such fluids depends on the shear rate. Here we consider the flows of a class of incompressible fluids with viscosity that depends on the pressure and shear rate. We establish the existence of weak solutions for the steady flows of such fluids subjected to homogeneous Dirichlet boundary conditions and to specific body forces that are not necessarily assumed to be small. A novel aspect of the study is the manner in which we treat the pressure that allows us to establish its compactness, as well as that of the velocity gradient. The method draws upon the physics of the problem, namely that the notion of incompressibility is an idealization that is attained by letting the compressibility of the fluid to tend to zero.

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