Index

Bingham law

Ver: 1
 

DESCRIPTION

For a generalized Newtonian fluid, the constitutive equation has the form

S = 2 * eta * D

where S is the extra-stress tensor, D is the rate of deformation tensor, and eta is the viscosity.

The shear-rate dependence of the viscosity is denoted by a function F(g), where g is the shear-rate.
For the Bingham law, the function F(g) is written as follows :
 
F(g) = fac + ystr / g when g > gcrit
= fac + ystr / gcrit  * (2 - g/gcrit)  when g < gcrit

where fac is the zero shear-rate viscosity, ystr is a yield stress, and gcrit is a critical shear-rate. The above mentioned expression for the Bingham law has been selected in view of its C1-continuity at g = gcrit.

By default, fac = 1, ystr = 1 and gcrit = 1.
 

OPTIONS
 
 -1   Upper level menu
  1   Modify  fac    = 1.0000000E+00
  2   Modify  ystr   = 1.0000000E+00
  3   Modify  gcrit  = 1.0000000E+00
NOTES In many situations, the use of a Picard iteration for the viscosity is recommeded instead of a full Newton iteration.
An evolution scheme can also be used.

The units for g and the parameters fac, ystr and gcrit are :
 
 parameter
mass
length
time
temperature
g, gcrit
-
-
-1
 -
fac
1
-1
-1
 -
ystr
1
-1
-2
 -

SEE ALSO
generalized Newtonian fluids (UM)
continuum equations (UM)
shear-rate dependence of viscosity
evolution (UM)
s-dependence
create a new task
system of units