Non newtonian viscoelastic fluid
1 - A classification of fluids
2 -Descrition of viscoelastic fluids
There are both viscous and elastic : elasticity generates a memory effect whereas viscosity reduces it in time. This phenomenom is called evanescent memory. Thus we can define a characteristic time and a memory function for these fluids.
where M(t-t') is a decreasing memory function.
Examples ( R.I. Tanner)
Fluid type |
Temperature (K) |
Relax time (s) |
Water |
293 |
10^{-12} |
High-density polyethylene |
453 |
0.07 |
Glass |
300 |
>10^{5} |
3 - Behaviour laws of viscoelastic fluids
As there is a huge diversity of fluids, plenty of laws exists and so makes modelling difficult. Here we gives three examples of differential law ( an other form is the integral written used to express the memory function).
This comes from an approach of fluid such a continous
material.
Newton laws for viscous material
Hooke's law for elastic material
Maxwell's law - synthesis of the previous expressions
that became
a = -1 : under-convected derivate
a = 0 : Jaumann's derivate
a = 1 : over-convected derivate
Macromolecules can be modelled by "elastic dumbbell". We use :
The over-convected Oldroyd's law is :
It comes from modelling of high-density polymeres with "networks models".