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.

Examples ( R.I. Tanner)

Fluid type

Temperature (K)

Relax time (s)

Water

293

10-12

High-density polyethylene

453

0.07

Glass

300

>105

 

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".