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)




High-density polyethylene







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".