Perspectives on Using Implicit Type Constitutive Relations in the Modelling of the Behaviour of Non-Newtonian Fluids

Abstract

We discuss the benefits of using the so-called implicit type constitutive relations introduced by K. R.

Rajagopal, J. Fluid Mech. 550, 243-249 (2006) and K.

R. Rajagopal, Appl.

Math. 48, 279-319 (2003) in the description of the behaviour of non-Newtonian fluids. In particular, we focus on the benefits of using the implicit type constitutive relations in the mathematical modelling of fluids in which the shear stress/shear rate dependence is given by an S-shaped curve, and in modelling of fluids that exhibit nonzero normal stress differences.

We also discuss a thermodynamical framework that allows one to cope with the implicit type constitutive relations.

Keywords

• law-like rheology
• incompressible fluids
• irreversible-processes
• reciprocal relations
• polymer-solutions
• steady flows
• stresses