# The Basic Equations of Non-Newtonian Fluid Mechanics

- 472 Downloads

## Abstract

Every fluid is a collection of groups of atoms and the behaviour of the constituent parts of these individual particles and their interactions has been described mathematically with a degree of success. We can imagine solving a fluid flow problem, in theory, by considering every individual particle and interaction in a system and solving the equations that govern them. These types of equations are very difficult and such systems have only been solved approximately for a small number of atoms. This atomic ‘bottom-up’ solution scheme is extremely difficult for most of the macroscopic flow problems of interest to the rheologist. Fortunately this presents no real obstacle as the position and motion of very particle in a fluid is of no concern to bulk measurement. Macroscopic phenomena such as flow rate or pressure distribution occur over length and time scales well in excess of the microscopic behaviour of a fluid e.g. the average polymer length or mean free flight time of a gas molecule. Consequently we are afforded the luxury of the continuum mechanics perspective. From this viewpoint, every fluid is seen as a continuous medium interacting with itself rather than as a collection of particles interacting with each other. The velocity and forces within a fluid are characterised by vector and tensor fields over a continuous domain rather than by assigning a velocity vector to a discrete number of particles and a force vector to bonds between particles.

## Keywords

Constitutive Equation Extensional Viscosity Giesekus Model Normal Stress Coefficient Upper Convect Maxwell## Preview

Unable to display preview. Download preview PDF.

## Selected References

- [1.]OLDROYD, J.G. (1984) J. Non-Newtonian Fluid Mechanics
**14**, 9–46.zbMATHCrossRefGoogle Scholar - [2.]TRUESDELL, C. AND NOLL, W. (1956) “The non-Linear Field Theories of Mechanics” Springer Verlag.Google Scholar
- [3.]LODGE, A.S. (1974) “Body-Tensor fields in Continuum Mechanics” Pergamon Press.Google Scholar
- [4.]SCHOWALTER, W.R. (1978) “Mechanics of non-Newtonian Fluids” Pergamon Press.Google Scholar
- [5.]BIRD, R.B., ARMSTRONG, R.A. AND HASSAGER, O. (1987) “Dynamics of Polymeric Liquids” Vol 1 Fluid Mechanics, 2nd Edition. John Wiley and Sons.Google Scholar
- [6.]BARNES, H.A., HUTTON, J.F. AND WALTERS, K. (1989) “An Introduction to Rheology” Elsevier.zbMATHGoogle Scholar
- [7.]WALTERS, K. AND WATERHOUSE, W.M. (1977) J. Non-Newtonian FluidMechanics
**3**, 293–296.CrossRefGoogle Scholar - [8.]WHITE, J.L. AND METZNER, A.B. (1963) J.Appl.Polym.Sci.
**7**, 1867–1889.CrossRefGoogle Scholar - [9.]CRIMINALE, W.O., ERICKSEN, J.L. AND FILBEY, G.L. (1958) Arch.Rat. Mech.Anal.
**1**, 410–417.MathSciNetzbMATHCrossRefGoogle Scholar - [10.]GIESEKUS, H. (1963) Rheol.Acta.
**3**, 59–71.CrossRefGoogle Scholar - [11.]TANNER, R.I. AND PIPKIN, A.C. (1969) Trans.Soc.Rheol.
**13**, 471–484.CrossRefGoogle Scholar