The Basic Equations of Non-Newtonian Fluid Mechanics

  • R. N. Jones
  • K. Walters
Part of the NATO ASI Series book series (NSSE, volume 302)


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.


Constitutive Equation Extensional Viscosity Giesekus Model Normal Stress Coefficient Upper Convect Maxwell 
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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • R. N. Jones
    • 1
  • K. Walters
    • 1
  1. 1.Department of MathematicsUniversity of WalesAberystwythUK

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