We here attempt to give a complete but concise treatment of the theory
of steady viscometric flows of simple (non-Newtonian) fluids and to use
that theory to discuss the design and interpretation of ex- periments.
We are able to present the theory with less mathematical machinery than
was used in our original papers, partly because this Tract has more
limited aims than those papers, and partly because we employ a method,
found by Noll and published here for the first time, for dealing with
visco metric flows without the apparatus of rela- tive Cauchy-Green
tensors and reduced constitutive equations. To make the theory
accessible to students not familiar with modern mathematics, we have
added to our Tract an appendix explaining some of the mathe- matical
concepts essential to continuum physics. Pittsburgh, July 1965 BERNARD
D. COLEMAN HERSHEL MARKOVITZ WALTER NOLL CONTENTS I. Introduction
page 1. Limitations of the Classical Theory of Navier and Stokes. 1 5 2.
Incompressible Simple Fluids. . . . . . . . . . . . 3. Plan and Scope of
this Monograph . . . . . . . . . 7 II. Theory of Incompressible Simple
Fluids 4. Kinematics. . . . . . . . . . . . 10 5. The Dynamical
Equations . . . . . . . . . . . 12 6. The Principle of Material
Objectivity . . . . . . 14 7. The Definition of an Incompressible Simple
Fluid . 17 8. Static Behavior of Simple Fluids . . . . . . . . 19 III.
General Theory of Viscometric Flows 9. The Kinematics of Simple Shearing
Flow 21 10. The Viscometric Functions . . . . . . . . . . 22 11. The
Dynamics of Simple Shearing Flow; Viscosity 26 12. The Definition of a
Viscometric Flow 29 13. Curvilineal Flows. . . . . . . . 30 1.
Kinematical Description . . . .
