On the Mechanics of Non-Newtonian Media

Abstract

The extension of Newton’s shearing law is aimed at the tensions being expressed by means of a general type equation. The case of the Bingham type media is considered and the components of the tensions tensor for homogeneous isotropic bodies are obtained in an orthogonal system of coordinates. The notion of viscosity is also extended by the introduction of viscosities of any order n, having the dimensions (M/L)Tn−2 . The equation of motion upon any direction xi is then derived, extending thus the Navier-Stokes equations. Further the particular cases of incompressible fluids and steady motions are considered. Applications to simple cases are performed: The motion in tubes, coaxial cylinders, or between solid parallel surfaces. These applications lead, as particular forms of the general formulas obtained, to result in good agreement with those found by other authors (Paslay and Slibar, Milne, and so on). The flow between parallel plates is studied too, for different shearing laws. Finally, a more general form of the shearing stresses is considered and by the proposed generalization, the possibility of a direct unitary study of various continuous bodies of a great practical importance is obtained.