On the Motion of an Infinite Cylinder in Rotating ‘Non‐Newtonian’ Viscous Fluid

Abstract

The simple shear flow of pseudo-plastic and dila- tant fluids is expressed to a considerable degree of accuracy by the WAELE-OSTWALD'S formula where t is the shearing stress, du/dy is the velocity gradient, ppsu corresponds to the viscosity coefficient and has the dimensions (mass). / (1ength)n (time)zn - 1. The parameter n occurring in the formula (1) is a constant, denoting the rheological constant for the fluid and is usually a non-integral quantity. In the special case of n = 1 the relation (1) is linear and this situation corresponds to the case of NEwToNian fluids. The flow is non-Nl3wToNian for other values of n and is called pseudo-plastic if 7i > 1 and is called dilatant if n < 1. The constitutive relation connecting the stress and rate of strain components is non- linear in these cases and a mathematical study of the hydrodynamical propert,ies of such fluids has been initiated by Y. TOMITA [l] by adopting the law