円すい管内における非ニュートン流動の一般理論

抄録

The general theory of steady slow motion of non-Newtonian fluids through a tapered tube is presented in the present paper.
The general formulae for shear stress, velocity and flow have been obtained for a straight tube, a rotating coaxial cylinder viscometer, a cone and plate viscometer, and a double cone viscometer. However, no similar formula in general for non-Newtonian fluid through a tapered tube has yet been available.
It is assumed that the fluid is characterized by a time-independent flow curve f(τ), and that the tapering angle α is very small. It is further assumed that the coefficient of viscosity η which appears in the relationship between the stress and the strain rate of non-Newtonian fluid is not constant, but a function of the velocity gradient. Under these assumptions the following formulae for the shear stress, velocity, and flow have been obtained, which will be taken in general.
τ_a being the shear stress on the wall. These formulae, quite similar to those for a straight tube of uniform cross section, are applied to the following particular fluids: Newtonian fluid, power law fluid, Bingham body and the fluid obeying Casson's equation.