Flow of elastico-viscous liquids in channels under the influence of a periodic pressure gradient, part 1

Abstract

The flow of a non-Newtonian incompressible liquid in a straight pipe of circular cross-section under the influence of a periodic pressure gradient is investigated; the viscous and elastic properties of the liquid are defined in terms of a spectrum of relaxation times. Such a flow is of interest to the experimentalist, because the flow could be readily attained and controlled in practice. A solution is obtained which determines the variation in the mean-square velocity over the section of the pipe. In the numerical illustrations given, it is shown that the general nature of the flow is similar to that of a purely viscous liquid of constant viscosity, a high peak of average velocity occurring near the wall of the pipe. However, it is shown that elasticity of the type considered could strongly affect the value and position of this peak of the average velocity.