On the flow of an elastico-viscous liquid in a curved pipe under a pressure gradient

Abstract

Consideration is given to the flow of an idealized elastico-viscous liquid in a curved pipe under a pressure gradient. By using the series expansion method of Dean (1927, 1928) in powers of a/R where a is the radius of the pipe and R the radius of curvature of its ‘central line’, it is shown that the general nature of the motion is similar to that of the motion of a Newtonian viscous liquid, the liquid elements moving along the pipe in two sets of spirals separated by the central plane. However elasticity of the type considered could strongly affect the pitch of these spirals. To the approximation considered, the flow pattern of the elastico-viscous liquid depends only on the limiting (zero-shear-rate) viscosity η₀ and the first moment, K₀, of the distribution of relaxation times. The corresponding stress components involve also the second moment of this distribution.It is also shown that the presence of elasticity in the liquid increases the rate of discharge of the liquid.