Skewed Poiseuille-Couette flows of sPTT fluids in concentric annuli and channels

Abstract

Analytical solutions have been derived for the helical flow of PTT fluids in concentric annuli, due to inner cylinder rotation, as well as for Poiseuille flow in a channel skewed by the movement of one plate in the spanwise direction, which constitutes a simpler solution for helical flow in the limit of very thin annuli. Since the constitutive equation is a non-linear differential equation, the axial and tangential/spanwise flows are coupled in a complex way. Expressions are derived for the radial variation of the axial and tangential velocities, as well as for the three shear stresses and the two normal stresses. For engineering purposes expressions are given relating the friction factor and the torque coefficient to the Reynolds number, the Taylor number, a nondimensional number quantifying elastic effects ( εDe 2) and the radius ratio. For axial dominated flows fRe and C M are found to depend only on εDe 2 and the radius ratio, but as the strength of rotation increases both coefficients become dependent on the velocity ratio ( ξ) which efficiently compacts the effects of Reynolds and Taylor numbers. Similar expressions are derived for the simpler planar case flow using adequate non-dimensional numbers.