Annular Effect in Viscoelastic Fluids

Abstract

In the oscillating motion of an incompressible viscoelastic fluid in a pipe, at high Reynolds number the root‐mean‐square axial velocity has its maximum value in a boundary layer at the wall of the tube. The elasticity of the fluid can make this annular effect much more pronounced than it is in the case of a Newtonian viscous fluid. The analysis is carried out for small‐amplitude oscillations of a general viscoelastic fluid, and the exact solution for this case is compared with the solution obtained by the boundary‐layer approximation. The solution in the case of slow motion of arbitrary amplitude is also considered, and it is shown that no annular effect occurs in this case.