Journal of Theoretical
and Applied Mechanics

12, 4, pp. 561-576, Warsaw 1974

Powolne przepływy cieczy lepkosprężystych w obszarach wejściowych rur i kanałów

Stefan Zahorski
Viscoelastic flows in the inlet regions of tubes and plane channels are discussed under the assumption of small Reynolds numbers (quasi-static approximation) and small ratios of the tube diameter or the channel height to the entrance lengths. In a static analysis of the problem, nothing specific is assumed about the constitutive equations, which may be those describing an incompressible simple fluid. Certain solutions for stresses or normal thrusts on the walls are obtained in the form involving three arbitrary functions subjected to boundary conditions. The entrance lengths can be determined if, apart from the first normal stress difference, the corresponding entrance lengths and pressure drops are known for a purely viscous fluid flowing under the same geometry. A simplified kinematic analysis for previously determined distributions of shear and normal stresses is presented under the assumption of an incompressible second grade fluid. It is shown, among other properties, that certain subregions of ,,solid-like'' or ,,semi-rigid'' behaviour may appear just at the entries. These subregions may extend across the entire duct, requiring either fluid fracture or slip at the walls for continued flow.