Stability Problems for Viscoelastic Fluids

Abstract

Molten plastics, petroleum oil additives and whipping creams are examples of incompressible viscoelastic fluids. The flow of such fluids requires effects without parallel in the flow of Newtonian fluids like air and water. Particularly striking effects occur when there are free surfaces which give a visual display of normal stresses which must exist in viscoelastic fluids when strong shearing motions are forced. For example, the rotation of a small rod in water induces a depression in the free surface around the rod; when the same rod rotates in certain viscoelastic fluids, the fluid will climb the rod (see Figs. 95.1, 2, 3). When a horizontal water jet is extruded from a capillary tube at a high Reynolds number, the jet will contract; when certain viscoelastic fluids are extruded at the same Reynolds number from the same tube, the jet may swell to several times its final diameter (see Fig. 95.6a, b). Tall Taylor cells in viscoelastic fluids may stand four times taller than cells which exist under equivalent conditions in Newtonian fluids (see Figs. 95.7, 8). There is a stability problem for each of the three examples shown in the figures (see § 95).