Motion of spheres and cylinders in viscoelastic fluids: Asymptotic behavior

Abstract

Experiments were conducted to elucidate the effect of fluid elasticity on the motion of single spherical and cylindrical particles in viscoelastic fluids. Aqueous solutions of polyacrylamide in the concentration range of 0.35–0.6% wt./vol. were used as test fluids. The phenomenon of drag enhancement was observed. The maximum drag enhancement occurred at a Weissenberg number (Wi) of 60, beyond which the inertial effects dominate over the viscoelastic effects. In order to signify the relative importance of fluid elasticity and inertia, the results in terms of drag enhancement are represented as a function of elasticity number (E = Wi/Re). The drag enhancement exhibited asymptotic behavior with variation in elasticity number which depicts the dominance of elastic and inertial forces over each other. Based on the observed experimental data, a correlation used to predict drag for the particles falling in viscoelastic fluids has been proposed by incorporating the fluid elasticity and inertia in terms of corrective elasticity number function f(E). Experiments were also conducted to investigate the effect of fluid elasticity on the orientation of cylindrical particles settling in Newtonian, non Newtonian inelastic and viscoelastic fluids. It is found that the tilt angle (with vertical, α), characterizing the orientation of cylinders, decreases with fluid elasticity. However, the reverse behavior is observed with similar particles settling in inelastic fluid with increase in Reynolds number, whereas tilt angle remains constant in Newtonian fluid. Further, an attempt has been made to generate a correlation used to predict the tilt angle as a function of elasticity number and aspect ratio.