SEDIMENTATION OF PARTICLES IN POLYMER-SOLUTIONS

In this paper, we present detailed and systematic experimental results on the sedimentation of solid particles in aqueous solutions of polyo x and polyacrylamide, and in solutions of polyox in glycerin and water . The tilt angles of long cylinders and flat plates falling in these v iscoelastic liquids were measured. The effects of particle length, par ticle weight, particle shape, liquid properties and liquid temperature were determined. In some experiments, the cylinders fall under gravit y in a bed with closely spaced walls. No matter how or where a cylinde r is released the axis of the cylinder centres itself between the clos e walls and falls steadily at a fixed angle of tilt with the horizonta l. A discussion of tilt angle may be framed in terms of competition be tween viscous effects, viscoelastic effects and inertia. When inertia is small, viscoelasticity dominates and the particles settle with thei r broadside parallel or nearly parallel to the direction of fall. Norm al stresses acting at the comers of rectangular plates and squared-off cylinders with flat ends cause shape tilting from the vertical. Cylin ders with round ends and cone ends tilt much less in the regime of slo w flow. Shape tilting is smaller and is caused by a different mechanis m to tilting due to inertia. When inertia is large the particles settl e with their broadside perpendicular to the direction of fall. The til t angle varies continuously from 90-degrees when viscoelasticity domin ates to 0-degrees when inertia dominates. The balance between inertia and viscoelasticity was controlled by systematic variation of the weig ht of the particles and the composition and temperature of the solutio n. Particles will turn broadside-on when the inertia forces are larger than viscous and viscoelastic forces. This orientation occurred when the Reynolds number Re was greater than some number not much greater t han one in any case, and less than 0.1 in Newtonian liquids and very d ilute solutions. In principle, a long particle will eventually turn it s broadside perpendicular to the stream in a Newtonian liquid for any Re > 0, but in a viscoelastic liquid this turning cannot occur unless Re > 1. Another condition for inertial tilting is that the elastic len gth lambdaU should be longer than the viscous length nu/U where U is t he terminal velocity, nu is the kinematic viscosity and lambda = nu/c2 is a relaxation time where c is the shear wave speed measured with th e shear wave speed meter (Joseph 1990). The condition M = U/c > 1 is p rovisionally interpreted as a hyperbolic transition of solutions of th e vorticity equation analogous to transonic flow. Strong departure of the tilt angle from theta = 90-degrees begins at about M = 1 and ends with theta = 0-degrees when 1 < M < 4.