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Sedimentation of particles in polymer solutions

Published online by Cambridge University Press:  26 April 2006

Yaoqi Joe Liu  and
Daniel D. Joseph
Yaoqi Joe Liu
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street SE, Minneapolis, MN 55455, USA
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, 107 Akerman Hall, 110 Union Street SE, Minneapolis, MN 55455, USA
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Abstract

In this paper, we present detailed and systematic experimental results on the sedimentation of solid particles in aqueous solutions of polyox and polyacrylamide, and in solutions of polyox in glycerin and water. The tilt angles of long cylinders and flat plates falling in these viscoelastic liquids were measured. The effects of particle length, particle weight, particle shape, liquid properties and liquid temperature were determined. In some experiments, the cylinders fall under gravity in a bed with closely spaced walls. No matter how or where a cylinder is released the axis of the cylinder centres itself between the close walls and falls steadily at a fixed angle of tilt with the horizontal. A discussion of tilt angle may be framed in terms of competition between viscous effects, viscoelastic effects and inertia. When inertia is small, viscoelasticity dominates and the particles settle with their broadside parallel or nearly parallel to the direction of fall. Normal stresses acting at the corners of rectangular plates and squared-off cylinders with flat ends cause shape tilting from the vertical. Cylinders with round ends and cone ends tilt much less in the regime of slow flow. Shape tilting is smaller and is caused by a different mechanism to tilting due to inertia. When inertia is large the particles settle with their broadside perpendicular to the direction of fall. The tilt angle varies continuously from 90° when viscoelasticity dominates to 0° when inertia dominates. The balance between inertia and viscoelasticity was controlled by systematic variation of the weight of the particles and the composition and temperature of the solution. 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 than one in any case, and less than 0.1 in Newtonian liquids and very dilute solutions. In principle, a long particle will eventually turn its 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 length λU should be longer than the viscous length ν/U where U is the terminal velocity, ν is the kinematic viscosity and λ = ν/c2 is a relaxation time where c is the shear wave speed measured with the shear wave speed meter (Joseph 1990). The condition M = U/c > 1 is provisionally interpreted as a hyperbolic transition of solutions of the vorticity equation analogous to transonic flow. Strong departure of the tilt angle from θ = 90° begins at about M = 1 and ends with θ = 0° when 1 < M < 4.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 565 - 595
Copyright
© 1993 Cambridge University Press

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