Radial migration of spherical particles in couette systems

Abstract

Several studies have been made in Couette systems of the primary motion (angular translation and rotation) of spheres suspended in viscous liquids. Radial migration trajectories, however, have been unreported for single spheres.In this study, a prediction of radial migration is developed and compared with experimental measurements. The predicted trajectories were found to agree well with the measured ones.Ultimately, radiolly migrating spheres reached an equilibrium position located approximatelY midway between the cylinder walls. The model developed predicted on equilibrium position just slightly inside the midpoint, while measured equilibrium positions fell between the midpoint and 0.4, the annular thickness from the inner cylinder walls. The differences in equilibrium positions are attributed to the approximate nature of the model.Segrk and Silberberg's (1) observation of radial migration of spheres suspended in a Newtonian liquid flowing through a tube stimulated considerable interest in such migration phenomena. Most subsequent experimental and theoretical works have been restricted to tube systems. Although Poiseuille flow systems have been given considerable attention, a basically simpler system, the Couette system, has been essentially ignored. Because the shear induced in a properly proportioned Couette system is nearly constant, it offers theoretical problems which are more simply approached than those posed by the Poiseuille system. The present work derives a semiempirical lateral force for use in predicting radial migration in a Couette system, a system more easily analyzed than the tube system, and hence more adapted to establishing the fundamental reasons for migration phenomena.Segrk and Silberberg's (1 ) initial observations with neutrally buoyant spheres, freely translating and rotating, convincingly demonstrated the existence of laterally directed forces. Extensions of their observations include those to nonrotating spheres (2) and to spheres with a density different from the density of the liquid (3). Several other authors have reported on various aspects of this phenomena (4, 5 ) .Several authors have derived expressions for the lateral force acting on a sphere under viscous flow conditions. Rubinow and Keller (6) derived such an expression by considering a rotating sphere translating through a stationary Newtonian fluid and applying the method of matched asymptotic expansions.A laterally directed force proportional to the velocity of translation of the sphere and its rate of rotation was derived. This result has been applied to explain migration phenomena in Poiseuille systems even though the result applies only to a quiescent fluid. While limited success has been obtained with this result in explaining experimental Poiseuille data, there are fundamental objections to such applications (7).Saffman (8) calculated a laterally directed surface force by considering a rotating sphere translating through a sheared fluid. The direction of translation was parallel to the free stream velocity. Saffman...

CFD simulation of an internal spin-filter: evidence of lateral migration and exchange flow through the mesh

“…Cell concentrations very close to the mesh are decreased approximately to the half of the bulk concentration. Such a depletion of cells in the vicinity of the sieve is consistent with the lateral migration observed in Taylor-Couette flow (Halow and Wills 1970). Therefore, it can be stated that the CFD model predicts the occurrence of lateral particle migration.…”

Elastic moduli of a solid containing spherical inclusions

“…When the viscosity of a suspension is measured in a Couette viscometer, the dispersed spheres tend to migrate away from the walls (Halow and Wills, 1970), creating an inhomogeneous suspension. Similar concentration inhomogeneities occur in other types of viscometers (see Leal, 1980).…”

Inertial migration of deformable droplets in a microchannel

“…The closed-form solutions for the lateral force of neutrally buoyant spheres were in good agreement with experimental observations in terms of equilibrium positions and trajectories of migrations. [39][40][41] The general form 6 of the lift force indicated that the interaction of the disturbance stresslet and its wall correction with the bulk shear produces a force toward the centerline, while the interaction between the stresslet and the curvature of the bulk velocity profile tends to cause migration in the direction of increasing (absolute) shear rate, where the stresslet is the symmetric first moment of the surface stress of a body in a flowing fluid.…”