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...
In this paper we explore the global dynamics of an agent-type model for bubbles in gas-fluidized beds and demonstrate that these features are consistent with experimentally observed behavior. The model accounts for the simultaneous interactions of thousands of individual bubbles and includes mass-transfer and first-order reactions between the gas and solids so that the impact of the dynamics is reflected in reactant conversion. We start with model parameters that have been demonstrated to produce time average behavior consistent with experimental reactor measurements. By observing the temporal variations of spatially averaged bubble properties, we are able to clearly distinguish the onset of global low-dimensional features that appear to be consistent with previous observations. The most prominent of these features is a large-scale oscillation that exhibits intermittency with power-law scaling in the vicinity of a critical gas flow. We show that the oscillation occurs as the result of a globally synchronized horizontal movement of the bubbles toward the center of the reactor. The oscillation appears to be consistent with the occurrence of the so-called "slugging" phenomenon, which is known to have large effects on fluidized bed reactor performance. Although this model can clearly be further improved, its success in replicating several of the key features of slugging indicates that this approach can serve as a useful tool for understanding and possibly controlling fluidized bed dynamics. We also conjecture that this model may be useful for more generally understanding the occurrence of global features in high-dimensional, multi-agent systems.
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