Particle Motion in a Liquid Film Rimming the Inside of a Partially Filled Rotating Cylinder

Both lighterand hydrophobic heavier-than-liquid particles will float on liquid–air surfaces. Capillary forces cause the particles to cluster in typical situations identified here. This kind of clustering causes particles to segregate into islands and bands of high concentrations in thin liquid films rimming the inside of a slowly rotating cylinder partially filled with liquid. A second regime of particle segregation, driven by secondary motions induced by off-centre gas bubbles in a more rapidly rotating cylinder at higher filling levels, is identified. A third regime of segregation of bidisperse suspensions is found in which two layers of heavierthan-liquid particles that stratify when there is no rotation, segregate into alternate bands of particles when there is rotation. Disciplines Engineering | Mechanical Engineering Comments Suggested Citation: Joseph, Daniel D. et. al. (2003). Particle motion in a liquid film rimming the inside of a partially filled rotating cylinder. Journal of Fluid Mechanics. Vol. 496. p. 139-163. Copyright 2003 Cambridge University Press. http://dx.doi.org/10.1017/S0022112003006451 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/meam_papers/208 J. Fluid Mech. (2003), vol. 496, pp. 139–163. c © 2003 Cambridge University Press DOI: 10.1017/S0022112003006451 Printed in the United Kingdom 139 Particle motion in a liquid film rimming the inside of a partially filled rotating cylinder By D. D. JOSEPH, J. WANG, R. BAI, B. H. YANG AND H. H. HU Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA (Received 19 August 2002 and in revised form 24 July 2003) Both lighterand hydrophobic heavier-than-liquid particles will float on liquid–air surfaces. Capillary forces cause the particles to cluster in typical situations identified here. This kind of clustering causes particles to segregate into islands and bands of high concentrations in thin liquid films rimming the inside of a slowly rotating cylinder partially filled with liquid. A second regime of particle segregation, driven by secondary motions induced by off-centre gas bubbles in a more rapidly rotating cylinder at higher filling levels, is identified. A third regime of segregation of bidisperse suspensions is found in which two layers of heavier-than-liquid particles that stratify when there is no rotation, segregate into alternate bands of particles when there is rotation. 1. Capillary forces The deformation of the air–liquid interface due to floating light particles or due to trapped heavy small particles gives rise to capillary forces on the particles. These forces may be qualitatively understood from simple arguments. Three kinds of force act on particles: forces due to gravity; forces due to the action of contact angles; and the pressure forces. These three kinds of force are at play in the vertical force balance, but require a somewhat more elaborate explanation for horizontal force balance. The effects of gravity are usually paramount for heavier-than-liquid floating particles in which one particle will fall into the depression of the second. A heavier-than-liquid particle will fall down a downward sloping meniscus while an upward buoyant particle will rise. Capillary forces cause particles to cluster, as shown in figure 4. In this section, we shall review the nature of capillary forces which cause the particles to cluster; in § 2, we show how these forces produce islands and bands of segregated particles in a thin liquid film rimming the inside of a slowly rotating cylinder. 1.1. Vertical forces The simplest analysis relevant to understanding the forces on small particles is the vertical force balance on a sphere floating on the interface between fluids which, for convenience, is here called water and air. This analysis was given first by Princen (1969), then by Rapacchietta & Neumann (1977) and by Kotah, Fujita & Imazu (1992), who used the floating ball to measure contact angles. 140 D. D. Joseph, J. Wang, R. Bai, B. H. Yang and H. H. Hu Tangent to point of contact Tangent to meniscus Air