Free Fall of a Sphere in a Partially Lubricated Cylinder

[+] Author and Article Information
Roger F. Gans

Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627

J. Appl. Mech 58(3), 812-819 (Sep 01, 1991) (8 pages) doi:10.1115/1.2897267 History: Received November 09, 1989; Revised March 13, 1990; Online March 31, 2008


The entrainment of lubricant at the entrance of a lubrication zone, such as that of a partially starved slider bearing, is analyzed in a closed system using the method of matched asymptotic expansions. A sphere falling together with a small lens of lubricant in a closely fitting tube is shown to fall under gravity at a speed

V = (Mg − Fc)[(RC − RS)/RC]/(16π2μRC)
, where M denotes the total mass of the system, sphere plus lubricant, g the acceleration of gravity, F c the differential contact force, μ the viscosity of the lubricant, and R C and R S the radii of the tube and the sphere, respectively. Potential biological applications and experimental verification are discussed.

Copyright © 1991 by The American Society of Mechanical Engineers
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