The motion of a single rigid sphere entrained in a glycerine-water solution flowing downward through a cylindrical tube has been investigated throughout a range of particle Reynolds numbers of 6.0 to 120.0, tube Reynolds numbers of 208 to 890, and particle-to-tube diameter ratios of 0.120 to 0.190. Trajectories of the sphere, calculated for various particle Reynolds numbers by using the Rubinow-Keller expression for the transverse force, were found to agree satisfactorily with experimentally determined trajectories when the particle Reynolds number was below 40.0. In all cases the sphere was observed to migrate to the axis of the tube. At the lower particle Reynolds numbers the sphere approached the axis asymptotically, whereos a t the higher particle Reynolds numbers the sphere oscillated across the axis of the tube one or more times during migration. All observations were made with spheres which were less dense than the fluid, the density difference being as high as 10% of the fluid density.Particle migration in a shear field refers to that phenomenon in which particles entrained in a flowing fluid move across fluid streamlines as a consequence of fluid dpamic forces. In systems where numerous particles are entrained in the fluid this phenomenon is frequently referred to as the tubular pinch effect or sigma effect (20).the' transport of solid particles by fluids through pipeline3 and the determination of suspension viscosity by the capillary tube technique (6, 13, 23 to 25) are examples where this effect is known to occur. Although the majority of the processes where migration is an important factor involve multiparticle suspensions, research on single particle systems is a logical place to start toward gaining a better understandin of the more complicated systems reconcerned with migration of a single rigid sphere entrained in a straight tube of circular cross section.All of the previous research on particle migration ( 5 , 9, 10, 12, 15, 16, 21, 27) have been conducted within a particle Reynolds number range where fluid inertia effects were small and, with two exceptions (9, 16), under circumstances where the particle and fluid were closely matched in density. While all reported theoretical solutions to this problem (1, 2, 1 7 to 19) have shown that no transverse force results unless the inertial terms are retained in the Navier-Stokes equations, none of these solutions-by virtue of the techniques used to obtain the solutions-have considered inertial effects where these effects were quite large.Because the effect of fluid inertia on a sphere entrained in a Poiseuille flow field had not been previously studied ferred to above. T f e research reported in this paper is
C. D. Denson is with General Electric Research and DevelopmentCenter, Schenectady, New York. in a systematic manner. an investigation was initiated to study migration in a particle Reynolds number range where the fluid inertia effects would be larger than in previous studies; the results of this work are summarized in this paper. In this investiga...