RETARDATION OF FALLING SPHERES BY HYDRODYNAMIC OSCILLATIONS

Terminal velocities of gravitational fall of four sizes of precision sapphire spheres (0·794-0·4764 cm dia.) and six sizes of glass spheres (0·0208-0·505 cm dia.) have been measured in a vertically oscillating water column at conditions of constant velocity, amplitude, acceleration and frequency of vibration. Vibration conditions encompassing frequency and amplitude ranges of 5-50 c/s and 0-1·0 cm respectively have been studied. The experimental terminal velocities have been compared with oscillation-retarded asymptotic velocities predicted theoretically by the numerical solution on a digital computer of a nonlinear Langevin equation proposed by Houghton (1966) as representing a force balance on a free particle in an accelerating fluid. For the larger spheres the experimental velocities were found to be lower than those predicted theoretically using steady state drag coefficients with a negligible phase lag for the displaced fluid-these velocity differences are primarily attributed to oscillation-induced increases in the drag coefficient, with appreciable secondary influences arising from changes in phase lag, drag exponent and virtual mass. Experimental velocities for the smaller particles were found to be higher than those predicted theoretically, the differences being attributed to primary reductions in the drag exponent, with second order effects arising from oscillation-induced alterations in drag coefficient, virtual mass and phase lag. © 1968.