A STUDY OF THE OSCILLATIONS OF A VISCOUS FLUID DROP MOVING IN A BACKGROUND FLUID MEDIUM

Abstract

The oscillations of a drop moving in a hackgorund fluid medium have been studied by including the contributions from the viscosifies of the two phases, the inertial eSfects causerd by the drop motion and the deformation of the drop. The nonspherical shape of the drop alfer the expression for frequency of a spherical drop by uncluding correction terms explaining many of the exprrintentai reszrirs on highly & formed drops. The ivscoits terms split the mode 0-f frequency into one lower and the other higher than Lambs. Experimenal evidence exists for both the lower and the higher fiequerry  modes. If the size of the drop is smaller than a certain enitical value, ( ~ P vZ/T, p the rlensitv, v the kinematic viscosity and T mterfacial temioir befmcen the two phases) the pertutbations On the drop surface will be damped aperioiiically. This critical size which is very small (- 10-6cm.) for a sysrrrn like u liquid drop in free space, becomrs prominent (~ a few mrm) for a fiuid drop in a dense viscous liquid mediunz This can be a possible explanation for the nonobservance of oscillations in highly dense viscous systems. Detailea calculations are given in the limiting case (a' > > 1, o'- 1, a' 1 ) of an oscillation parameter  being the oscillation frequency, a rhe radius of rhe drop and U the terminal xelocity of the drop in the fiuid mediam.