Generation of an average flow by a semi-submerged oscillating sphere

Abstract

The paper presents the results of an experimental study into the structure of an average flow generated by a semi-immersed oscillating sphere. The average flow in the considered situation is induced by (1) an inhomogeneous viscous boundary layer on the submerged part of the sphere, generating an axisymmetric flow with a pronounced jet from the lower pole of the sphere, and (2) a traveling surface wave drifting the subsurface liquid layer in the direction of its propagation. The paper is mainly focused on the flow induced by the wave mechanism and on the change in its structure depending on the characteristics of the vibrations and the state of the interface associated with the presence or absence of an adsorbed layer of a surfactant on the surface. The wave configuration and the structure of the average flow were investigated in experiments. The main part of the experiments was carried out with isopropyl alcohol, which excluded the formation of an adsorbed layer. It has been found that a traveling cylindrical wave generates an axisymmetric centrifugal flow along the interface, the intensity of which grows with increasing amplitude of vibrations. When the amplitude exceeds a critical value, the cylindrical wave becomes unstable, which results in the formation of two spiral waves propagating in opposite azimuthal directions and having the frequency two times less than the oscillation frequency of the sphere. The amplitude of the resulting wave turns out to be modulated in the azimuthal direction, as a result of which the radial flow velocity also turns out to be a periodic function of the azimuthal coordinate. Additionally, a series of qualitative experiments with water of various purity degrees was carried out to determine the effect of the adsorbed surfactant layer on the structure of the average flow. It is shown that the presence of a surfactant leads either to complete immobilization of the surface or to the formation of a multi-vortex flow on the interface, depending on the surfactant content. In conclusion, the results obtained are compared with the data reported in earlier studies on the problem under consideration.