Dynamics of Rotating Two-phase System Under Transversal Vibration

Abstract

Mean dynamics of light granular matter in liquid in the rotating horizontal cylinder subjected to transversal vibrations is experimentally investigated. The excitation of outstripping and lagging azimuth motion of the interface with respect to the cavity is revealed at definite ratios of rotation and vibration frequencies υ r . The motion is generated by the inertial oscillations arising in the system in a resonant way. The formation of regular spatial structures on the interface is revealed at intensive outstripping motion. These structures have azimuth and axial periodicity and their shape depends on the type of inertial waves arising in the cavity. Intensity and direction of azimuth flows as well as shape of patterns on the granular matterliquid interface are determined by the ratio υ r . It is shown, that the lagging motion exists at υ r < 1, and the outstripping one exists at υ r > 1. Combined action of vibrations and rotation provides an efficient mechanism of mass transfer control, the intensity of mean flows in the cavity frame can be of the same order of magnitude as the rotation velocity.

Effect of vibration on two-liquid system in rotating cylinder

“…It was theoretically shown for the frequencies of the centrifugal waves in [ 16], where the natural frequencies in equations were normalized over the rotation frequency. This result was later supported by experiments on vibrations [18][19][20][21]24]. In the discussion, we will use the term eigenfrequency meaning the frequencies of two circumferential modes of waves on the interface, n + ≡ Ω 0+ /Ω r and n − ≡ Ω 0− /Ω r , excited in the positive and negative resonances, respectively.…”

“…Simultaneously, the curves plotted through points 4 -6 (three different two-phase systems) are in qualitative agreement with the curves plotted through points 1 (a detailed study of the two-fluid system). Point 6 is obtained for a liquid-saturated light granular matter in liquid [ 20].…”

“…This is due to the generation of an average force in the Stokes layers during the circular oscillations of the body. If the body is replaced by a light granular matter saturated with a liquid, an intensive motion in the resonance provokes the development of instability in form of a relief with azimuthal or axial periodicity [ 20].…”

Vibrational Suspension of Light Sphere in a Tilted Rotating Cylinder with Liquid

“…For instance the action of transverse vibrations on the free boundary of the centrifuged liquid [2] leads to the excitation of an azimuthal wave and excitation of intensive averaged liquid flow. Similar resonance effects occur when the free flowing medium [3] or a light cylindrical body [4] are in rotating system instead of a gas phase. In the last case, the vibration leads to the oscillation of the body and the emergence of its intensive differential rotation relative to the cavity, called "vibrational hydrodynamic top. "…”

“…The cavity filled with a liquid is set in a horizontal position on table 3 of an electrodynamic vibrator, providing the translational vibrations perpendicular to the rotation axis. The length and the radius of the cavity are = 7.20 cm and = 2.60 cm, respectively, the radius of the sphere is = 1.77 cm; the average density = 0.17 g/cm 3 . The relative size of the sphere is 2 / = 0.49.…”