Interface Waves Excited by Vertical Vibration of Stratified Fluids in a Circular Cylinder

Abstract

The excitation of interface waves by vertical vibration of stratified immiscible fluids in a circular cylinder is studied experimentally and analytically. The excitation of linear capillary-gravity waves by the time-dependent fluid acceleration combined with the fluid-wall relative motion is considered in the analysis. The analytical results show that the interface responses are dominated by the modes predicted by the Mathieu equation when the excitation amplitude and frequency lie in an unstable region of the Mathieu equation governing the acceleration-driven interface oscillation. Otherwise, symmetrical harmonic modes are excited by the capillary force associated with the fluid-wall relative motion. These changes in the instability modes agree to those observed in the experiments conducted with oil (kerosene) and water in an acrylic pipe. The amplitudes of the symmetrical harmonic waves in the experiments are well predicted by using the contact line model of Miles. The interface motion in the experiments, however, is found to include cyclic formation of a thin film of oil on which the oil-water interface behaves as if it “slips” without being much affected by the capillary force, and thus to be far more complicated than assumed by the model.

KEYWORDS:

• stratified fluids
• vertical vibration
• interface wave
• Mathieu equation
• fluid-wall relative motion
• surface tension
• contact line
• capillarity effects
• linear analysis
• optical measurement