Three-dimensional large-amplitude drop oscillations: experiments and theoretical analysis

Abstract

Three-dimensional large-amplitude oscillations of a mercury drop were obtained by electrical excitation in low gravity using a drop tower. Multi-lobed (from three to six lobes) and polyhedral (including tetrahedral, hexahedral, octahedral and dodecahedral) oscillations were obtained as well as axisymmetric oscillation patterns. The relationship between the oscillation patterns and their frequencies was obtained, and it was found that polyhedral oscillations are due to the nonlinear interaction of waves.A mathematical model of three-dimensional forced oscillations of a liquid drop is proposed and compared with experimental results. The equations of drop motion are derived by applying the variation principle to the Lagrangian of the drop motion, assuming moderate deformation. The model takes the form of a nonlinear Mathieu equation, which expresses the relationships between deformation amplitude and the driving force's magnitude and frequency. IntroductionLiquid drop oscillation has attracted the attention of many scientists since the 19th century, since it is not only an interesting basic phenomenon but is also important in such diverse areas as nuclear physics, cloud physics and chemical engineering. Since it has become possible to conduct experiments in microgravity, understanding liquid drop oscillation has become more important, not only from an academic viewpoint but also for the practical aspects of material processing in containerless levitation and measurement of the physical properties of molten materials in space. In a microgravity environment, a free liquid assumes a spherical shape due to surface tension and it is easy to levitate and manipulate a relatively large liquid drop without a container. This is one of the advantages of the space environment. Understanding the nature of drop oscillations is indispensable for future applications of containerless processing. In addition, nonlinear effects resulting from the interaction of finite-amplitude waves are of interest from physical and mathematical points of view, and experimental realization of large-amplitude oscillations is useful for the study of these effects.The first large-amplitude drop oscillation experiments were conducted by acoustically exciting a drop suspended in an immiscible liquid (a mixture of silicone oil and carbon tetrachloride suspended in distilled water) in 1 g conditions (Trinh & Wang 1982). These experiments showed oscillating patterns in the l = 2, 3, 4 axisymmetric (m = 0) modes and also showed the dependence of the amplitude of oscillation of the second mode on oscillation frequency.

Oscillatory behavior of nanodroplets

“…The resulting frequency shift for the second-mode oscillation was in agreement with the predictions of the theory [5] for A Ͻ 0.3. Azuma and Yoshihara [12] employed electrical excitation to obtain 3D, large amplitude oscillations of a mercury drop. A relationship between drop oscillation modes and frequencies was found.…”

Effect of rising motion on the damped shape oscillations of drops and bubbles

“…Several theoretical, 11,12 numerical, 13,14 and experimental 15,16 works considered nonlinear effects for finite deformations. They described several couplings between modes and showed an effect of the amplitude on the frequency of the oscillations.…”

Chaotic Shape and Translational Dynamics of 2D Incompressible Bubbles under Forced Vibration in Microgravity

“…The most important feature of large amplitude oscillations ( D/D > 0.1), where D is the bubble/droplet diameter and D is the variation in diameter, is the appearance of nonlinear oscillations that cause different modes of oscillations to interact (Basaran 1992;Trinh and Wang 1982;Trinh et al 1996). Energy transfer between different modes of oscillations (modes 2, 3, 4, 6) have been reported in studies considering the shape oscillation of a liquid droplet under acoustic forcing, while neglecting translational motion (Trinh et al 1998;Azuma and Yoshihara 1999).…”