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The evolution of axisymmetric equilibrium shapes of a rotating liquid drop can be extended beyond the 2-lobed shape bifurcation point if the rotating drop is driven in the n=2 axisymmetric shape oscillation (perturbation), where n is the mode of oscillation.
Nonlinear phenomena associated with the dynamics of free drops and bubbles are investigated analytically, numerically and experimentally. Although newly developed levitation and measurement techniques have been implemented, the full experimental validation of theoretical predictions has been hindered by interfering artifacts associated with levitation in the Earth gravitational field. The low gravity environment of orbital space flight has been shown to provide a more quiescent environment which can be utilized to better match the idealized theoretical conditions. The research effort described in this paper is a closely coupled collaboration between predictive and guiding theoretical activities and a unique experimental program involving the ultrasonic and electrostatic levitation of single droplets and bubbles. The goal is to develop and to validate methods based on nonlinear dynamics for the understanding of the large amplitude oscillatory response of single drops and bubbles to both isotropic and asymmetric pressure stimuli. The first specific area on interest has been the resonant coupling between volume and shape oscillatory modes isolated gas or vapor bubbles in a liquid host. The result of multiple time-scale asymptotic treatment, combined with domain perturbation and bifurcation methods, has been the prediction of resonant and near-resonant coupling between volume and shape modes leading to stable as well as chaotic oscillations. Experimental investigations of the large amplitude shape oscillation modes of centimeter-size single bubbles trapped in water at 1 G and under reduced hydrostatic pressure, have suggested the possibility of a low gravity experiment to study the direct coupling between these low frequency shape modes and the volume pulsation, sound-radiating mode. The second subject of interest has involved numerical modeling, using the boundary integral method, of the large amplitude shape oscillations of charged and uncharged drops in the presence of a static or time-varying electric field. Theoretically predicted non linearity in the resonant frequency of the fundamental quadrupole mode has been verified by the accompanying experimental studies. Additional phenomena such as hysteresis in the frequency response of ultrasoncially levitated droplets in the presence of a time varying electric field, and mode coupling in the oscillations of ultrasonically modulated droplets, have also been uncovered. One of the results of this ground-based research has been the identification and characterization of phenomena strictly associated with the influence of the gravitational field. This has also allowed us to identify the specific requirements for potential microgravity investigations yielding new information not obtainable on Earth.
We investigate the phenomenon of acoustic pressure-induced nucleation by using a novel approach involving the large amplitude resonant radial oscillations and collapse of a single bubble intentionally injected into a supercooled liquid. Using a combination of previously developed and proven techniques, the bubble is suspended in a fluid host by an ultrasonic field which supplies both the levitation capability as well as the forcing of the radial oscillations. We observe the effects of an increase in pressure (due to bubble collapse) in a region no larger than 100 microns within the supercooled melt to rigorously probe the hypothesis of pressure-induced nucleation of the solid phase. The use of single bubbles operating in narrow temporal and spatial scales will allow the direct and unambiguous correlation between the origin and location of the generation of the disturbance and the location and timing of the nucleation event. In a companion research effort, we are developing novel techniques for the non-contact measurements of the surface tension and viscosity of highly viscous supercooled liquids. Currently used non-invasive methods of surface tension measurement for the case of undercooled liquids generally rely of the quantitative determination of the resonance frequencies of drop shape oscillations, of the dynamics of surface capillary waves, or of the velocity of streaming flows. These methods become quickly ineffective when the liquid viscosity rises to a significant value. An alternate and accurate method which would be applicable to liquids of significant viscosity is therefore needed. We plan to develop such a capability by measuring the equilibrium shape of levitated undercooled melt droplets as they undergo solid-body rotation. The experimental measurement of the characteristic point of transition (bifurcation point) between axisymmetric and two-lobed shapes will be used to calculate the surface tension of the liquid. Such an approach has already been validated through the experimental verification of numerical modeling results. The experimental approach involves levitation, melting, and solidification of undercooled droplets using a hybrid ultrasonic-electrostatic technique in both a gaseous as well as a vacuum environment. A shape relaxation method will be investigated in order to derive a reliable method to measure the viscosity of undercooled melts. The analysis of the monotonic relaxation to equilibrium shape of a drastically deformed and super-critically damped free drop has been used to derive interfacial tension of immiscible liquid combinations where one of the component has high viscosity. A standard approach uses the initial elongation of a droplet through shear flows, but an equivalent method could involve the initial deformation of a drop levitated in a gas by ultrasonic radiation pressure, electric stresses, or even solid body rotation. The dynamic behavior of the free drop relaxing back to equilibrium shape will be modeled, and its characteristic time dependence should provide a quantitative means to evaluate the liquid viscosity.
An account is given of an experiment involving the equilibrium shapes of the dynamics of a rotating and oscillating drop conducted aboard the Space Shuttle in April 1985. The Drop Dynamics Module used in the experiments was fabricated and tested at JPL. In the experiment, a one-inch drop was spun out and then controlled acoustically so that physical contact with it could be avoided. In the axysymmetric shape region, the drop behaved nicely, but once it got to the bifurcation point it deviated from the theory substantially; the fission point agreed with theory but the shapes were different.
Molten aluminum and tin drops were levitated in a high vacuum by controlled electric fields, and they were systematically rotated by applying by a rotating magnetic field. When the evolution of the drop shape was measured as a function of rotation frequency, it agreed quantitatively well with the Brown and Scriven's theoretical prediction. The normalized rotation frequencies at the bifurcation point agreed with the predicted value 0.559, within 2%. An anomalous phenomenon which totally deviated from the prediction was observed in rotating molten tin drops when they were kept in a high rotation rate for several hours. No anomaly was observed in aluminum drops when they underwent similar condition. It was speculated that under the strong centrifugal force in the drop the tin isotopes must be separating. Since Al-27 is essentially the only naturally abundant isotope in the aluminum drops, the same anomaly is not expected. Based on the shape deformation of a rotating drop, an alternate approach to the surface tension measurement was verified. This new surface tension measurement technique was applied to a glassforming alloy, Zr(41.2)Ti(13.8)Cu(12.5)Ni(10.0)Be(22.5) in its highly viscous states. Also demonstrated in the paper was a use of a molten aluminum drop to verify the Busse's prediction of the influence of the drop rotation on the drop oscillation frequency.