Abstract
The phenomenon of liquid droplets "levitating" or bouncing off a liquid vibrating surface has attracted attention of scientists due to its possible application in microfluidics and novel nanostructured superhydrophobic materials. Several models have been suggested in the literature, and the effect is usually attributed to non-linear viscosity. Here we suggest a simple model relating the effect to the parametric resonance as described by the Mathieu equation, which explains stabilization of an inverted pendulum with vibration foundation. Small fast vibrations can be substituted by an effective "levitation" force. We present modeling and experimental results for oil droplets and discuss how the mathematical separation of the slow and fast motion provides insights on the relation of vibro-levitation of oil droplets and soft materials with the vibro-stabilization of an inverted pendulum, and the "Indian rope" and "Cornstarch monster" tricks.
Highlights
IntroductionLevitation (from Latin levitas lightness) is the process by which an object is suspended by a physical force against gravity
Levitation is the process by which an object is suspended by a physical force against gravity
The phenomenon is based on the non-linear nature of intense sound waves which results in acoustic radiation pressure creating an average positive force on a suspended object which resists the weight of the object.[3]
Summary
Levitation (from Latin levitas lightness) is the process by which an object is suspended by a physical force against gravity. A detailed model of such effects remains quite complex and several ideas have been suggested in the literature.[23,24,25] It was suggested[26] that the classical stability problem of an inverted pendulum on vibrating foundation has relevance to a diverse class of non-linear effects involving dynamic stabilization of statically unstable systems ranging from the vibrational stabilization of beams, to novel “dynamic materials,” the transport and separation of granular material, so matter, bubbles and droplets, to synchronization of rotating machinery. Phase transitions,[29] as well as possible applications for “smart” dynamic nanocomposite materials.[30]
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