What is it about?

In this theoretical study, we investigate the effect of elastic deformations on the load capacity of squeeze-film levitation systems. Background: Squeeze-film levitation, a phenomenon observed as early as the 1950s, refers to oscillation-induced repulsion between two objects whose parallel surfaces are separated by a thin film of air. In a typical system, one of the objects oscillates at a high frequency along an axis perpendicular to the surfaces, producing a pulsating fluid flow that perturbs the fluid in the thin film and its periphery. Due to the inherently nonlinear dynamics of the flow, a time-averaged (steady) overpressure emerges in the film, providing strong repulsive forces. For systems that use a nominally rigid oscillator, this repulsive force, of up to several kilograms, has been observed to transition to very weak attraction, of less than a gram, within a highly limited range of operation conditions. Several recent studies have proven that this transition occurs due to a sufficiently large drop in steady pressure across a small, peripheral flow region. Current work: A revolutionary experiment in 2021, however, demonstrated an unprecedented attractive load capacity of over 600 grams, using a thin disk that performed pronounced flexural oscillations. Data showed that, when the disk was oscillating at a resonant frequency, the distribution of suction pressure inside the film surged near the nodes of the standing wave, producing the largest attractive forces measured. In this paper, we apply the method of matched asymptotic expansions to construct a semi-analytical model of the fluid flow both in the film and in its periphery. The unified model is used to predict the steady film pressure distribution for various harmonic oscillation modes, providing fundamental insights into the differences between rigid-body and flexural levitation systems. Results: In particular, we find that (i) the range of operating conditions under which attraction is possible, as well as the maximum attractive load capacity itself, expands substantially as the disk oscillates with larger wavenumbers. (ii) the pressure drop across the periphery is practically negligible compared to those near the nodes of the standing wave, allowing computation of the attractive levitation force using closed-form expressions in a fraction of a second!

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Why is it important?

The most significant potential application of attractive squeeze-film levitation in the modern era appears to be the contactless assembly-line transport of sensitive objects, such as electronic components and glass substrates in LCD screens. Contact-based devices may contaminate such objects or provide unreliable release mechanisms due to electrostatic adhesion. Among fluid-based grippers, which avoid these issues, flexural squeeze-film levitation has shown a substantial increase in energy efficiency over common pneumatic devices such as the Bernoulli gripper. The results of our analysis provide fundamental insights that can be applied and extended to improve the load capacity and stability of flexural squeeze-film systems. Additionally, the closed-form asymptotic equations that we have derived may be integrated as a rapid, low-fidelity model into multi-disciplinary optimization software in the design of next-generation squeeze-film levitators.


As the speed and power of computation simulations grow in the 21st century, motivation to understand fundamental concepts by formulating and solving canonical problems seems to be taking a back seat. I am deeply grateful to my PhD advisor for involving me in the project that has lead to this publication, and I hope that the present paper (as well as its precursor listed below) serves as an inspirational example for other students who struggle and aspire to improve their skills in analytical mathematical modeling.

Sankaran Ramanarayanan
University of California San Diego

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This page is a summary of: On the enhanced attractive load capacity of resonant flexural squeeze-film levitators, AIP Advances, October 2022, American Institute of Physics, DOI: 10.1063/5.0106730.
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