Abstract
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory.
Highlights
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids
A deformed microjet cavity is formed by a cross-sectional segment of a fluidic microjet, which undergoes surface oscillation owing to surface tension acting as a restoring force
Even for non-optofluidic application such as optical fiber spinning and film blowing[11], accurate determination of multipolar components is required for consistent material processing
Summary
Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. A deformed microjet cavity is formed by a cross-sectional segment of a fluidic microjet, which undergoes surface oscillation owing to surface tension acting as a restoring force (see Fig. 1 for illustration) It provides a high quality factor owing to its clear and smooth surface and high output directionality based on internal ray and wave dynamics. It may seem that these difficulties in measurement might be compensated for by a theoretical approach It is because there exists a well-established hydrodynamic theory to describe the surface oscillation of a liquid jet, mostly owing to Lord Rayleigh and Sir Lamb[12,18]. Direct experimental verification of the multipolar surface oscillation amplitudes has not been reported
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