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A note on the damping and oscillations of a fluid drop moving in another fluid

Published online by Cambridge University Press:  29 March 2006

S. V. Subramanyam
S. V. Subramanyam
Affiliation:
Department of Physics, Indian Institute of Science, Bangalore 12, India
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Abstract

The oscillations of a drop moving in another fluid medium have been studied at low values of Reynolds number and Weber number by taking into consideration the shape of the drop and the viscosities of the two phases in addition to the interfacial tension. The deformation of the drop modifies the Lamb's expression for frequency by including a correction term while the viscous effects split the frequency into a pair of frequencies—one lower and the other higher than Lamb's. The lower frequency mode has ample experimental support while the higher frequency mode has also been observed. The two modes almost merge with Lamb's frequency for the asymptotic cases of a drop in free space or a bubble in a dense viscous fluid but the splitting becomes large when the two fluids have similar properties. Instead of oscillations, aperiodic damping modes are found to occur in drops with sizes smaller than a critical size ($\sim\hat{\rho}\hat{\nu}^2/T $). With the help of these calculations, many of the available experimental results are analyzed and discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 37 , Issue 4 , 28 July 1969 , pp. 715 - 725
Copyright
© 1969 Cambridge University Press

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