Journal ArticleDOI
Free oscillations of drops and bubbles: the initial-value problem
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In this paper, the authors study the initial value problem posed by the small amplitude free oscillations of free drops, gas bubbles, and drops in a host liquid when viscous effects cannot be neglected.Abstract:
We study the initial-value problem posed by the small-amplitude (linearized) free oscillations of free drops, gas bubbles, and drops in a host liquid when viscous effects cannot be neglected. It is found that the motion consists of modulated damped oscillations, with the damping parameter and frequency approaching only asymptotically the results of the normal-mode analysis. The connexion with the normal-mode method is demonstrated explicitly and the experimental relevance of our results is discussed.read more
Citations
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Journal ArticleDOI
Linear motion of multiple superposed viscous fluids.
TL;DR: The small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem and results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that can be inverted numerically.
Journal ArticleDOI
Mechanism of damped oscillation in microbubble coalescence
Ron Chen,Jianhuan Zeng,Huidan Yu +2 more
TL;DR: In this article, the authors numerically explore the mechanism of damped oscillation in microbubble coalescence characterized by the Ohnesorge (Oh) number and explore the competition between driving and resisting forces.
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Enhanced damping of capillary bridge oscillations using velocity feedback
TL;DR: In this article, an optical system is used to detect the (2,0)-mode amplitude, which is an axisymmetric varicose mode of one wavelength in the axial direction, and a mode-coupled Maxwell stress profile is generated in proportion to the modal velocity.
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VOF evaluation of the surface tension by using variational representation and Galerkin interpolation projection
TL;DR: A variational approach with cell-to-point Galerkin projections for studying two-phase interface advection problems dominated by surface tension using the variational formulation of the Navier-Stokes equation and avoiding differentiation is proposed.
References
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Journal ArticleDOI
Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
TL;DR: An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method, and the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t.
Journal ArticleDOI
The oscillations of a fluid droplet immersed in another fluid
C. A. Miller,L. E. Scriven +1 more
TL;DR: In this paper, a general dispersion equation is derived by which frequency and rate of damping of oscillations can be calculated for arbitrary values of droplet size, physical properties of the fluids, and interfacial viscosity and elasticity coefficients.
Journal ArticleDOI
Viscous effects on perturbed spherical flows
TL;DR: In this paper, the problem of describing free oscillations of a viscous liquid drop and of a bubble in a fluid is studied in detail, and it is shown that the oscillations are initially describable in terms of an irrotational approximation, and that the normal-mode results are recovered as t −* <».
Journal ArticleDOI
The oscillations of a viscous liquid drop
TL;DR: In this article, it was shown that for the diffraction of an arbitrary two-dimensional incident pulse by a wedge of angle n, the ratio of the resultant velocity potential to the corresponding value of the incident pulse at the corner of the wedge at any instant is equal to 2x/ (2x n) n; and that for a threedimensional pulse diffraction by a cone of solid angle u>, the ratio at the vertex of the cone is equal tO 4ir/ (47T ) co).