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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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An improved height function technique for computing interface curvature from volume fractions
TL;DR: In this paper, an improved height function technique for calculating the interface curvature from volume fractions in 3D volume fractions is presented, and a detailed analysis of the performance of the technique shows that appropriate discretization of the partial derivatives of the height function may considerably reduce the computed interface curvatures.
Journal ArticleDOI
An arbitrary Lagrangian Eulerian method for moving-boundary problems and its application to jumping over water
TL;DR: In this article, an ALE (Arbitrary Lagrangian Eulerian) moving mesh method was developed for solving two-dimensional and axisymmetric moving-boundary problems, including the interaction between a free-surface and a solid structure.
Journal ArticleDOI
Modeling, Simulation, and Optimization of Electrowetting
TL;DR: Computer simulations done with the Surface Evolver program and a template library combined with a graphical user interface (GUI) that facilitates standard tasks in the simulation of electrowetting arrays are presented.
Journal ArticleDOI
Nonlinear dynamics of viscous droplets
TL;DR: In this paper, the Navier-Stokes equation for nonlinear viscous droplet oscillations is analyzed by solving the mode expansions with modified solutions of the corresponding linear problem.
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On the dynamics and breakup of a bubble rising in a turbulent flow
TL;DR: In this article, the deformation dynamics of a deformable bubble rising in a uniform turbulent flow are investigated, and three-dimensional shape recognition from three perpendicular camera views is performed.
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).