Two-dimensional cusped interfaces

Joseph, Daniel D.; Nelson, James R.; Renardy, Michael; Renardy, Yuriko

doi:10.1017/s0022112091001477

Cited by 117 publications

(101 citation statements)

References 29 publications

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“…Free-surface flows are also very sensitive to the formation of cusp singularities (Joseph et al, 1991) even in seemingly innocuous flow situations. It seems as if surface tension should make the surface more regular, thus simplifying simulations.…”

Section: Simulationsmentioning

confidence: 99%

Nonlinear dynamics and breakup of free-surface flows

1997

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Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems. [S0034-6861(97)00303-6] CONTENTS

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Section: Simulationsmentioning

confidence: 99%

Nonlinear dynamics and breakup of free-surface flows

1997

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“…As the initial size of the bubble increases, the bottom edge becomes sharper and the cusp configuration is clearly observed. In particular, for the case of (d) R 0 = 30Δx, it is found that the cusp can be fitted to the functional form | x | 2/3 predicted by Joseph et al (28) for a two-dimensional cusp created by the flow induced in two counter-rotating cylinders.…”

Section: Journal Of Computational Science and Technologymentioning

confidence: 73%

Lattice Boltzmann Simulation of Two-Phase Viscoelastic Fluid Flows

Yoshino

Toriumi

Arai

2008

JCST

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A lattice Boltzmann method (LBM) for two-phase viscoelastic fluid flows is proposed. The method is mainly an extension of the LBM for two-phase flows with large density differences proposed by Inamuro et al. [Journal of Computational Physics Vol.198, No.2 (2004), pp.628-644]. The viscoelastic effects are introduced by the constitutive equation based on the Maxwell model, which has a spring and a dashpot connected with each other in series. The method is applied to simulations of a drop under shear flow in viscoelastic fluids and of a bubble rising in viscoelastic fluids. In the simulation of drop deformation under shear flows, the effects of viscoelasticity on the deformation and orientation angle are evaluated. In the simulation of bubble rising in viscoelastic fluids, a cusp configuration at the trailing edge is investigated and compared with the theoretical prediction and other numerical results.

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“…This cuspidal tale occurs only in gas bubbles rising freely in non-Newtonian liquids. Joseph et al [8] defined the cuspidal tails as point singularities of curvature. They also stated that the build-up of extensional stresses near stagnation points may favor the formation of cusps.…”

Section: Fluid Mechanics Of Two-dimensional Cusping At the Trailing Ementioning

confidence: 99%

Potential flow of a second‐order fluid over a tri‐axial ellipsoid

Viana

Funada

Joseph

et al. 2005

Journal of Applied Mathematics

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The problem of potential flow of a second-order fluid around an ellipsoid is solved, and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge. A thin flat trailing edge gives rise to a large stress which makes the thin trailing edge thinner.

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Two-dimensional cusped interfaces

Cited by 117 publications

References 29 publications

Nonlinear dynamics and breakup of free-surface flows

Nonlinear dynamics and breakup of free-surface flows

Lattice Boltzmann Simulation of Two-Phase Viscoelastic Fluid Flows

Potential flow of a second‐order fluid over a tri‐axial ellipsoid

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