Surface Tension Driven Flows

Keller, Joseph B.; Miksis, Michael J.

doi:10.1137/0143018

Cited by 240 publications

(239 citation statements)

References 7 publications

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“…Keller and Miksis [12] present a very interesting scaling theory for the singularity in the nonviscous case. There are two important differences between our problem and theirs: Their Geometry is two-dimensional rather than three-dimensional-axisymmetric, and they study the time after the breakup.…”

Section: Nature Of Singularitiesmentioning

confidence: 99%

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

1994

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We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.

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Section: Nature Of Singularitiesmentioning

confidence: 99%

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

1994

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“…Note that the received equation differs from equation (1), proposed in [17], by a constant coefficient, given the initial radius of the bridge, and, in contrast to equation (1), allows us to calculate the duration of thinning of the bridge from the initial value r br0 to zero. Thus, the duration of the third stage (bridge breakaway time) is equal to:…”

Section: Modeling the Stage Of Tearing The Bridge And The Formatiomentioning

confidence: 99%

“…A crucial role in this case is played by the force of inertia and the force of surface tension. However, in contrast to the model described in [17], we shall take into account the expression for the initial radius of a bridge and the condition of flow by gravity. We shall also assume that the thickness of the shell of a capsulated drop is much smaller than the radius of supply pipe d<<r0.…”

Section: Modeling the Stage Of Tearing The Bridge And The Formatiomentioning

confidence: 99%

“…Kinetics of thinning the bridge, as already stated, is described in theory in article [17]. By following their model, we shall also assume that in the area of the bridge the flow is fast enough, while the gradients of velocity are small, so viscous friction will be neglected.…”

Section: Modeling the Stage Of Tearing The Bridge And The Formatiomentioning

confidence: 99%

“…1. Stages of separation of a real water drop: time between shots is 0.1 s. Images are taken from article [12] One of the first attempts at describing the kinetics of tearing a bridge was made by authors in [17]. Underlying the theory is the model, according to which, regardless of the viscosity of fluid flow by gravity, the area around the bridge is controlled only by the forces of inertia and surface tension.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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Analysis of kinetics pattern in the formation and separation of a drop of fluid in the form of a capsule

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Pyvovarov

2017

EEJET

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Представлено кінетичну модель процесу формоутворення крапель капсульованих рідин, починаючи від етапу формування зародка кра-плі до моменту її відриву під дією фізичних сил та технологічних параметрів. Одержані рів-няння являються теоретичним описом проце-су капсулоутворення та обґрунтовують три-валість процесу, розмірні характеристики кінцевого продукту та потужність конструк-тивних машин для одержання капсул Ключові слова: ліпіди, капсулювання, кіне-тика відриву краплі, оболонка альгінат каль-цію, відрив краплі, перемичка краплі, зародок краплі Представлена кинетическая модель процес-са формообразования капель капсулированных жидкостей, начиная от этапа формирования зародыша капли до момента ее отрыва под дей-ствием различных физических сил и техноло-гических параметров. Полученные уравнения являются теоретическим описанием процесса капсулообразования и обосновывают продол-жительность процесса, размерные характе-ристики конечного продукта и мощность кон-структивных машин для получения капсул Ключевые слова: липиды, капсулирование, кинетика отрыва капли, оболочка альгинат кальция, отрыв капли, перемычка капли, заро-дыш капли UDC 544.2

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Singularity formation in thin jets with surface tension

Pugh

Shelley

1998

Comm. Pure Appl. Math.

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We derive and study asymptotic models for the dynamics of a thin jet of fluid that is separated from an outer immiscible fluid by fluid interfaces with surface tension. Both fluids are assumed to be incompressible, inviscid, irrotational, and density‐matched. One such thin jet model is a coupled system of PDEs with nonlocal terms—Hilbert transforms—that result from expansion of a Biot‐Savart integral. In order to make the asymptotic model well‐posed, the Hilbert transforms act upon time derivatives of the jet thickness, making the system implicit. Within this thin jet model, we demonstrate numerically the formation of finite‐time pinching singularities, where the width of the jet collapses to zero at a point. These singularities are driven by the surface tension and are very similar to those observed previously by Hou, Lowengrub, and Shelley in large‐scale simulations of the Kelvin‐Helmholtz instability with surface tension and in other related studies. Dropping the nonlocal terms, we also study a much simpler local model. For this local model we can preclude analytically the formation of certain types of singularities, though not those of pinching type. Surprisingly, we find that this local model forms pinching singularities of a very similar type to those of the nonlocal thin jet model. © 1998 John Wiley & Sons, Inc.

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Surface Tension Driven Flows

Cited by 240 publications

References 7 publications

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

Analysis of kinetics pattern in the formation and separation of a drop of fluid in the form of a capsule

Singularity formation in thin jets with surface tension

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