On the shape of a gas bubble in a viscous extensional flow

Youngren, Gary K.; Acrivos, Andreas

doi:10.1017/s0022112076000724

Cited by 107 publications

(52 citation statements)

References 10 publications

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“…As is well known, this method reduces the dimensionality by one, resulting in savings of computational time and storage, and allowing a continuous representation of the solution inside the domain. This method was first successfully applied to flows past a particle of arbitrary shape by Youngren & Acrivos (1975), extended to free-surface flows in the work of Youngren & Acrivos (1976), and later used extensively in various drop and bubble problems, including effects of surfactants, as in the work by Stone & Leal (1990). In two dimensions, the advantages of the streamfunctionvorticity representation for the biharmonic problem (2.3)…”

Section: Boundary-integral Formulationmentioning

confidence: 99%

Surfactant effects in the Landau–Levich problem

Krechetnikov

Homsy

2006

J. Fluid Mech.

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In this work we study the classical Landau-Levich problem of dip-coating. While in the clean interface case and in the limit of low capillary numbers it admits an asymptotic solution, its full study has not been conducted. With the help of an efficient numerical algorithm, based on a boundary-integral formulation and the appropriate set of interfacial and inflow boundary conditions, we first study the film thickness behaviour for a clean interface problem. Next, the same algorithm allows us to investigate the response of this system to the presence of soluble surface active matter, which leads to clarification of its role in the flow dynamics. The main conclusion is that pure hydrodynamical modelling of surfactant effects predicts film thinning and therefore is not sufficient to explain the film thickening observed in many experiments.

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Section: Boundary-integral Formulationmentioning

confidence: 99%

Surfactant effects in the Landau–Levich problem

Krechetnikov

Homsy

2006

J. Fluid Mech.

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“…The boundary-integral method has been applied to the low-Reynolds-number deformation of bubbles and drops in an external flow by Youngren & Acrivos (1976), Rallison & Acrivos (1978) and Rallison (1981). The technique is well suited to free-boundary problems since the interfacial velocities may be obtained directly, without the necessity of determining the velocity field in the entire flow domain.…”

Section: Numerical Solution Of the Motion Of An Elongated Drop Via Thmentioning

confidence: 99%

An experimental study of transient effects in the breakup of viscous drops

1986

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A computer-controlled four-roll mill is used to examine two transient modes of deformation of a liquid drop: elongation in a steady flow and interfacial-tensiondriven motion which occurs after the flow is stopped abruptly. For modest extensions, drop breakup does not occur with the flow on, but may occur following cessation of the flow as a result of deterministic motions associated with internal pressure gradients established by capillary forces. These relaxation and breakup phenomena depend on the initial drop shape and the relative viscosities of the two fluids. Capillary-wave instabilities at the fluid-fluid interface are observed only for highly elongated drops. This study is a natural extension of G. I. Taylor's original studies of the deformation and burst of droplets in well-defined flow fields.

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“…Stokes flows with free surfaces, on the other hand, have until recently received much less attention, but there has been much more activity following the demonstration by Hopper [20,21] and Richardson [41] that explicit unsteady solutions could be constructed (steady solutions were given earlier in [4,17,37,39,49]). A bibliography listing more than 600 papers in both areas can be found at the web address http://www.maths.ox.ac/~howison/ .…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional Stokes and Hele-Shaw flows with free surfaces

Cummings¹,

Howison²,

King

1999

Eur. J. Appl. Math.

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We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between the two problems. We give a detailed discussion of conserved quantities for Stokes flows, and relate them to the Schwarz function of the moving boundary and to the Baiocchi transform of the Airy stress function. We compare the results with the corresponding results for Hele-Shaw flows, the principal consequence being that for Hele-Shaw flows the singularities of the Schwarz function are controlled in the physical plane, while for Stokes flow they are controlled in an auxiliary mapping plane. We illustrate the results with the explicit solutions to specific initial value problems. The results shed light on the construction of solutions to Stokes flows with more than one driving singularity, and on the closely related issue of momentum conservation, which is important in Stokes flows, although it does not arise in Hele-Shaw flows. We also discuss blow-up of zero-surface-tension Stokes flows, and consider a class of weak solutions, valid beyond blow-up, which are obtained as the zero-surface-tension limit of flows with positive surface tension.

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On the shape of a gas bubble in a viscous extensional flow

Cited by 107 publications

References 10 publications

Surfactant effects in the Landau–Levich problem

Surfactant effects in the Landau–Levich problem

An experimental study of transient effects in the breakup of viscous drops

Two-dimensional Stokes and Hele-Shaw flows with free surfaces

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