Pinchoff and satellite formation in compound viscous threads

Matar, Omar; Papageorgiou, Demetrios T.

doi:10.1063/1.1611879

Cited by 15 publications

(14 citation statements)

References 41 publications

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“…The situation in which a compound jet breaks, on the other hand, is practically important in a number of applications involving microencapsulation. 36 Craster et al 37 have used a onedimensional, long-wave model to analyze the pinch-off dynamics of compound jets. Such models, as their single-fluid counterparts, 9,38,39 assume that the radial velocity is negligible compared to the axial velocity throughout the pinch-off process.…”

Section: Discussionmentioning

confidence: 99%

Non-self-similar, linear dynamics during pinch-off of a hollow annular jet

2004

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Based on an experimental and computational study of the breakup of a drop (jet) of small viscosity in an ambient fluid of large viscosity, Doshi et al. [Science 302, 1185] have shown that the breakup of a drop (jet) of zero viscosity in a very viscous ambient fluid gives rise to an unexpected, nonuniversal form of singularity. Doshi et al. conjectured that the nonuniversal dynamics result from the fact that stresses exerted by the inner fluid are negligible. To verify this conjecture and overcome computational difficulties associated with simulating systems in which the disparity between the viscosities of the inner and the outer fluids is large, the breakup of an annular jet whose core is a gas of negligible viscosity is analyzed. Calculations show that as the jet's minimum radius h min → 0, both core-and shell-side pressures remain bounded while surface tension pressure, which diverges as 1 / h min , is balanced by viscous normal stress exerted by the shell fluid. Simulations show that interfacial points move radially inward with the same velocity. Fourier decomposition of interface shapes confirms that the dynamics are linear. As h min → 0, the axial length scale remains finite, its value varying with imposed initial and boundary conditions. Thus, the breakup is not self-similar and the final breakup profile is nonuniversal.

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Section: Discussionmentioning

confidence: 99%

Non-self-similar, linear dynamics during pinch-off of a hollow annular jet

2004

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“…Their algorithm, however, was unable to simulate highly deformed jet shapes due to the use of Lagrangian mesh in which grid points were convected with the fluid velocity. Recently, Craster et al 74 studied the breakup of viscous compound threads of both pure and surfactant-laden liquids using asymptotic methods in the long-wave limit. In this slender-jet analysis, the authors assumed that the axial velocity, to the leading order, was independent of the radial coordinate.…”

Section: Dynamics Of Compound Jetsmentioning

confidence: 99%

Nonlinear dynamics and breakup of compound jets

2006

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Finite-amplitude deformation and breakup of a compound jet, whose core and shell are both incompressible Newtonian fluids, that is surrounded by a passive gas are analyzed computationally by a temporal analysis. The means is a method of lines algorithm in which the Galerkin/finite element method with elliptic mesh generation is used for spatial discretization and an adaptive finite difference method is employed for time integration. The dynamics are initiated by subjecting the inner and the outer interfaces of a quiescent compound jet to axially periodic perturbations that are either in phase ͑ =0͒ or radians out phase ͑ = ͒, where is the phase shift between the disturbances imposed on the two interfaces. The initial growth rates of disturbances obtained from computations are compared and demonstrated to be in excellent agreement with predictions of linear theory ͓Chauhan et al., J. Fluid Mech. 420, 1 ͑2000͔͒. Computations reveal that recirculating flows occur commonly during the deformation and pinch-off of compound jets, and hence render inapplicable the use of slender-jet type approximations for analyzing the dynamics in such cases. Moreover, as the deformations of one or both of the interfaces of the compound jet grow, the resulting shapes at the incipience of pinch-off are asymmetric and lead to the formation of satellite drops. Calculations are carried out over a wide range of Reynolds numbers of the core fluid, ratios of the viscosity and density of the shell fluid to those of the core fluid, ratio of the surface tension of the outer interface to the interfacial tension of the inner interface, the ratio of the unperturbed radius of the outer cylindrical interface to that of the inner cylindrical interface, wavenumber, and perturbation amplitudes to determine their effects on breakup time and whether both interfaces pinch at the same instant in time to result in the formation of compound drops. Conditions are also identified for which the dynamical response of compound jets subjected to initial perturbations with = 0 differ drastically from those subjected to ones with = .

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“…A wide range of viscosities were investigated and several conclusions (in line with previous work where appropriate) were drawn. It was shown that in the Stokes limit satellites form at breakup even though the surrounding region is a gas -a phenomenon attributed to the electric field since a viscous external shear is required to produce satellites in the non-electrified case (see Lister & Stone (1998), Craster et al (2003), Craster et al (2005)). In addition, the size of the satellite drops was found to increase in the presence of the electric field (also implying that the main drop volume decreases as found by Huebner & Chu (1971) and Magarvey & Outhouse (1962)).…”

Section: Introductionmentioning

confidence: 99%

“…Recent and ongoing analytical studies concentrate on describing the pinching process asymptotically by utilizing the separation of radial and axial scales and mapping the dynamics to a class of self-similar solutions which are universal when inertia is present; notable studies include the work of Eggers (1993), Eggers & Dupont (1994), Papageorgiou (1995), Brenner et al (1996) for jets surrounded by a passive medium; Craster et al (2002), Craster et al (2003), Craster et al (2005), for surfactant-covered or compound jets; Conroy et al (2010), for core-annular arrangements in the presence of electrokinetic effects. Significant computational work has also been carried out with the aim of simulating the phenomena and evaluating the asymptotic theories (the latter are considerably less demanding numerically) -see Newhouse & Pozrikidis (1992), Pozrikidis (1999), Lister & Stone (1998), Sierou & Lister (2003), who simulate Stokes flows using boundary integral methods, and Ambravaneswaran et al (2002), Chen et al (2002), Notz et al (2001), Notz & Basaran (2004), Collins et al (2007), Hameed et al (2008) who compute the flow at arbitrary Reynolds number and in some instances include the effects of surfactants and electric fields -the extensions and novel aspects of the present work are outlined later.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

Wang

Papageorgiou

2011

J. Fluid Mech.

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The nonlinear dynamics of a viscous filament surrounded by a second viscous fluid arranged in a core-annular configuration when a radial electric field acts in the annular region, are studied analytically and computationally using boundary element methods. The flow is characterized by the viscosity ratio, an electric Weber number measuring the strength of the electric field, a geometrical parameter measuring the thickness of the undisturbed annular region, as well as a computational parameter that fixes the wavenumber of the undulations. Axisymmetric solutions are computed by direct numerical simulations in the Stokes limit for general values of the parameters when the two fluids have equal viscosities, and an asymptotic theory is carried out to produce a novel evolution equation for thin film dynamics valid when the undisturbed annular thickness is small and the viscosity ratio is of order one. It is established (in agreement with previous computations in the absence of electric fields) that a sufficiently thick annulus enables thread breakup while a sufficiently thin one (approximately one fifth of the undisturbed thread radius for the case of equal viscosities, for instance) suppresses pinching and drives the interface to approach the tube wall asymptotically without actually touching it. The present simulations show that the electric field affects the dynamics drastically in several ways. First, it promotes interfacial wall touchdown in finite time and a comparison between direct simulations and the asymptotic solutions are in fair agreement. Second, the electric field acts to suppress pinching in the sense that solutions that lead to jet breakup due to a thick enough viscous annulus are driven to wall touchdown. When pinching takes place we find that the ultimate pinching solutions are self-similar and recover the non-electrified ones to leading order for the range of parameters studied.

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Pinchoff and satellite formation in compound viscous threads

Cited by 15 publications

References 41 publications

Non-self-similar, linear dynamics during pinch-off of a hollow annular jet

Non-self-similar, linear dynamics during pinch-off of a hollow annular jet

Nonlinear dynamics and breakup of compound jets

Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities

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