The effect of surfactant on the stability of a liquid thread

Timmermans, Mary-Louise E.; Lister, Joseph

doi:10.1017/s0022112002008224

Cited by 93 publications

(138 citation statements)

References 25 publications

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“…It is worthwhile noting that, in disagreement with recent theoretical predictions (Timmermans & Lister 2002), albeit for insoluble surfactants, the final interfacial tension is not that of pure water. In principle, it remains possible that there is an ultimate state of breakup in which the surface is completely devoid of surfactants.…”

Section: Inertial Casecontrasting

confidence: 69%

“…Theoretical work on drop formation with insoluble surfactants suggests that the ultimate stages of the thinning of the fluid neck just before breakup may be accompanied by a total depletion of the surfactants from the rupture zone leaving the surface bare, i.e. without surfactant (Timmermans & Lister 2002). That the surfactant is depleted significantly from the rupture zone, engendering large gradients of the surface concentration of the surfactant has been confirmed by numerical work for both soluble (Craster et al 2009) and insoluble surfactants (Craster et al 2002;Xu et al 2007).…”

Section: Introductionmentioning

confidence: 84%

“…When drop formation from such surfactant-laden solutions is considered, the detailed dynamics of the rupture process leading to drop formation and eventually to satellite drops will be affected by the properties of the surface (Eggers 1997;Eggers & Villermaux 2008). Several studies have focused on drop formation in the presence of insoluble surfactants (Ambravaneswaran & Basaran 1999;Craster, Matar & Papageorgiou 2002;Timmermans & Lister 2002;Liao, Franses & Basaran 2006;McGough & Basaran 2006;Xu, Liao & Basaran 2007). Fewer studies have been devoted to soluble surfactants (Jin, Gupta & Stebe 2006;Craster, Matar & Papageorgiou 2009).…”

Section: Introductionmentioning

confidence: 99%

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Dynamic interfacial tension effects in the rupture of liquid necks

et al. 2012

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By examining the rupture of fluid necks during droplet formation of surfactant-laden liquids, we observe deviations from expected behaviour for the pinch-off of such necks. We suggest that these deviations are due to the presence of a dynamic (time-varying) interfacial tension at the minimum neck location and extract this quantity from our measurements on a variety of systems. The presence of such dynamic interfacial tension effects should change the rupture process drastically. However, our measurements show that a simple ansatz, which incorporates the temporal change of the interfacial tension, allows us to understand the dynamics of thinning. This shows that this dynamics is largely independent of the exact details of what happens far from the breakup location, pointing to the local nature of the thinning dynamics.

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Section: Inertial Casecontrasting

confidence: 69%

Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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Dynamic interfacial tension effects in the rupture of liquid necks

et al. 2012

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“…To discuss the general linear stability properties we note that in the absence of electric fields, the core thread is subject to Rayleigh instability when the wavenumber of the perturbation is below the critical value k = 1. The presence of the annular fluid provides a long wavelength cut-off with the growth rate becoming zero at k = 0 as opposed to the constant value predicted by Stokes flow (see Timmermans & Lister (2002) for a discussion of this and several other limits in the linear regime). Such effects are shown in figure 2 when an electric field is also present; the dotted lines in panels (a) and (b) represent the results for a single fluid Stokes jet and agree with Wang et al (2009).…”

Section: Linear Stability Analysismentioning

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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“…More complete linear stability studies of surfactant effects on CAF arrangements can be found in for quiescent fluids and Kwak, Fyrillas & Pozrikidis (2001) for liquid threads in extensional flow. The linear stability studies of surfactant-laden liquid threads by Hansen, Peters & Meijer (1999) and Timmermans & Lister (2002) are also of interest as well as the nonlinear models and calculations of Craster, Matar & Papageorgiou (2002).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of core-annular film flows in the presence of surfactant

2009

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The nonlinear stability of two-phase core-annular flow in a cylindrical pipe is studied. A constant pressure gradient drives the flow of two immiscible liquids of different viscosities and equal densities, and surface tension acts at the interface separating the phases. Insoluble surfactants are included and we assess their effect on the flow stability and ensuing spatio-temporal dynamics. We achieve this by developing an asymptotic analysis in the limit of a thin annular layer -this is usually the relevant regime in applications -to derive a coupled system of nonlinear evolution equations that govern the dynamics of the interface and the local surfactant concentration on it. In the absence of surfactants the system reduces to the Kuramoto-Sivashinsky (KS) equation and its modifications due to viscosity stratification (present when the phases have unequal viscosities) are derived elsewhere. We report on extensive numerical experiments to evaluate the effect of surfactants on KS dynamics (including chaotic states, for example), both in the absence and presence of viscosity stratification. We find that chaos is suppressed in the absence of viscosity differences and that the new flow consists of successive windows (in parameter space) of steady-state travelling waves separated by time-periodic attractors. The intricate structure of the travelling pulses is also explained physically. When viscosity stratification is present we observe a transition from time-periodic dynamics, for instance, to steady-state travelling wave pulses of increasing amplitudes and speeds. Numerical evidence is presented that indicates that the transition occurs through a reverse Feigenbaum cascade in phase space.

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The effect of surfactant on the stability of a liquid thread

Cited by 93 publications

References 25 publications

Dynamic interfacial tension effects in the rupture of liquid necks

Dynamic interfacial tension effects in the rupture of liquid necks

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

Nonlinear dynamics of core-annular film flows in the presence of surfactant

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