Global stability of stretched jets: conditions for the generation of monodisperse micro-emulsions using coflows

Gordillo, José Manuel; Sevilla, A.; Campo-Cortés, F.

doi:10.1017/jfm.2013.600

Cited by 45 publications

(43 citation statements)

References 42 publications

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“…The global stability analysis is greatly simplified by the use of onedimensional approximations to the full conservation equations, since the eigenvalue problem involves only the axial coordinate as an eigendirection (see e.g. Sauter & Buggisch 2005;Rubio-Rubio et al 2013;Gordillo et al 2014). In particular, a global stability analysis of the leading-order one-dimensional model for viscous liquid columns (García & Castellanos 1994;Eggers & Dupont 1994) was first applied to gravitationally stretched viscous jets by Sauter & Buggisch (2005), and refined later on by Rubio-Rubio et al (2013).…”

Section: Introductionmentioning

confidence: 99%

The nonlinear states of viscous capillary jets confined in the axial direction

Martínez-Calvo¹,

Rubio-Rubio²,

Sevilla³

2017

J. Fluid Mech.

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We report an experimental and theoretical study of the global stability and nonlinear dynamics of vertical jets of viscous liquid confined in the axial direction due to their impact on a bath of the same liquid. Previous works demonstrated that in the absence of axial confinement the steady liquid thread becomes unstable due to an axisymmetric global mode for values of the flow rate, Q, below a certain critical value, Q c , giving rise to oscillations of increasing amplitude that finally lead to a dripping regime (Sauter & Buggisch 2005;Rubio-Rubio et al. 2013). Here we focus on the effect of the jet length, L, on the transitions that take place for decreasing values of Q. The linear stability analysis shows good agreement with our experiments, revealing that Q c increases monotonically with L, reaching the semi-infinite jet asymptote for sufficiently large values of L. Moreover, as L decreases a quasi-static limit is reached, whereby Q c → 0 and the neutral conditions are given by a critical length determined by hydrostatics. Our experiments have also revealed the existence of a new regime intermediate between steady jetting and dripping, in which the thread reaches a limit-cycle state without breakup. We thus show that there exist three possible states depending on the values of the control parameters, namely steady jetting, oscillatory jetting and dripping. For two different combinations of liquid viscosity, ν, and injector radius, R, the boundaries separating these regimes have been determined in the Q-L parameter plane, showing that steady jetting exists for small enough values of L or large enough values of Q, dripping prevails for small enough values of Q or sufficiently large values of L, and oscillatory jetting takes place in an intermediate region whose size increases with ν and decreases with R.

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Section: Introductionmentioning

confidence: 99%

The nonlinear states of viscous capillary jets confined in the axial direction

Martínez-Calvo¹,

Rubio-Rubio²,

Sevilla³

2017

J. Fluid Mech.

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“…Yet another instance occurs when a liquid jet enters a coaxially and more rapidly flowing immiscible liquid. In suitable conditions the tip of the jet becomes pointed until a very thin filament, which ultimately breaks up into small drops, issues from Interfacial stability near a point where ω = 0 7 it; an example from Gordillo et al (2014) is shown in figure 1(c). This arrangement, referred to as flow focusing, has recently become the object of intense research in view of its importance for many microfluidic applications; see e.g.…”

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confidence: 99%

Local interfacial stability near a zero vorticity point

Tseng

Prosperetti

2015

J. Fluid Mech.

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It is often observed that small drops or bubbles detach from the interface separating two co-flowing immiscible fluids. The size of these drops or bubbles can be orders of magnitude smaller than the length scales of the parent fluid mass. Examples are tip-streaming from drops or coaxial jets in microfluidics, selective withdrawal, 'skirt' formation around bubbles or drops, and others. It is argued that these phenomena are all reducible to a common instability that can occur due to a local convergence of streamlines in the neighbourhood of a zero-vorticity point or line on the interface. When surfactants are present, this converging flow tends to concentrate them in these regions weakening the effect of surface tension, which is the only mechanism opposing the instability. Several analytical and numerical calculations are presented to substantiate this interpretation of the phenomenon. In addition to some idealized cases, the results of two-dimensional simulations of co-flowing jets and a rising drop are presented.

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“…While previous works focus on the zero flow rate limit Qð0; tÞ ! 0 in a linear straining flow [22] or pressure driven flow [34,35], this work focuses on Qð0; tÞ ¼ pa 2 Uð0Þ in a nonlinear free surface extensional flow with position-dependent viscosity.…”

Section: Problem Formulationmentioning

confidence: 99%

A Long Wavelength Model for Manufacturing of Continuous Metal Microwires by Thermal Fiber Drawing From a Preform

Zhao

2017

Journal of Micro and Nano-Manufacturing

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Thermal drawing from a preform recently emerges as a scalable manufacturing method for the high volume production of continuous metal microwires for numerous applications. However, no model can yet satisfactorily provide effective understanding of core diameter and continuity from process parameters and material properties during thermal drawing. In this paper, a long wavelength model is derived to describe the dynamics of a molten metal micro-jet entrained within an immiscible, viscous, nonlinear free surface extensional flow. The model requires numerical data (e.g., drawing force and cladding profile) be measured in real time. Examination of the boundary conditions reveals that the diameter control mechanism is essentially volume conservation. The flow rate of molten metal is controlled upstream while the flow velocity is controlled downstream realized by solidification of the molten metal. The dynamics of the molten metal jet are found to be dominated by interfacial tension, stress in the cladding, and pressure in the molten metal. Taylor's conical fluid interface solution (Taylor, 1966, “Conical Free Surfaces and Fluid Interfaces,” Applied Mechanics, Springer, Berlin, pp. 790–796.) is found to be a special case of this model. A dimensionless capillary number Ca=2Fa/γA(0) is suggested to be used as the indicator for the transition from continuous mode (i.e., viscous stress dominating) to dripping mode (i.e., interfacial tension dominating). Experimental results showed the existence of a critical capillary number Cacr, above which continuous metal microwires can be produced, providing the first ever quantitative predictor of the core continuity during preform drawing of metal microwires.

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Global stability of stretched jets: conditions for the generation of monodisperse micro-emulsions using coflows

Cited by 45 publications

References 42 publications

The nonlinear states of viscous capillary jets confined in the axial direction

The nonlinear states of viscous capillary jets confined in the axial direction

Local interfacial stability near a zero vorticity point

A Long Wavelength Model for Manufacturing of Continuous Metal Microwires by Thermal Fiber Drawing From a Preform

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