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

Published online by Cambridge University Press:  05 December 2013

J. M. Gordillo ,
A. Sevilla  and
F. Campo-Cortés
J. M. Gordillo*
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingenería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n, 41092 Sevilla, Spain
A. Sevilla*
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos. Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
F. Campo-Cortés
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingenería Aeroespacial y Mecánica de Fluidos, Universidad de Sevilla, Avenida de los Descubrimientos s/n, 41092 Sevilla, Spain
*
†Email addresses for correspondence: [email protected], [email protected]
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

In this paper we reveal the physics underlying the conditions needed for the generation of emulsions composed of uniformly sized drops of micrometric or submicrometric diameters when two immiscible streams flow in parallel under the so-called tip streaming regime after Suryo and Basaran (Phys. Fluids, vol. 18, 2006, 082102). Indeed, when inertial effects in both liquid streams are negligible, the inner to outer flow-rate and viscosity ratios are small enough and the capillary number is above an experimentally determined threshold which is predicted by our theoretical results with small relative errors, a steady micrometre-sized jet is issued from the apex of a conical drop. Under these conditions, the jet disintegrates into drops with a very well-defined mean diameter, giving rise to a monodisperse microemulsion. Here, we demonstrate that the regime in which uniformly sized drops are produced corresponds to values of the capillary number for which the cone-jet system is globally stable. Interestingly enough, our general stability theory reveals that liquid jets with a cone-jet structure are much more stable than their cylindrical counterparts thanks, mostly, to a capillary stabilization mechanism described here for the first time. Our findings also limit the validity of the type of stability analysis based on the common parallel flow assumption to only those situations in which the liquid jet diameter is almost constant.

JFM classification

Instability: Absolute/convective instability Drops and Bubbles: Drops Low-Reynolds-number flows: Slender-body theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 738 , 10 January 2014 , pp. 335 - 357
Copyright
©2013 Cambridge University Press 

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Gordillo Arias de Saavedra supplementary movie

Non regular drop formation process for $\lambda=0.01$ and Ca=0.9, with Ca

Download Gordillo Arias de Saavedra supplementary movie(Video)
Video 1.7 MB

Gordillo Arias de Saavedra supplementary movie

Drop formation process for $\lambda=0.01$ and Ca\simeq Ca^*. Observe that there are two well defined frequencies of drop formation.

Download Gordillo Arias de Saavedra supplementary movie(Video)
Video 1.9 MB

Gordillo Arias de Saavedra supplementary movie

Drop formation process for $\lambda=0.01$ and $Ca=1.12$, with $Ca>Ca^*$. Observe that the drops ejected are virtually identical.

Download Gordillo Arias de Saavedra supplementary movie(Video)
Video 1.6 MB