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Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries

P. Guillot, A. Colin, A. Ajdari — Phys. Rev. E 78 (2008) 107807

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We address the question of the stability of a confined coflowing jet at low Reynolds number in various
geometries. Our study is motivated by recent experiments in microfluidic devices. When immiscible fluids flow
in microchannels, either monodisperse droplets or parallel flows are obtained depending upon the flow rate of
the aqueous phase and the oil phase. In these experiments, the confining and the shape of the geometry play a
fundamental role. In a previous paper -Guillot et al., Phys. Rev. Lett 99, 104502 -2007—, we analyzed the
stability of the jet in the framework of the lubrication approximation at low Reynolds number in a cylindrical
geometry, and we related the transition between the droplets regime and the jet regime to the absoluteconvective
transition of the Rayleigh plateau instability. In this work, the effect of the channel geometry and
the jet position within the microfluidic device are discussed. New flow patterns are pointed out. Bidimensional
jets are encountered in square and rectangular geometry. Contrary to jets occuring in circular geometry, these
two-dimensional jets are absolutely stable. Focusing on situations where the inner fluid is more viscous than
the outer one, we evidence a range of parameters where droplets are produced through a blocking and pinching
mechanism. In this particular case, the flow is unstable, the growing perturbations are convected upstream. This
induces the clogging of the channel by the internal phase and its pinching by the external one. In a future
presentation we will give a comparison between this model and experimental data.