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Droplets in Microchannels: Dynamical Properties of the Lubrication Film

Abstract : We study the motion of droplets in a confined, micrometric geometry, by focusing on the lubrication film between droplet and wall. When capillary forces dominate, the lubrication film thickness evolves non linearly with the capillary number due to viscous dissipation between meniscus and wall. However, this film may become thin enough (tens of nanometers) that intermolecular forces come into play and affect classical scalings. Our experiments yield highly resolved topographies of the shape of the interface and allow us to bring new insights into droplet dynamics in microfluidics. We report the novel characterization of two dynamical regimes as the capillary number increases: (i) at low capillary numbers, the film thickness is constant and set by the disjoinging pressure, while (ii) above a critical capillary number, the interface behavior is well described by a viscous scenario. At a high surfactant concentration, structural effects lead to the formation of patterns on the interface , which can be used to trace the interface velocity that yield direct confirmation of boundary condition in viscous regime. The dynamics of a droplet confined between solid walls and pushed by a surrounding liquid is an old problem, however recent theories are still being developed to describe unexplored regimes and experimental characterizations are still lacking to shed light on these novel developments. A complete understanding of the droplet velocity calls for accurate knowledge of the dissipation mechanisms involved, particularly in the lubrication film. Our understanding of the lubrication properties of menisci travelling in confined geometries has been steadily refined since the pioneering work of Taylor & Saffman [1]. Notably, the influence of the lubrication film left along the wall by the moving meniscus was first taken into account by Bretherton, who investigated the motion of an inviscid bubble in a cylindrical tube [2]. Far from the meniscus, this dynamical film reaches a uniform thickness h ∞ , related to the bubble velocity through the capillary number Ca = µ f U d /γ, where U d is the bubble velocity , µ f the viscosity of the continuous phase, and γ the surface tension. When the capillary pressure dominates over the viscous stress, i.e. in the regime where Ca 1, the thickness of the film follows h Breth = 1.34 r Ca 2/3 , where r is the radius of the capillary tube. Besides bubbles , the case of viscous droplets remains however largely unexplored. A recent theoretical advance in the field by Hodges et al. [3] shows by numerical calculations of the whole flow pattern that significant corrections in the thickness of lubrication films can arise at very low Ca. Furthermore, the regime of the Bretherton theory is only valid for lubrication films thicker than the molecular sizes or than the range of interfacial interactions. The typical velocities and lengthscales involved in droplet-based microfluidics would lead to lubrication films h ∞ ∼ 7
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Submitted on : Wednesday, September 23, 2015 - 10:14:58 AM
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Axel Huerre, Olivier Theodoly, Alexander Leshansky, Marie-Pierre Valignat, Isabelle Cantat, et al.. Droplets in Microchannels: Dynamical Properties of the Lubrication Film. Physical Review Letters, American Physical Society, 2015, 115 (6), pp.064501. ⟨10.1103/PhysRevLett.115.064501⟩. ⟨hal-01201928⟩

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