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

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 & Basaran (2006). 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 micron-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 micro-emulsion. 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.