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We report experiments in which a flow rate ${Q}_{i} $ of a fluid with a viscosity ${\\ensuremath{\\mu} }_{i} $ discharges into an immiscible liquid of viscosity ${\\ensuremath{\\mu} }_{o} $ that flows in parallel with the axis of the injector. When the outer capillary number verifies the condition ${\\mathit{Ca}}_{o} = {\\ensuremath{\\mu} }_{o} {U}_{o} / \\sigma ~\\geqslant ~5$, where ${U}_{o} $ and $\\sigma $ indicate, respectively, the outer velocity and the interfacial tension coefficient, and if the inner-to-outer velocity ratio is such that ${U}_{i} / {U}_{o} = {Q}_{i} / (\\lrm{\\pi} {U}_{o} { R}_{i}^{2} )\\ll 1$, with ${R}_{i} $ the inner radius of the injector, a jet is formed with the same type of cone–jet geometry as predicted by the numerical results of Suryo & Basaran (Phys. Fluids, vol. 18, 2006, p. 082102). For extremely low values of the velocity ratio ${U}_{i} / {U}_{o} $, we find that the diameter of the jet emanating from the tip of the cone is so small that drops with sizes below $1~\\lrm{\\ensuremath{\\mu}} \\mathrm{m} $ can be formed. We also show that, through this simple method, concentrated emulsions composed of micrometre-sized drops with a narrow size distribution can be generated. Moreover, thanks to the information extracted from numerical simulations of boundary-integral type and using the slender-body approximation due to Taylor (Proceedings of the 11th International Congress of Applied Mechanics, Munich, 1964, pp. 790–796), we deduce a third-order, ordinary differential equation that predicts, for arbitrary values of the three dimensionless numbers that control this physical situation, namely, ${\\mathit{Ca}}_{o} $, ${\\ensuremath{\\mu} }_{i} / {\\ensuremath{\\mu} }_{o} $ and ${U}_{i} / {U}_{o} $, the shape of the jet and the sizes of the drops generated. Most interestingly, the influence of the geometry of the injector system on the jet shape and drop size enters explicitly into the third-order differential equation through two functions that can be easily calculated numerically. Therefore, our theory can be used as an efficient tool for the design of new emulsification devices.

Here we extend the results in Gordillo et al.  ( J. Fluid Mech. , vol. 866, 2019, pp. 298–315), where the spreading of drops impacting perpendicularly a solid wall was analysed, to predict the time-varying flow field and the thickness of the liquid film created when a spherical drop of a low viscosity fluid, like water or ethanol, spreads over a smooth dry surface at arbitrary values of the angle formed between the drop impact direction and the substrate. Our theoretical results accurately predict the time evolving asymmetric shape of the border of the thin liquid film extending over the substrate during the initial instants of the drop spreading process. In addition, the particularization of the ordinary differential equations governing the unsteady flow when the rim velocity vanishes provides an algebraic equation for the asymmetric final shapes of the liquid stains remaining after the impact, valid for low values of the inclination angle. For larger values of the inclination angle, the final shape of the drop can be approximated by an ellipse whose major and minor semiaxes can also be calculated by making use of the present theory. The predicted final shapes agree with the observed remaining stains, excluding the fact that a liquid rivulet develops from the bottom part of the drop. The limitations of the present theory to describe the emergence of the rivulet are also discussed.

A robust method for the generation of phospholipid-covered monodisperse microbubbles of diameters smaller than 10 μm at production rates larger than 10 5  Hz is presented here. We show that bubbles are periodically formed from the tip of a long and thin gas ligament stabilized thanks to both the strong favorable pressure gradient existing at the entrance region of a long rectangular PDMS–PDMS channel and to the pinning of the gas–liquid interface at a centered groove of several microns' width placed on one of its walls. Moreover, the long exit channel incorporated in our design favors the transport of phospholipid molecules toward the gas–liquid interface. Our experiments show that the resulting phospholipid shell inhibits both the diffusion of the gas in the surrounding liquid and the coalescence between contacting bubbles. These evidences indicate that the proposed method is suitable for the generation of monodisperse microbubbles for diagnosis or therapeutical applications.