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The breakup of a charged liquid column is studied numerically using Volume-OF-Fluid (VOF) for a range of timescales where electrokinetic phenomena may become significant, i.e when the time to breakup becomes comparable or shorter than the diffusion and the electroosmotic migration times of charged species. Here we propose a conservative method to deal with the diffusion of a tracer in VOF schemes when the diffusion is limited to one of the phases. The method consists in weighing the diffusivity with the value of the volume fraction computed from the analytically reconstructed interface. In this way, the interface is made impermeable to the tracer, which is conservatively kept within one of the phases. The performance of this method is first tested by comparing simple configurations with existing analytical solutions. In the cases when the diffusion, electroosmotic motion and hydrodynamic singularities compete, the results indicate that, after breakup, charges distribute between droplets differently from models assuming homogeneous and constant electrical conductivities (i.e. no electrokinetic effects). However, such departure does not alter the main hydrodynamic balances leading to well-established scaling laws of breakup. [ABSTRACT FROM AUTHOR]

• We describe the whipping instability in gaseous flow focusing. • Whipping instability is explained in terms of the global stability analysis. • We analyze the influence of the geometry on the whipping instability. We study both theoretically and experimentally the whipping instability in axisymmetric gaseous flow focusing realized in a converging-diverging nozzle. The lateral oscillation of both the tapering meniscus and emitted jet is explained in terms of the global linear instability of the lateral mode with the azimuthal number m = 1. A comparison with previous experiments shows good agreement. The distance between the feeding capillary and the nozzle neck hardly affects the m = 1 stability limit for the conditions considered in those experiments. We analyze the influence of the nozzle shape on the parameter conditions leading to whipping. As the nozzle convergence rate (the inverse of the length over which the diameter reduction takes place) increases, the flow becomes more stable under m = 1 perturbations. The above results are in marked contrast with those of the axisymmetric mode m = 0. For the axisymmetric mode, the minimum flow rate increases with the nozzle convergence rate, while the capillary-to-neck distance has considerable influence on the jetting-to-dripping transition. We also conduct experiments with different nozzles and capillary-to-neck distances to examine the effect of those factors on the stability of the jetting regime. The experiments allow us to distinguish between absolute whipping, in which both the tapering meniscus and the emitted jet oscillate, and convective whipping, in which the jet oscillates while the meniscus remains practically steady. Absolute whipping is observed for water and 1-cSt silicone oil focused with the nozzle with the smallest convergence rate and capillary-to-neck distance. The increase of the liquid viscosity stabilizes the liquid meniscus, producing the transition from absolute to convective whipping. In the high-viscosity case, the oscillation of the emitted jet far away from the discharge orifice is considerably affected by the shape of the nozzle in front of its neck. In fact, the increase of the convergence rate and capillary-to-neck distance eliminates the convective whipping as well. The reduction of surface tension enhances absolute whipping. We explain the appearance of the two types of whipping in terms of the flow pattern induced by the nozzle shape in front of the neck. [ABSTRACT FROM AUTHOR]

A novel microfluidic technique has been recently proposed to produce quasi-monodisperse collections of microbubbles with a controlled size. In this technique, a gaseous stream is injected through a T-junction into a microchannel transporting a liquid current. The gas adheres to a hydrophobic strip printed on the channel surface. When the gas and liquid flow rates are set appropriately, a gaseous rivulet flows over that strip. The rivulet breaks up downstream due to a capillary pearling instability, which leads to a quasi-monodisperse collection of microbubbles. Motivated by this application, we here analyze the stability of both gas and liquid rivulets coflowing with a current in a quadrangular microfluidic channel. The results essentially differ from those of cylindrical jets because the contact-line-anchorage condition affects fundamentally the rivulet’s instability nature. The temporal stability analysis shows that the rivulet becomes unstable not only for (unperturbed) contact angles larger than 90° (as can be expected) but also for values smaller than that angle. Interestingly enough, the maximum growth factor exhibits a non-monotonic dependence with respect to the Reynolds number (i.e., the viscosities). In fact, there are intervals of that parameter where the fluid system becomes unstable, while all the perturbations are damped outside that interval. The gaseous rivulet does not stabilize as the Reynolds number decreases, which means that it can be unstable even in the Stokes limit and for contact angles less than 90°. In addition, the stability of a flowing liquid rivulet is not determined by its contact angle exclusively (as occurs in the static case), but by the Reynolds number as well. Liquid rivulets with contact angles less than 90° can be unstable for sufficiently high Reynolds numbers. [ABSTRACT FROM AUTHOR]

• We analyze the stability of transonic flow focusing. • We determine the minimum liquid flow rate for steady jetting. • We derive a scaling law for the jet diameter. We study numerically and experimentally the stability of the transonic flow focusing used in serial femtosecond crystallography (SFX) to place complex biochemical species into the beam focus. Both the numerical and experimental results indicate that the minimum flow rate for steady jetting increases slightly with the gas stagnation pressure. There is a remarkable agreement between the stability limit predicted by the global stability analysis and that obtained experimentally. Our simulations show that the steady jetting interruption at the critical flow rate is caused by the growth of a perturbation with a constant phase shift. This result is consistent with the experimental observations, which indicate that both the meniscus tip and the emitted jet collapse almost simultaneously at the stability limit. We derive a scaling law for the jet diameter as a function of the liquid flow rate and gas density/pressure from more than one hundred simulations. The scaling law provides accurate predictions for the jet diameter within the range of values [0.549,10.9] μ m analyzed in this work. [ABSTRACT FROM AUTHOR]