Unconditional jetting

Capillary jetting of a fluid dispersed into another immiscible phase is usually limited by a critical Capillary number, a function of the Reynolds number and the fluid properties ratios. Critical conditions are set when the minimum spreading velocity of small perturbations $v^*_-$ along the jet (marginal stability velocity) is zero. Here we identify and describe parametrical regions of high technological relevance, where $v^*_- > 0$ and the jet flow is always supercritical independently of the dispersed liquid flow rate: within these relatively broad regions, the jet does not undergo the usual dripping-jetting transition, so that either the jet can be made arbitrarily thin (yielding droplets of any imaginably small size), or the issued flow rate can be made arbitrarily small. In this work, we provide illustrative analytical studies of asymptotic cases for both negligible and dominant inertia forces. In this latter case, requiring a non-zero jet surface velocity, axisymmetric perturbation waves ``surf'' downstream for all given wave numbers while the liquid bulk can remain static. In the former case (implying small Reynolds flow) we found that the jet profile small slope is limited by a critical value; different published experiments support our predictions.Comment: Submitted first (24-August-2008) to Physics of Fluids, withdrawn from that journal on 6-April-2008, and submitted to Physical Review E the same da

Opposed flow focusing: evidence of a second order jetting transition

We propose a novel microfluidic "opposed-flow" geometry in which the continuous fluid phase is fed into a junction in a direction opposite the dispersed phase. This pulls out the dispersed phase into a micron-sized jet, which decays into micron-sized droplets. As the driving pressure is tuned to a critical value, the jet radius vanishes as a power law down to sizes below 1 $\mu$m. By contrast, the conventional "coflowing" junction leads to a first order jetting transition, in which the jet disappears at a finite radius of several $\mu$m, to give way to a "dripping" state, resulting in much larger droplets. We demonstrate the effectiveness of our method by producing the first microfluidic silicone oil emulsions with a sub micron particle radius, and utilize these droplets to produce colloidal clusters

Spatiotemporal instability of a confined capillary jet

Recent experimental studies on the instability appearance of capillary jets have revealed the capabilities of linear spatiotemporal instability analysis to predict the parametrical map where steady jetting or dripping takes place. In this work, we present an extensive analytical, numerical and experimental analysis of confined capillary jets extending previous studies. We propose an extended, accurate analytic model in the limit of low Reynolds flows, and introduce a numerical scheme to predict the system response when the liquid inertia is not negligible. Theoretical predictions show a remarkable accuracy with results from the extensive experimental exploration provided.Comment: Submitted to the Physical Review E (20-March-2008

Dripping to jetting transition for cross-flowing liquids

International audienceWe experimentally study drops formed from a nozzle into an immiscible, cross-flowing phase. Depending on the operating conditions, drops are generated either in dripping or jetting mode. We investigate the impact of the continuous and dispersed phase velocities, dispersed phase viscosity, and interfacial tension on the drop generation mode and size. We find that a dripping to jetting transition (DJT) takes place at a critical inner Weber number, a function of the outer capillary and Ohnesorge numbers. Two jetting regimes occur depending on the phase velocity ratio. When the continuous phase velocity is significantly greater (respectively lower) than the dispersed phase velocity, jet narrowing (respectively widening) occurs. In jet widening, the critical inner Weber number depends little on the outer capillary number whereas in jet narrowing, it sharply decreases as the outer capillary number increases. We propose a comprehensive model to describe the DJT based on the attached drop equation of motion. The model satisfactorily predicts the DJT and the effect of the outer capillary number on the critical inner Weber number. It also well accounts for the drop diameter in jet narrowing

Quantitative analysis of the dripping and jetting regimes in co-flowing capillary jets

We study a liquid jet that breaks up into drops in an external co-flowing liquid inside a confining microfluidic geometry. The jet breakup can occur right after the nozzle in a phenomenon named dripping or through the generation of a liquid jet that breaks up a long distance from the nozzle, which is called jetting. Traditionally, these two regimes have been considered to reflect the existence of two kinds of spatiotemporal instabilities of a fluid jet, the dripping regime corresponding to an absolutely unstable jet and the jetting regime to a convectively unstable jet. Here, we present quantitative measurements of the dripping and jetting regimes, both in an unforced and a forced state, and compare these measurements with recent theoretical studies of spatiotemporal instability of a confined liquid jet in a co-flowing liquid. In the unforced state, the frequency of oscillation and breakup of the liquid jet is measured and compared to the theoretical predictions. The dominant frequency of the jet oscillations as a function of the inner flow rate agrees qualitatively with the theoretical predictions in the jetting regime but not in the dripping regime. In the forced state, achieved with periodic laser heating, the dripping regime is found to be insensitive to the perturbation and the frequency of drop formation remains unaltered. The jetting regime, on the contrary, amplifies the externally imposed frequency, which translates in the formation of drops at the frequency imposed by the external forcing. In conclusion, the dripping and jetting regimes are found to exhibit the main features of absolutely and convectively unstable flows respectively, but the frequency selection in the dripping regime is not ruled by the absolute frequency predicted by the stability analysis.Comment: 10 pages, 12 figures, to appear in Physics of Fluid

Scaling the drop size in coflow experiments

We perform extensive experiments with coflowing liquids in microfluidic devices and provide a closed expression for the drop size as a function of measurable parameters in the jetting regime that accounts for the experimental observations; this expression works irrespective of how the jets are produced, providing a powerful design tool for this type of experiment