We experimentally study drops formed from a nozzle into an immiscible, crossflowing 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, 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 (resp. lower) than the dispersed phase velocity, jet narrowing (resp. 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. I. INTRODUCTION Membrane emulsification is an industrial process used to generate emulsions by forcing a dispersed phase through an inorganic, porous membrane into a continuous cross-flowing phase. 1 This process is usually operated in dripping (drop by drop) mode. The shear stress exerted by the continuous phase controls drop formation, so drag and the retaining capillary force are the main forces involved. In dripping mode, the drop diameter decreases with increasing shear stress, while remaining greater than the membrane pore size. A first estimate of the drop diameter may be given by a simple torque balance about the pore edge. 2 More recently, alternative fabrication methods based on microfluidics have appeared, such as flow-focusing and coflowing devices. These devices commonly operate in dripping or jetting (continuous jet) mode. 3-6 In jetting mode, the liquid thread breaks up by Plateau-Rayleigh instabilities. In certain operating conditions, drops much smaller than the nozzle diameter may be produced. The same trend is expected for membrane emulsification operated in jetting mode. Thus, it is of high interest to study the dripping to jetting transition (DJT) in this process. A DJT can occur if the liquid thread exiting the nozzle grows to a length comparable to its radius and if the pinch-off time is larger than the thread growth time. 7 The simplest case is the dripping faucet, where a dispersed phase flows from a nozzle into a stagnant, immiscible outer phase. Smith and Moss 8 studied mercury jets into gases and found that above a critical velocity (named the jetting velocity), the liquid exits the nozzle as a jet. They proposed an empirical expression for the jetting velocity, which can be recovered from a simple balance between the jet momentum flux and the retaining capillary force. Scheele and Meister 9 investigated the DJT for fifteen l...

We experimentally investigate single drop formation from a vibrating capillary tube immersed in a second immiscible liquid. At set forcing frequencies, significantly smaller drops are generated when a threshold amplitude is reached. We show that a drop grows and resonates in first mode once the drop resonance frequency and the forcing frequency coincide. The drop then detaches by a stretching mode if its elongation ratio exceeds a critical value, function of the drop to pore diameter ratio. The detached drop diameter is well described by the Bisch et al. expression for bound drop resonance frequency. Otherwise, the drop grows, leaves the first-mode resonance range and detaches at a larger size by dripping. The threshold and drop diameters are well predicted by a simple LFHO-based model. Introduction.-Controlling drop breakup is key for industries performing emulsification such as the food, pharmaceutical and chemical industries. Indeed, drop size and distribution affect emulsion rheological properties and stability. Membrane emulsification (ME) consists in forcing a dispersed phase through a porous membrane. The drops are directly generated on the other side of the membrane into a continuous flowing phase, which exerts shear on the drops [1]. ME is commonly operated in dripping (drop by drop) mode.

Drop generation from an axially vibrating nozzle exhibits a transition in drop diameter when varying the vibration amplitude. Below a threshold amplitude, forcing has essentially no effect on drop size and drops form in dripping mode. Above the threshold, drop size is controlled by forcing: drops detach at resonance, i.e., when the first eigenfrequency of the growing drop coincides with the forcing frequency. We experimentally study the impact of the nozzle inner diameter, dispersed phase flow rate, interfacial tension, and dispersed phase viscosity on this transition. Drop diameter is well correlated to the mode 1 eigenfrequency of Strani and Sabetta for a drop in partial contact with a spherical bowl. We propose a transient model to describe drop dynamics until detachment. The drop is modelled as a linearly forced harmonic oscillator, with the eigenfrequency of Strani and Sabetta. Since the dispersed phase does not wet the nozzle tip, an additional damping coefficient is introduced to account for the viscous dissipation in the film of continuous phase between the drop and nozzle surface. The model adequately reproduces the effect of the different parameters on the threshold amplitude.