Droplet Pinch-off Research Articles

Electric field-induced pinch-off of a compound droplet in Poiseuille flow

We address the pinch-off dynamics of a compound droplet that is suspended in a carrier fluid in a parallel plate microchannel. The droplet is subjected to a transverse electric field in the presence of an imposed pressure-driven flow. When a concentric compound droplet migrates in a pressure driven flow, the inner droplet deviates from the concentric position and forms an eccentric configuration that finally leads to the pinch-off of the outer shell. Our results reveal that the temporal evolution of droplet eccentricity as well as the kinetics of the thinning of the outer droplet is markedly influenced by the strength of the electric field as well as the electric properties of the fluids. We also bring out the conversion of different modes of droplet pinch-off, such as the equatorial cap breakup or the equatorial hole-puncture mode, by altering the electric field strength and electrical properties of the fluids. We also identify the relevant pointers that dictate the pinch-off time as well as the location of the pinch-off. This, in turn, opens up novel means of modulating the morphology of double emulsion in a confined channel by applying an electric field.

Wetting controls of droplet formation in step emulsification

The formation of droplets is ubiquitous in many natural and industrial processes and has reached an unprecedented level of control with the emergence of milli- and microfluidics. Although important insight into the mechanisms of droplet formation has been gained over the past decades, a sound understanding of the physics underlying this phenomenon and the effect of the fluid's flow and wetting properties on the droplet size and production rate is still missing, especially for the widely applied method of step emulsification. In this work, we elucidate the physical controls of microdroplet formation in step emulsification by using the wetting of fluidic channels as a tunable parameter to explore a broad set of emulsification conditions. With the help of high-speed measurements, we unequivocally show that the final droplet pinch-off is triggered by a Rayleigh-Plateau-type instability. The droplet size, however, is not determined by the Rayleigh-Plateau breakup, but by the initial wetting regime, where the fluid's contact angle plays a crucial role. We develop a physical theory for the wetting process, which closely describes our experimental measurements without invoking any free fit parameter. Our theory predicts the initiation of the Rayleigh-Plateau breakup and the transition from dripping to jetting as a function of the fluid's contact angle. Additionally, the theory solves the conundrum why there is a minimal contact angle of α = 2π/3 = 120° for which droplets can form.

Pinch-off of microfluidic droplets with oscillatory velocity of inner phase flow

When one liquid is introduced into another immiscible one, it ultimately fragments due to hydrodynamic instability. In contrast to neck pinch-off without external actuation, the viscous two-fluid system subjected to an oscillatory flow demonstrates higher efficiency in breaking fluid threads. However, the underlying dynamics of this process is less well understood. Here we show that the neck-thinning rate is accelerated by the amplitude of oscillation. By simply evaluating the momentum transfer from external actuation, we derive a dimensionless pre-factor to quantify the accelerated pinch-off. Our data ascribes the acceleration to the non-negligible inner fluid inertia, which neutralizes the inner phase viscous stress that retards the pinch-off. Moreover, we characterize an equivalent neck-thinning behavior between an actuated system and its unactuated counterpart with decreased viscosity ratio. Finally, we demonstrate that oscillation is capable of modulating satellite droplet formation by shifting the pinch-off location. Our study would be useful for manipulating fluids at microscale by external forcing.

Depletion forces induce visco-elasto-capillary thinning of non-Brownian suspensions

Droplet pinch-off, which occurs when a drop of liquid detaches from a capillary, can be strongly modified in the presence of complex fluids such as polymer solutions and suspensions giving rise to long and slender filaments that thin slowly in time. While for polymers, the molecular conformations of the molecules in the filament are responsible for such a behavior, in suspensions the mechanisms at play remain to be deciphered. Here we show, experimentally, that while liquid bridges of non-Brownian suspensions of moderate concentrations have a thinning behavior very close to that of the solvent, the addition of short-chain polymers inducing depletion attractions between the particles in the suspension changes the thinning dynamics and gives rise to exponential thinning in time. The characteristic time of this dynamics increases with polymer concentration and therefore the intensity of the depletion forces at play. The tunability of this dynamics may be important for injket and 3D printing applications where short rupture times are sought for or in other situations where drop formation has to be minimized or inhibited.

Asymmetric collapse by dissolution or melting in a uniform flow.

An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton-Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). The model raises fundamental mathematical questions about broken symmetries in finite-time singularities of both continuous and stochastic dynamical systems.

Thin-finger growth and droplet pinch-off in miscible and immiscible displacements in a periodic network of microfluidic channels

We report the results of experimental and numerical studies of two-phase flow in a periodic, rectangular network of microfluidic channels. This geometry promotes the formation of anisotropic, dendrite-like structures during viscous fingering experiments. The dendrites then compete with each other for the available flow, which leads to the appearance of hierarchical growth pattern. Combining experiments and numerical simulations, we analyze different growth regimes in such a system, depending on the network geometry and fluid properties. For immiscible fluids, a high degree of screening is present which results in a power-law distribution of finger lengths. Contrastingly, for miscible fluids, strong lateral currents of displaced fluid lead to the detachment of the heads of the longest fingers from their roots, thus preventing their further growth.

Droplet pinch-off in acoustically actuated flow-focusing devices

The evolution of the interfacial profile for one complete droplet formation process in a flow-focusing device was investigated. Two critical curvature values that represent the liquid thread detachment from walls and the onset of pinch-off were discovered. The rate of curvature evolution depends on the flow-rate ratio between the two immiscible fluids and was modulated by acoustic actuation. Three distinct evolution regions which represent, respectively, the periods before and after the liquid thread detachment from walls and after the onset of pinch-off till final breakup are shown. In the case under acoustic actuation, the droplet formation process is accelerated; both the time till the liquid thread detachment from walls and the onset of pinch-off are speeded up. Phase-averaged two-phase micro-particle-image-velocimetry (µPIV) was applied to extract the oscillating flow fields in the two immiscible phases. Periodic contracting and expanding streaming flow fields in the dispersed phase and steady streaming flow fields in the continuous phase were obtained. The steady streaming flow in the continuous phase provides an additional driving force which helps to drive the continuous phase into the gutters. This additional flow facilitates the onset of breakup and thus smaller droplets are formed upon acoustic actuation.

One-dimensional simulation of thin liquid-film-edge retraction

The phenomenon of liquid film retraction, occurring in bursting bubbles, is investigated in the simplest case of a semi-infinite sheet of inviscid liquid. Discretized equations of motion are solved on a staggered grid, with the boundary condition adapted to handle movement and breakup of liquid domain. Two independent approaches show a perfect agreement. The calculation shows a periodic pinchoff of small droplets, in contrast to the published results on viscid fluids where the liquid accumulates at the rim. A quantitative analysis of simulated liquid profiles shows that the characteristic parameters are very close to the theoretical predictions obtained from energy conservation and laws of motion.

Detailed simulation of primary atomization mechanisms in Diesel jet sprays (isolated identification of liquid jet tip effects)

In this study, the atomization characteristics of Diesel jet front tip have been investigated to elucidate the physical mechanisms by detailed numerical simulation. The computations are carried out with the finest grid resolutions ever that can resolve the final droplet generation by surface tension. The numerical methods are based on level-set interface tracking. The methods were validated by test cases and the grid resolution survey shows that the resolutions for the present study are sufficient. The present flow setup excludes nozzle disturbances to investigate how the disturbances from the liquid jet front would lead to atomization where the liquid jet impacts against the quiescent gas. The liquid jet front becomes an umbrella-like shape. From the front umbrella tip edge, ligament breakup first occurs. Ligament breakup is strongly correlated with the gas motion in the vicinity. The gas region behind the front is highly disturbed by atomization. By the gas recirculation motion here, air and some droplets are entrained and mixed. Also, the disturbances are fed back to the front umbrella by this motion and become synchronized with the breakup. Droplet pinch-off is mainly in the short-wave mode, but some ligaments are elongated by local gas stretch to finally have a long-wave mode shape, namely a mode shift occurs. The above findings of liquid jet front umbrella formation, atomization at the umbrella edge, mixing and atomization loop in the recirculation flow region and droplet generation mode give an insight to the modeling of droplet generation in actual sprays.

Partial universality: pinch-off dynamics in fluids with smectic liquid crystalline order

Droplet pinch-off of fluids with liquid crystalline order is a common yet poorly understood process. We report on measurements of pinch-off dynamics for a lyotropic surfactant/water solution in the lamellar phase and a thermotropic liquid crystal in the smectic phase. We find pinch-off is universal and well described by a similarity solution for a strain thinning power-law fluid. This finding is consistent with bulk rheology measurements which show these materials shear thin with the appropriate power-law dependence. Remarkably, we find depending on material processing, this universal pinch-off cuts off at different length scales. Collectively, these phenomena lead to an exceptional form of singularity where pinch-off is both universal and dependent on initial conditions.

Application of Smoothed Particle Hydrodynamics Method to Free Surface and Solidification Problems

The smoothed particle hydrodynamics (SPH) method is developed to simulate free surface and solidification problems. A new treatment is included to handle particles near the free and solidification interfaces. The method is applied to a droplet impacting on substrates with different roughnesses. Spreading, solidification, oxide redistribution, and droplet pinch-off are presented in two- and three-dimensional geometry configurations. This work demonstrates the SPH model as a powerful tool to study transport phenomena in problems with free surface deformation and solidification.

A coupled quadrilateral grid level set projection method applied to ink jet simulation

A coupled level set-projection method on quadrilateral grids is developed for piezoelectric ink jet simulations. The model is based on the Navier–Stokes equations for incompressible two-phase flows in the presence of surface tension and density jump across the interface separating ink and air, coupled to an electric circuit model which describes the driving mechanism behind the process, and a macroscopic contact model which describes the air–ink–wall dynamics. We simulate the axisymmetric flow on quadrilateral grids using a combination of second-order finite difference projection methods to solve the fluid equations and level set methods to track the air/ink interface. To improve the mass conservation performance of the coupled level set method, a bicubic interpolation is combined with the Fast Marching Method for level set re-initialization on quadrilateral grids. The numerical method is used to analyze the motion of the interface, droplet pinch off, formation of satellites, effect of nozzle geometry on droplet size and motion, and the dynamics for droplet landing. The simulations are faithful to the dimensions and physics of a particular class of inkjet devices.