Breakup Of Threads Research Articles

Surfactant-laden liquid thread breakup driven by thermal fluctuations

The breakup of liquid threads into droplets is crucial in various applications, such as nanoprinting, nanomanufacturing, and inkjet printing, where a detailed understanding of the thinning neck dynamics allows for a precise droplet control. Here, the role of surfactant in the breakup process is studied by many-body dissipative particle dynamics, in particular, the various regime transitions and thread profiles, shedding light on molecular-level intricacies of this process hitherto inaccessible to continuum theory and experiments. Moreover, the role of surfactant in the most unstable perturbation, the formed droplet size, and surfactant distributions have been unraveled. As surfactant concentration rises, both the wavelength and time to breakup steadily increase due to the lowering of surface tension below the critical micelle concentration (CMC) and viscous effects introduced by micelles above the CMC. These changes prior to the breakup lead to larger droplets being formed in cases with higher surfactant concentration. We also compared the thinning dynamics to existing theoretical predictions, revealing that the surfactant-laden breakup starts at the inertial regime and transitions into the thermal fluctuation regime when the concentration is increased. Thus, we illuminate the hitherto poorly investigated and intricate breakup process of surfactant-laden liquid threads driven by thermal fluctuations, contributing to a deeper understanding of this process at molecular scales.

Pinching Dynamics and Multiple Droplet Generation in Partial Coalescence.

When a drop merges with its homophase, a liquid cylinder appears in certain conditions, which is pinched off leading to partial coalescence. We investigate the process experimentally and numerically, and find that the Rayleigth-Plateau instability is able to pinch off the cylinder when its height-to-neck ratio exceeds one. Surfactants are found to attenuate the cylinder and produce multiple droplets at moderate concentrations. For both the pinch-off of the mother drop and the subsequent breakup of the liquid threads in partial coalescence, the neck thinning is initially in the inertial (I) regime and then shifts to the inertial-viscous (IV) regime. An intermediate regime is seen at larger surfactant concentrations, which accelerates the thinning and favours the generation of multiple droplets.

Liquid thread breakup and the formation of satellite droplets

The breakup of liquid threads into smaller droplets is a fundamental problem in fluid dynamics. In this study, we estimate the characteristic wavelength of the breakup process by means of many-body dissipative particle dynamics. This wavelength shows a power-law dependence on the Ohnesorge number in line with results from stability analysis. We also discover that the number of satellite droplets exhibits a power-law decay with exponent 0.72 ± 0.04 in the product of the Ohnesorge and thermal capillary numbers, while the overall size of main droplets is larger than that based on the characteristic wavelength thanks to the asynchronous breakup of the thread. Finally, we show that the formation of satellite droplets is the result of the advection of pinching points toward the main droplets in a remaining thinning neck, when the velocity gradient of the fluid exhibits two symmetric maxima.

Identification and Mapping of Three Distinct Breakup Morphologies in the Turbulent Inertial Regime of Emulsification—Effect of Weber Number and Viscosity Ratio

Turbulent emulsification is an important unit operation in chemical engineering. Due to its high energy cost, there is substantial interest in increasing the fundamental understanding of drop breakup in these devices, e.g., for optimization. In this study, numerical breakup experiments are used to study turbulent fragmentation of viscous drops, under conditions similar to emulsification devices such as high-pressure homogenizers and rotor-stator mixers. The drop diameter was kept larger than the Kolmogorov length scale (i.e., turbulent inertial breakup). When varying the Weber number (We) and the disperse-to-continuous phase viscosity ratio in a range applicable to emulsification, three distinct breakup morphologies are identified: sheet breakup (large We and/or low viscosity ratio), thread breakup (intermediary We and viscosity ratio > 5), and bulb breakup (low We). The number and size of resulting fragments differ between these three morphologies. Moreover, results also confirm previous findings showing drops with different We differing in how they attenuate the surrounding turbulent flow. This can create ‘exclaves’ in the phase space, i.e., narrow We-intervals, where drops with lower We break and drops with higher We do not (due to the latter attenuating the surrounding turbulence stresses more).

Effect of confinement on weakly nonlinear temporal instability analysis of a viscous planar liquid sheet sandwiched between two co-flowing gas streams at equal velocities

Extensive number of applications like rocket jet engine and gas turbines carry out atomization within a confined environment as it provides faster atomization and good mixing efficiency. Literature suggests that the effect of confinement on breakup of droplets, liquid threads, and annular jets is not elementary, but it varies with liquid viscosity, surrounding medium viscosity, and the confinement strength. Through the present weakly nonlinear temporal analysis, we unveil if a similar dynamic effect of confinement persists on the breakup of planar two-dimensional liquid sheets of varying viscosities. Moreover, to mimic air assisted atomization, the surrounding gases are considered to be flowing with non-zero velocities. Our study reveals that presence of confinement at higher gas-to-liquid velocity ratios of 2.5 and 3 produces no apparent improvement in atomization at all liquid Reynolds numbers. However, at relatively low gas-to-liquid velocity ratios of 2 and 2.25, confinement produces faster breakup as compared to an unconfined one, more so when Reynolds number is relatively low (Re < 100). The overall influence of confinement on non-dimensional breakup time is, however, weak as compared to how it affects the linear growth rate. A counteracting effect of confinement on the linear maximum growth rate and normalized second order disturbance amplitude is identified as the primary reason. Our study also identifies the minimum confinement height CH-1 which is just enough for the liquid sheet to achieve breakup without touching the solid walls. Interestingly, the maximum linear growth rate and minimum breakup time for a particular flow condition are always registered when confinement height equals to CH-1. The values of CH-1 display a strong dependence upon Reynolds number and gas-to-liquid velocity ratios.

Effects of heat transfer on particle suspended Drop-on-Demand inkjet printing using lattice Boltzmann method

Inkjet printing is attracting significant attention as a next-generation process for display production. However, the heat generated during printing and the particles contained in the ink deteriorate the injection accuracy and reliability. Therefore, in this study, an integrated simulation model, including multiphase flow, particle dynamics, and heat transfer, was constructed to analyze the droplet injection process. The effects of particles and heat on asymmetric ejection and satellite droplet formation were analyzed via this numerical model. Even at very low particle concentrations with negligible rheological property changes, the effect of particles on the ejection behavior differed from that of pure ink. The particle-laden droplet was asymmetrically ejected via thread recovery, substrate impact, and capillary processes. The particles in the thread moved the thread breakup point from the main droplet to the end of the thread, thereby accelerating satellite droplet formation. The temperature distribution of the droplets was observed when heat was applied to the print head. The heat transferred to the droplet accelerated the main droplet separation. Recovery of the thread did not occur because of rapid thread breakage, which resulted in poor injection accuracy.

Instability mediated self-templating of drop crystals.

The breakup of liquid threads into droplets is prevalent in engineering and natural settings. While drop formation in these systems has a long-standing history, existing studies typically consider axisymmetric systems. Conversely, the physics at play when multiple threads are involved and the interaction of a thread with a symmetry breaking boundary remain unexplored. Here, we show that the breakup of closely spaced liquid threads sequentially printed in an immiscible bath locks into crystal-like lattices of droplets. We rationalize the hydrodynamics at the origin of this previously unknown phenomenon. We leverage this knowledge to tune the lattice pattern via the control of injection flow rate and nozzle translation speed, thereby overcoming the limitations in structural versatility typically seen in existing fluid manipulations paradigms. We further demonstrate that these drop crystals have the ability to self-correct and propose a simple mechanism to describe the convergence toward a uniform pattern of drops.

Effects of topological changes in microchannel geometries on the hydrodynamic formation and breakup of all-aqueous droplets

Microfluidic gravity-driven droplet generation in aqueous two-phase systems (ATPS) has recently emerged as an effective technique used to passively create all-biocompatible environments. The hydrodynamic formation and breakup of all-aqueous viscous threads in flow-focusing microfluidic devices were experimentally studied by applying different intersection angles (θ). Four typical flow regimes are observed over a range of 0.2–2 kPa, namely, transitional, jetting, threading, and tubing. The flow rate ratio based on the specifications of the entire device was calculated, and the flow regimes were mapped based on the capillary number of the flows. Scaling laws that describe the flow behavior are then put forth based on physical arguments. In the jetting regime, droplet size and jet width are measured and correlated with flow rate ratio. The critical thread length before droplet pinch-off is determined by flow rate ratio and the capillary number of any of the phases. In the transitional regime, droplet length is affected by flow rate ratio and the capillary number of the continuous phase. In addition, through variations in θ, the influence of altering the geometry of the device on the flow regimes was considered. The findings presented in this article provide insight into the intricate process of droplet generation in passive ATPS microfluidics.

Breakup Dynamics of Droplets in Symmetric Y-Junction Microchannels

The experimental method is used to study the droplet breaking characteristics of an immiscible liquid–liquid t8wo-phase fluid in symmetric Y-junction microchannels. Silicone oil is used as the dispersed phase and distilled water containing 0.5% SDS is used as the continuous phase. Three breakup behaviors were observed: breakup with permanent obstruction, breakup with gaps, and no breakup. Two stages of the change of the neck width of the sub-droplet during the breakup process were discovered: a rapid breakup stage and a thread breakup stage. The effect of the breakup behavior on the flow pattern was investigated and it was found that the breakup behavior of the droplets made the slug flow area smaller; further, a new flow pattern was observed, being droplet flow. The length of the sub-droplet increases with an increase of the volume flow rate of the dispersed phase and the ratio of the volume flow rate of the dispersed phase to the continuous phase, while decreasing with an increase of the volume flow rate and the capillary number of the continuous phase. Based on the influence of the two-phase flow parameters on the length of the sub-droplet, a correlation formula for the length of the sub-droplet with good predictive performance is proposed.

Stability of similarity solutions of viscous thread pinch-off

In this paper we compute the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with the surface tension. The stability of the similarity solution is determined using numerical continuation to find the dominant eigenvalues. Stability of the first two solutions (those with largest minimum radius) is considered. We find that the first similarity solution, which is the one seen in experiments and simulations, is linearly stable with a complex nontrivial eigenvalue, which could explain the phenomenon of break-up producing sequences of small satellite droplets of decreasing radius near a main pinch-off point. The second solution is seen to be linearly unstable. These linear stability results compare favorably to numerical simulations for the stable similarity solution, while a profile starting near the unstable similarity solution is shown to very rapidly leave the linear regime.

Effects of Surface Viscosity on Breakup of Viscous Threads.

In addition to surface tension lowering and Marangoni stresses, surfactants also induce surface rheological effects when they deform against themselves at fluid interfaces. Because surface viscosities are functions of surfactant concentration, surface rheological stresses can compete with capillary, Marangoni, and bulk stresses in surfactant-laden free surface flows with breakup. To elucidate the effects of surface rheology, we examine the breakup of a Stokes thread covered with a monolayer of insoluble surfactant when either surfactants are convected away from the space-time singularity or diffusion is dominant. Surprisingly, in both limits, surface rheological effects always enter the dominant balance of forces and alter the thread's thinning rate. Moreover, if surfactants are convected away from the singularity, we provide an analytical expression for thinning rate that explicitly depends on surface rheological parameters, providing a simple route for measuring surface viscosity.

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and non-linear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations.

Natural break-up and satellite formation regimes of surfactant-laden liquid threads

We report a numerical analysis of the unforced break-up of free cylindrical threads of viscous Newtonian liquid whose interface is coated with insoluble surfactants, focusing on the formation of satellite droplets. The initial conditions are harmonic disturbances of the cylindrical shape with a small amplitude $\epsilon$, and whose wavelength is the most unstable one deduced from linear stability theory. We demonstrate that, in the limit $\epsilon \to 0$, the problem depends on two dimensionless parameters, namely the Laplace number, $La=\rho \sigma_0 \bar{R}/\mu^2$, and the elasticity parameter, $\beta=E/\sigma_0$, where $\rho$, $\mu$ and $\sigma_0$ are the liquid density, viscosity and initial surface tension, respectively, $E$ is the Gibbs elasticity and $\bar{R}$ is the unperturbed thread radius. A parametric study is presented to quantify the influence of $La$ and $\beta$ on two key quantities: the satellite droplet volume and the mass of surfactant trapped at the satellite's surface just prior to pinch-off, $V_{sat}$ and $\Sigma_{sat}$, respectively. We identify a weak-elasticity regime, $\beta \lesssim 0.05$, in which the satellite volume and the associated mass of surfactant obey the scaling law $V_{sat} = \Sigma_{sat} = 0.0042 La^{1.64}$ for $La \lesssim 2$. For $La \gtrsim 10$, $V_{sat}$ and $\Sigma_{sat}$ reach a plateau of about $3 \%$ and $2.9 \%$ respectively, $V_{sat}$ being in close agreement with previous experiments of low-viscosity threads with clean interfaces. For $La<7.5$, we reveal the existence of a discontinuous transition at a critical elasticity $\beta_c (La)$, with $\beta_c \to 0.98$ for $La \lesssim 0.2$, such that $V_{sat}$ and $\Sigma_{sat}$ abruptly increase. The jumps experienced by both quantities reach a plateau when $La \lesssim 0.2$, while they decrease monotonically as $La$ increases up to $La = 7.5$, where both become zero.

What controls filament thinning in uniaxial extension?

Breakup of fluid threads is omnipresent in nature and highly relevant for technical processes such as atomization, printing, coating, or spinning. We discuss how to control the filament lifetime of shear-thinning, viscoelastic fluids during uniaxial extension without affecting their shear viscosity. Two commercial acrylic thickeners differing with respect to the co-polymerized hydrophobic monomers, and hence different hydrophobic intra- and intermolecular association, are mixed to obtain aqueous solutions with similar shear viscosity. The elongational relaxation time as determined by capillary breakup extensional rheometry, however, varies by almost two orders of magnitude. Filament lifetime of these solutions can be varied upon adding non-Brownian, plate-shaped particles, again without affecting shear viscosity. A trace amount of particles increases elongational relaxation time by about a factor of four. Car bodies are usually coated using high-speed rotary bell atomizers guaranteeing high transfer efficiency and high-quality appearance. We use the solutions and suspensions described above to investigate the effect of extensional viscosity on ligament formation at the bell edge as a decisive intermediate step prior to droplet formation. High-speed imaging reveals a logarithmic scaling of ligament length with extensional relaxation time for pure thickener solutions. In contrast, ligament length monotonically decreases with increasing particle concentration, i.e. extensional viscosity. Plate-shaped particles obviously act as defects promoting ligament breakup. Extended filament lifetimes are commonly observed during atomization and spraying as a consequence of fluid viscoelasticity. On the other hand, low viscosity fluid threads rupture quickly. Here, we demonstrate that a unique banding instability during extension of a low viscosity surfactant solution with no measurable elasticity leads to extremely long filament lifetimes and to the formation of remarkably long threads. Combining filament stretching and particle image velocimetry we found an unexpected heterogeneous, banded flow in opposing directions. This phenomenon is not limited to surfactant solutions but can also occur in biopolymer solutions, thus broadening the view on instabilities in complex elongational flows.

Heterogeneous flow inside threads of low viscosity fluids leads to anomalous long filament lifetimes

Formation and breakup of fluid threads is pervasive in nature and technology, where high extensibility of fluid filaments and extended filament lifetimes are commonly observed as a consequence of fluid viscoelasticity. In contrast, threads of low viscous Newtonian fluids like water rupture quickly. Here, we demonstrate that a unique banding instability during filament thinning of model surfactant solutions, with a viscosity close to water and no measurable elasticity, leads to extremely long filament lifetimes and to the formation of remarkably long threads. Complementary measurements in planar extension as well as in shear reveal that this flow instability is characterized by a multivalued stress, arising beyond a critical strain rate, irrespective of flow kinematics. Our work reports the first observation of such phenomena during extensional deformation and provides a unifying view on instabilities in complex flow fields.

Charged Satellite Drop Avoidance in Electrohydrodynamic Dripping.

The quality of electrohydrodynamic jet (e-jet) printing is crucially influenced by the satellite drop formed when the primary drop detaches from the meniscus. If the satellite drop falls onto the substrate, the patterns on the substrate will be contaminated. The electric charge carried by the satellite drop leads to more complex satellite/meniscus interaction than that in traditional inkjet printing. Here, we numerically study the formation and flight behavior of the charged satellite drop. This paper discovered that the charge relaxation time (CRT) of the liquid determines the electric repulsion force between the satellite drop and meniscus. The satellite drop will merge with the meniscus at long CRT, and fail to merge and deteriorate the printing quality at short CRT. The simulations are adopted to discover the mechanism of generation and flight behavior of charged satellite drops. The results show that the critical CRT decreases with the dielectric constant of the liquid and the supplied flow rate. Namely, for small dielectric constant and fixed CRT, the satellite drop is less likely to merge with the meniscus, and for high flow rate, the satellite drop is prone to merge with the meniscus due to the delay of necking thread breakup. These results will help to choose appropriate parameters to avoid the satellite drop from falling onto the substrate.

Droplet pinch-off with pressure fluctuations

Dynamics of Newtonian fluid pinch-off is universal, excluding the possibility of manipulating pinch-off behavior by varying initial and boundary conditions which is desirable in applications such as inkjet printing and microfluidics. Here we show that the dynamics of two-fluid pinch-off with disturbed inlet pressure (such as the profile of the conical liquid neck, cone slope, and neck thinning rate) depends on initial perturbations. The nonuniversality arises from pressure-fluctuation-induced nonlocal flow velocity that stretches the axial length scale of the pinch-off region. We renormalize the disturbed pinch-off using the linear ratio, (1 + βε), with β being the empirical constant and ε the dimensionless pressure fluctuation. We further apply the pressure fluctuation in engineering pinch-off where the disturbed and undisturbed systems have identical pinch-off dynamics but distinct material properties. Our results could provide useful guidelines for controlling the breakup of liquid threads with extreme physical properties, such as ultrahigh viscosity and ultralow interfacial tension, in inkjet printing and microfluidics for a range of applications.

A new experimental method based on volume measurement for determining axial scaling during breakup of drops and liquid threads

Thread breakup is ubiquitous in drop formation. As liquid threads thin, monitoring the time variation of the thread’s minimum radius hmin and the axial extent of the pinching zone z′ can help decipher the balance of forces governing breakup. The variation of hmin with time from pinch-off, τ ≡ tb − t (t is time; tb is breakup time)—radial scaling—can be determined experimentally from images of drops forming from a nozzle. Thus, all previous experimental studies report radial scaling, viz., hmin ∼ τa (a is the radial scaling exponent). Determination of axial scaling or how z′ varies with τ, z′ ∼ τb (b is the axial scaling exponent), however, is not as straightforward and hence rarely reported. Experimental determination of axial scaling is made difficult because thinning threads can be long and slender, and hence data on time evolution of z′ can be noisy. Moreover, inference of z′ from experiments can be challenging in situations involving suspension drops containing non-Brownian particles where particles can partially protrude out of the interface. We present a new way of determining axial scaling by experimental measurement of the time variation of the volume of the pinching zone and inferring z′ from volume measurements. The accuracy of the new method is tested by new experiments in which the scalings are determined during dripping of Newtonian liquids and are shown to be in excellent accord with scaling predictions and transitions between different regimes predicted from theory and simulation.

Role of Marangoni stress during breakup of surfactant-covered liquid threads: Reduced rates of thinning and microthread cascades

Simulations and experiments resolve a long-standing controversy that the gradient of surface tension---Marangoni stress---rather than surface tension lowering is responsible for decelerated thinning rates and microthread cascades during breakup of surfactant-covered threads.

Interfacial activity of reactive compatibilizers in polymer blends

The influence of a reactive block copolymer compatibilizer on the breakup of polymer fibers in the quiescent conditions is investigated using the breaking thread method (BTM). The compatibilizer is either localized at the interface of two polymers or incorporated in the bulk of thread phase. Moreover, the nominal interfacial tension between two polymers is estimated as a function of compatibilizer concentration for both types of samples using Tomotika theory. It is shown that assembling of compatibilizer molecules at the interface of two immiscible polymers can result in very different dynamic of thread breakup compared to samples containing the compatibilizer in the bulk phase. We observe a reduction in the rate of thread breakup (kinetic of stabilization) when compatibilizer is incorporated in the bulk of thread phase. Such effect is more significant when compatibilizer is localized at the interface of two fluids. Additionally, the mode of thread breakup is sensitive to the compatibilizer location since a beads-on-a-string (BOAS) morphology is observed when compatibilizer is localized at the interface. In conclusion, the usual attribution of interfacial activity of compatibilizer in polymer blends may be originated from their random presence at the interface rather than thermodynamically favored diffusion to the interface.