Capillary Instability Research Articles

A weakly compressible smoothed particle hydrodynamics framework for melting multiphase flow

In this study, the transient process of solid–liquid phase change is modeled and simulated by the multiphase smoothed particle hydrodynamics (SPH) method. First, to simulate the interfacial behaviors of melt liquids, the multiphase SPH model is established for immiscible viscous fluids with a large density ratio, where the environmental liquid surrounding the solid phase is considered, and the surface tension of the melt liquid can be accurately modeled by the continuum surface force method. Based on the multiphase model, the thermal dynamics model is incorporated to describe the heat conduction process. The solid–liquid phase change is realized by directly switching the state of the concerned SPH particle, where the absorbed latent heat is computed by the phase change model. Second, the model is validated by several simulation cases, including the Stefan problem, hydrostatic pressure of the evolving fluid interface, rising of two bubbles, and square droplet deformation, and the effects of numerical parameters on simulation accuracy and stability are also discussed. Third, the integrated SPH model is applied to simulate molten droplet formation and dropping processes. The results show that an initial solid–liquid interface disappears during the melting process, and new liquid–liquid interfaces gradually form and evolve under the action of surface tension, gravity, and viscosity. Phenomena such as thin-layer fluid dynamics and capillary instabilities are also reproduced, showing the effectiveness of the model for handling multiphase flow with heat conduction and phase change.

Application of finite volume particle method for axisymmetric modeling of droplet formation in dripping and Rayleigh regimes

An axisymmetric model has been developed in the finite volume particle method (FVPM). FVPM is a conservative, consistent, meshless particle method that incorporates properties of both smoothed particle hydrodynamics (SPH) and the mesh-based finite volume method (FVM). The surface tension effect amplifies capillary instability which is the main mechanism in dripping and jet disintegration. The simulations are performed in 2D cylindrical coordinates by only considering the liquid flow (one phase). The model is validated for free liquid droplet evolved from cylindrical state, dripping from a capillary tube, Rayleigh instability of capillary liquid cylinder columns, and Rayleigh breakup of viscous jets. The FVPM-predicted pressure and oscillating period are in good agreement with theoretical solution for a free droplet. The FVPM-computed dripping length shows good consistency with provided experimental data in literature. The predicted growth rate of capillary instability is in good agreement with analytical solutions for flows with different orders of Ohnesorge numbers. The numerical breakup length of jet with Weber numbers between 2.5 and 40 has been determined with good accuracy based on analytical experimental solution.

Capillary instability of a two-layer annular film: an airway closure model

Capillary instability of a two-layer liquid film lining a rigid tube is studied computationally as a model for liquid plug formation and closure of human airways. The two-layer liquid consists of a serous layer, also called the periciliary liquid layer, at the inner side and a mucus layer at the outer side. Together, they form the airway surface liquid lining the airway wall and surrounding an air core. Liquid plug formation occurs due to Plateau–Rayleigh instability when the liquid film thickness exceeds a critical value. Numerical simulations are performed for the entire closure process, including the pre- and post-coalescence phases. The mechanical stresses and their gradients on the airway wall are investigated for physiologically relevant ranges of the mucus-to-serous thickness ratio, the viscosity ratio, and the air–mucus and serous–mucus surface tensions encompassing healthy and pathological conditions of a typical adult human lung. The growth rate of the two-layer model is found to be higher in comparison with a one-layer equivalent configuration. This leads to a much sooner closure in the two-layer model than that in the corresponding one-layer model. Moreover, it is found that the serous layer generally provides an effective protection to the pulmonary epithelium against high shear stress excursions and their gradients. A linear stability analysis is also performed, and the results are found to be in good qualitative agreement with the simulations. Finally, a secondary coalescence that may occur during the post-closure phase is investigated.

Electrically modulated relaxation dynamics of pre-stretched droplets post switched-off uniaxial extensional flow.

Droplets are known to elongate in extensional flow and exhibit capillary instabilities following flow cessation. Under several practical scenarios, where the deformed drops are exposed to electrified environments, the interplay between capillary and electric forces can further modulate the capillary-driven instability that may lead to novel drop evolution, which has not yet been explored. In the present study, we probe the transient droplet deformation under combined electrohydrodynamic and extensional flows, with a particular focus on the relaxation dynamics in a post-elongation phase, as the external flow field is withdrawn while the electric field remains on. Based on pre-relaxed droplet morphology and electric field strength, the drops appear to relax faster or slower, leading to a steady-state or a plethora of breakup events. The slightly deformed drops relax into stable prolate or oblate shape depending on the electrophysical properties of the fluid pairs. On the other hand, under large deformation limit, our results reveal that in the post-elongation phase, the electric field may either stabilize the droplet or may enforce its breakup primarily via two modes: mid-pinching and end-pinching. We have shown that the post-relaxation events can be mapped into the relevant parametric phase space as a function of the relative strengths of the various forcing parameters as well as geometric parameters. These results present new avenues of droplet manipulation in industrial and microfluidic applications by utilizing unique connectivity between the relaxation kinematics and imposed electrical forcing, a paradigm that has hitherto remained unaddressed.

Reduced model for capillary breakup with thermal gradients: Predictions and computational validation

It was recently demonstrated that feeding a silicon-in-silica coaxial fiber into a flame—imparting a steep silica viscosity gradient—results in the formation of silicon spheres whose size is controlled by the feed speed [Gumennik et al., “Silicon-in-silica spheres via axial thermal gradient in-fiber capillary instabilities,” Nat. Commun. 4, 2216 (2013)]. A reduced model to predict the droplet size from the feed speed was then derived by Mowlavi et al. [“Particle size selection in capillary instability of locally heated coaxial fiber,” Phys. Rev. Fluids 4, 064003 (2019)], but large experimental uncertainties in the parameter values and temperature profile made quantitative validation of the model impossible. Here, we validate the reduced model against fully resolved three-dimensional axisymmetric Stokes simulations using the exact same physical parameters and temperature profile. We obtain excellent quantitative agreement for a wide range of experimentally relevant feed speeds. Surprisingly, we also observe that the local capillary number at the breakup location remains almost constant across all feed speeds. Owing to its low computational cost, the reduced model is therefore a useful tool for designing future experiments.

Thermocapillary instability of an ionic liquid-water mixture in a temperature gradient

This paper reports the separation dynamics of a binary solution placed in a temperature gradient. We show the existence of three separation regimes, depending on the volume fractions of the components. One of the regimes is associated with a capillary instability of which a typical pattern is shown in this picture. All the observed regimes are rationalized.

Effect of Oil Properties on the Generation of Nano-Aerosols During Bubble Bursting Through Crude Oil-Dispersant Slicks.

This study examines the effect of dispersant and oil properties on the aerosolization of fresh and weathered surface crude oil slicks by bursting of a plume of ∼0.7 mm bubbles. A scanning mobility particle sizer measures the size distribution of aerosols in the 20-400 nm range in a clean air chamber. The 500-μm-thick slicks contain oils with varying origin, viscosity, interfacial tension, and weathering state. Test are performed with and without premixed dispersant (Corexit 9500A), which reduces the oil-seawater interfacial tension by 2 orders of magnitude at a dispersant-to-oil ratio (DOR) of 1:25. When compared to aerosolization in clean seawater, the nano-aerosol concentration decreases for slicks without dispersant but increases by 27%-351% upon introduction of dispersant. For most cases, the airborne nanodroplet concentration increases with decreasing Capillary or Morton numbers as well as the ratio of the so-called inner to thermal length scales. To explain the airborne nanodroplet generation in an oil-dispersant mixture, we show that prior to bubble injection, even minimal agitation of the interface causes generation of a subsurface cloud of nanodroplets that diffuses away from the interface. This process appears to be caused by thermal capillary instability when the interfacial tension is low enough to increase the thermal length scale to a few nanometers.

Rayleigh instability of power-law viscoelastic liquid with heat and mass transfer

The theoretical study of Rayleigh instability (also known as capillary instability) at the interface of power-law viscoelastic liquid and inviscid gas is conducted when the interface is transferring heat and mass from one phase to another. The viscoelastic liquid and gas are confined in an annular region enclosed by two concentric cylinders. The dispersion relation based on linear stability analysis is achieved and the outcome of flow parameters on the stability of interface explains through various plots. The results indicate that system gets towards stability when more heat is transporting at the interface. It is also found that the interface that contains power-law liquid is more unstable than the interface of a Newtonian fluid.

Reversal and Inversion of Capillary Jet Breakup at Large Excitation Amplitudes

The evolution of the capillary breakup of a liquid jet under large excitation amplitudes in a parameter regime relevant to inkjet printing is analysed using three-dimensional numerical simulations. The results exhibit a reversal of the breakup length of the jet occurring when the velocity scales associated with the excitation of the jet and surface tension are comparable, and an inversion of the breakup from front-pinching to back-pinching at sufficiently large excitation amplitudes. Both phenomena are shown to be associated with the formation of vortex rings and a local flow obstruction inside the jet, which modify the evolution of the jet by locally reducing or even reversing the growth of the capillary instability. Hence, this study provides a mechanism for the well-known breakup reversal and breakup inversion, which are both prominent phenomena in inkjet printing. An empirical similarity model for the reversal breakup length is proposed, which is shown to be valid throughout the considered range of characteristic parameters. Hence, even though the fluid dynamics observed in capillary jet breakup with large excitation amplitudes are complex, the presented findings allow an accurate prediction of the behaviour of jets in many practically relevant situations, especially continuous inkjet printing.

Diffusive and capillary instabilities of viscous fluid threads in microchannels

We experimentally investigate the flow behavior of viscous oil threads in a a variety of miscible and immiscible low-molecular weight alcohols in microchannels. A comparative study is conducted between diffusive and capillary regimes using simple functional relationships for the thread characteristics, including diameter and detachment length. We develop a comprehensive classification of immiscible and miscible fluid dynamics in square microfluidic channels and provide a quantitative analysis of the evolution of multiphase flow properties across flow patterns.

Electrowetting-assisted direct ink writing for low-viscosity liquids

In conventional direct ink writing (DIW) process, low-viscosity liquids are usually nonprintable, which greatly limits the choices of inks and the potential applications of DIW. To address this challenge, the present work reports a novel electric-field-assisted method to enable DIW of low-viscosity liquids. An external electric field is applied between the dispensing nozzle and the substrate, to vertically pull the printed filament for decreasing the internal pressure along the printing direction. Our proposed method overcomes the common capillary instability characteristic of continuous extrusion of low-viscosity materials. Compared with conventional approaches, the electric-field-assisted DIW process significantly widens the available range of process parameters, increases the throughput by over 150%, and improves the printing accuracy by more than four-fold. These findings indicate an innovative approach for the fabrication of next-generation functional devices using low-viscosity liquids, which used to be difficult or even impossible to print.

Influence of injection conditions on viscoelastic ligament dynamics

This paper presents an experimental work on the determination of viscoelastic solution properties from the analysis of their behavior when subject to the capillary instability. Known as the jet rheometer method, such an approach is reserved for low-viscous viscoelastic solutions for which commercial techniques are unsuitable. In the present work, the injection conditions are free and cover a wide range of operating points. The analysis is statistical in nature and uses a multi-scale description tool that allows access to all dynamics involved and, in particular, to those of small characteristic scales. The results are numerous and evidence the presence of polymer mechanical degradation due to the injection. The influence of the operating conditions on this mechanism is highlighted.

Experimental study of single tracks obtained from a mixture of Ti and Al powders with varying selective laser melting parameters

The paper studies the effect of the laser scanning speed (vs) on the morphology of single tracks obtained from a mixture of Ti and Al powders in a stoichiometric ratio of 1 : 1 in longitudinal and cross sections. Droplets of splashed liquid were found on the outer surface of the track obtained at vs = 300 mm/s. Their appearance is resulted most likely from the release of gas bubbles formed due to the evaporation of aluminum having a lower melting point. A distortion of a single track along its length was observed with an increase in vs values up to 600 mm/s. It was found that tracks loose stability as the laser beam speed increases with «balls» formed on the track surface due to the significant Marangoni convection and the capillary liquid instability in the molten bath. An increase in the laser speed led to the appearance of pores mainly concentrated in the formed balls, and also influenced the track morphology in the cross section, namely, the width and height of the track, as well as the depth of substrate fusion. An increase in the scanning speed from 300 to 900 mm/s led virtually no substrate fusion, and the track width decreased from 194 to 136 μm, while its height increased almost 4 times – from 21 to 88 μm. X-ray microanalysis was conducted and element distribution maps were obtained to assess the structure of the tracks under study. It was found that the degree of liquid mixing in the molten bath is insufficient at scanning speeds of 300 and 600 mm/s, which leads to the segregation of elements over the track cross section. The central zone turns out to be enriched in aluminum, while titanium predominates at the base and is practically absent in the extreme zone (4.57 at.% Ti). X-ray microanalysis revealed the presence of unmelted titanium powder particles at vs = 900 mm/s. Presumably, it may be caused by insufficient laser power at such a high scanning speed.

Dripping and jetting of semi-dilute polymer solutions co-flowing in co-axial capillaries

This work is focused on the mechanisms of the dripping and jetting flow modes of viscoelastic semi-dilute polyacrylamide aqueous solutions co-flowing with silicone oil in co-axial capillaries. A phase diagram of the dripping, jetting, and intermediate flow modes is established. It was found that in the dripping mode, the elongation velocity of the filament between the terminal droplet and the inner capillary is controlled solely by the continuous phase rate. At the same time, the decrease in the filament diameter is due to both stretching and outflow of the polymer solution into the terminal droplet. In the jetting mode, the thread diameter was found to evolve in three stages. In the first stage, the average jet velocity increases, whereas in the second and third stages, it becomes constant and corresponds to the velocity of the continuous phase. The transition from the second to the third stage is defined by the appearance of capillary waves resulting in the formation of the beads-on-string structure. In the third stage, the filament diameter between the neighbor beads decreases exponentially and is governed by the relaxation time, which strongly depends on polymer concentration, but does not depend on the continuous phase flow rate. A simple physical model was proposed for describing the evolution of dimensions of filaments and beads during development of jet capillary instability. The universal character of the evolution of filaments and beads sizes, which is independent of concentration of semi-diluted polymer solutions and flow rates of the continuous phase, is revealed.

Controlling thermal-induced dewetting of As20Se80 thin films for integrated photonics applications

As the use of photonics circuits expands, the optical quality and performance of integrated components in the microscale become a major concern. Aiming to improve the performance while reducing the time processing, new microfabrication approaches are being investigated. The dewetting of glassy thin films have been recently proposed as an alternative for nano and microfabrication of chalcogenide optical components. Besides being the best materials for light transmission in the infrared region, chalcogenide glasses possess a flexible molecular structure that allows using a cheap and simple molding process. Here we investigate the thermal-induced dewetting of chalcogenide As20Se80 thin films, by studying the influence of temperature, atmosphere, and heating rate on the formation of self-assembled microstructures. We found that thin films between 150 and 700 nm dewet via structural relaxation, similarly to liquid agglomeration, and produce solid microstructures with the same composition and molecular structure as the initial film. By controlling the glass viscosity and the kinetics of the nucleation process it was possible to adjust the distribution and size of glassy microstructures. Additionally, we combine the dewetting process with standard photolithography and by avoiding the capillary instabilities, we are capable to obtain waveguides with the smooth and symmetric surfaces required for optical applications in the microscale size.

Simulation of binary droplet collision with different angles based on a pseudopotential multiple-relaxation-time lattice Boltzmann model

Understanding the physics of droplet collisions is of crucial importance in many industrial processes such as inkjet printing, spray cooling, and spray combustion. In this paper, a modified multiple-relaxation-time pseudopotential multiphase lattice Boltzmann model is proposed to investigate binary droplet collision with different collision angles. The surface tension can be adjusted independently under the condition of high Reynolds number and large density ratio using this model. Then the model validation is performed by simulating three benchmark cases including stationary droplet, oscillating droplet, and capillary wave instability, respectively. Finally, different regimes of binary droplet collision are presented, and collision features such as liquid filament and satellite droplet are investigated at collision angles of 30°, 60°, 90°, 120°, and 150°. The results show that there is no liquid filament or satellite droplet at the collision angle of 30°, yet both of them appear as the angle increases. When the collision angle is 60°, the percentage of satellite droplet to liquid phase reaches 30%, while the proportions are less than 10% at collision angles of 90°, 120°, and 150°. Besides, two break-up mechanisms of “end-pinching” and capillary wave instability are inspected. It is found out that the back-flow phenomena at the joints of droplets and the liquid filament are caused by the “end-pinching” mechanism, which further leads to the capillary wave instability of the liquid filament.

Study of heat and mass transport on the instability of a swirling viscoelastic liquid film.

In this article, we examine the response of transport of mass and heat at the viscous gas-viscoelastic liquid interface, while the instability of the interface is defined by capillary instability. The fluids are enclosed in an annular region bounded by two rigid cylinders. The Oldroyd B-type viscoelastic fluid is considered and the outer cylinder is swirling with a uniform angular velocity. The governing mathematical equations are work out through the viscoelastic-viscous potential flow theory. The well-known normal mode procedure is utilized and a critical value of wave-number is calculated to determine the stability/instability norm for the interface. Various plots showing the effect of swirling, heat/mass transfer, etc. have been made and illustrated physically. The addition of swirl prevents the development of disturbance waves. We achieve that the transport of mass/heat at the interface reduces the amplitudes of perturbations.

Temporal instability of Walter’s B viscoelastic fluid film

The stability of an interface formed by Walter’ B viscoelastic liquid and viscous incompressible fluid is examined. These fluids lie in an annular region enclosed by two cylindrical shapes rigid boundaries. The surface tension effect is considered at the interface and therefore, the interface obeys capillary instability. The potential flow theory of viscoelastic-viscous fluids is utilized to compute the solution of modeled equations and the normal mode technique is enforced for the calculation of perturbation’s growth. A two-degree algebraic equation is established to obtain the stability/instability criterion. We found that the perturbations grow slower at the interface containing Walter’s B viscoelastic fluid than the corresponding Newtonian fluid.

On aerodynamic droplet breakup

Abstract

A study of two unequal-sized droplets undergoing oblique collision

The oblique collision of two unequal-sized liquid droplets in a gaseous environment is investigated numerically. It is found that the asymmetry in the flow field arising due to unequal-sized droplets and oblique collision greatly alters the collision outcomes observed in the case of the head-on collision of identical droplets. Our results reveal that permanent coalescence occurs at intermediate collision angles, but head-on and large-angle collisions result in reflexive separation and stretching separation, respectively. Moreover, we found that the end-pinching mechanism is operational in the case of head-on collision, and the capillary wave instability is responsible for the ligament breakup for large collision angles. It is also observed that the droplets coalesce permanently for low velocity ratios and high radius ratios, but for high velocity ratios and low radius ratios, the droplets coalesce temporarily and then split again. By conducting a large number of numerical simulations, the collision outcomes and the boundary separating them are plotted on Rr−We and θ−We planes, where We, Rr, and θ represent the Weber number, radius ratio of droplets, and collision angle, respectively.