Session ZC19: Drops: Instability and Break-up II

Evaporation of acoustically levitated stable microemulsion droplets

Emulsified fuels have attracted significant interest due to their distinct combustion characteristics and have the potential to reduce harmful emissions in gas turbines and combustion engines. In this study, the evaporation characteristics of thermodynamically stable microemulsions with long stability have been explored. The influence of the water-to-surfactant molar ratio and volume fraction of the dispersed phase on the evaporation behavior of emulsions with different oils (decane, dodecane, and xylene) is discussed. The microemulsion droplets were introduced into a contactless environment using an ultrasonic acoustic levitator and then heated using an infrared continuous laser at different laser irradiation intensities. High-speed shadowgraphy and infrared thermography are employed to study the dynamics of the stable emulsion droplets. The droplets undergo three distinct stages of evaporation in their lifetime. We report that increasing the number density and size of water sub-droplets reduces the evaporation rate, while increasing the irradiation intensity results in faster evaporation. The residual structures obtained post-evaporation were analyzed using SEM imaging. In addition, a theoretical model has been proposed to predict the evaporation rate of the emulsion droplets.   

Dynamics of Coulombic Fissions on Evaporating Droplets of Water and Nanofluids

Electrically charged droplets are susceptible to Coulombic fissions (CF), a mechanism through which charges (and a small fraction of mass) are released upon reaching a charge limit (known as Rayleigh limit).  A stable evaporating droplet with a fixed amount of charge reaches the Rayleigh limit as its size decreases. After CF, the droplet returns to a stable state while evaporation continues, and the process repeats itself several times over the droplet lifetime.

CF in evaporating water droplets and water/alumina nanofluid droplets (NFD) were studied. Particle concentration is expected to vary with time and change the fluid properties, affecting the dynamics of its CF process. High-speed imagery was used to measure the droplet diameter and its deformations during CF.

Water droplets sustained successive CF at similar normalized diameters in various experiments regardless of initial droplet size and evaporation rate. Densely concentrated NFD deviated from this behavior and their deformations were damped compared to those of pure water due to higher viscosity. Dense NFD expelled larger amounts of mass during CF, with the droplet splitting in half in extreme cases. This study showed the differences between CF of pure and nanofluid droplets.   

Effects of surfactants on the retraction dynamics of a freely suspended viscous liquid sheet

In diverse applications including atomization and polymer processing, liquid sheets (liquid films with two free surfaces) are ejected from nozzles or dies. The cross-sections of sheets are virtually rectangular in shape but have rounded ends which contract or retract towards each other due to surface tension forces. Commonly, liquid sheets ejected from agricultural spray nozzles also have surfactants present at the air-liquid interface either by design or as contaminants. Previous studies have shown that surfactants drastically change the dynamics of planar films and filaments by either affecting the breakup dynamics or causing escape from end pinching (Wee et al., Phys. Rev. Fluids, 2022; Kamat et al., JFM, 2020). In this talk, we will report the results of a study investigating the effect of surfactants on the contraction dynamics of liquid sheets and extend the previous works of others on systems with clean interfaces (Notz and Basaran, JFM, 2004; Savva and Bush, JFM, 2009).   

Thermal Fluctuation break-up of Surfactant-Laden Liquid Threads

Formation of droplets is a fundamental process used in many industrial applications, such as inkjet printing and drug manufacturing.

The break-up of a liquid thread is influenced by an instability dependant on surface tension. We can reduce the surface tension by adding surfactants,

which are molecules that adsorb on the interface of liquids, and thus, change the break-up dynamics.

At certain systems with ultra-low surface tension or very small length scales, thermal fluctuations on the interface are capable of creating the instability

that leads to the formation of droplets and satellite droplets. In our study, we employ simulations of a coarse-grained model to determine the characteristic

wavelength of such instabilities on liquid nanothreads with various surfactant concentrations, above and below its critical aggregation concentration.

Also, we have identified the different break-up regimes and their time-scales. We anticipate that our study contributes to the understanding of a

fundamental process in nature and paves the way for further developments in this area for relevant applications.   

Voxelated Bioprinting: Digital Assembly of Viscoelastic Bio-ink Particle

Analogues of pixels to two-dimensional (2D) pictures, voxels –– in the form of small cubes or spheres –– are the basic units of three-dimensional (3D) objects. Digital assembly of bio-ink voxels may provide an approach to engineering heterogeneous yet tightly organized 3D tissue mimics. However, this approach requires precisely manipulating highly viscoelastic bio-ink voxels in 3D space, which represents a grand challenge in both soft matter science and biomanufacturing. Here, we introduce a voxelated bioprinting technology that enables the Digital Assembly of Spherical bio-ink Particles (DASP). First, I will discuss the criteria for printing viscoelastic bio-ink droplets with good fidelity in an aqueous environment without the help of large interfacial tension. Second, I will describe how to use DASP to create 3D structures consisting of interconnected yet distinguishable bio-ink particles. Finally, I will share our recent progress in applying DASP to encapsulate islets in multiscale porous scaffolds to treat type 1 diabetes. I will also discuss immediate applications and emerging challenges associated with voxelated bioprinting.   

Breakup of low viscosity liquid jets and drops

Breakup of low-viscosity liquid jets and drops in air has been of interest for over a century and is receiving increased attention because of emerging applications involving breakup of liquid metal jets which have viscosities μ comparable to but surface tensions γ and densities ρ much larger than water. The dynamics of breakup is governed by the Ohnesorge number Oh=μ/(ργR)^1/2 (R: nozzle or initial jet radius). When Oh«1, the thread initially thins as if it were inviscid and its minimum radius h_min obeys a universal scaling law h_min=A(γ/ρ)^1/3(t_b–t)^2/3 where t_b is the time t at which the thread breaks up and A≅0.717. As the interface overturns prior to breakup when Oh is sufficiently small, it has proven challenging to observe in simulations and experiments the value of the prefactor A obtained from theory and, furthermore, the transition of the dynamics as h_min→0 from the inviscid regime to a different scaling regime in which the effect of viscosity is no longer negligible. We use simulations to show that for sufficiently small Oh, the value of A predicted from computations agrees with the theoretical value to three decimal places and the inviscid power-law behavior can be observed over several decades in h_min as t_b–t→0. Transition out of the inviscid regime and into a viscous one is also demonstrated from simulations.   

Numerical simulation of bag-mode breakup of droplets: Insight into hole formation and droplet size distribution

In this study, we perform three-dimensional Direct Numerical Simulations of the bag film breakup of drops in uniform air flows. A mesh convergence study is conducted with a focus on the consistency of the location where the film first ruptures. We investigate the impact of the gas Reynolds number on the droplet breakup. Additionally, we compare droplet statistics from simulations with experimental results and those obtained using the Manifold Death (MD) algorithm, a numerical method for artificially perforating thin liquid films. The impact of the gas dynamics on the breakup of the liquid film is investigated. Throughout the studies we consistently observed crater formation and a localized pressure jump inside the liquid film at the position where the perforation will develop in later time. Morphological changes of deforming droplets are analyzed and compared for all the cases.   

Numerical Study of droplet deformation and jet formation inside a Liquid Medium

We conducted a numerical investigation on droplet deformation within a liquid medium and explored jet formation using the Volume of Fluid (VOF) method. A droplet moving at a higher velocity results in the creation of a mushroom-shaped jet. Our observations revealed that the velocity profile of the jet aligns well with the similarity solution for the axisymmetric free jet, expressed as u/um = (1+η2)-2, where η = σ`r/x is the similarity variable. Here, σ` is a constant, and um is the axial velocity along the centreline, i.e., u(x,y=0). Through capillary time scale and energy balance, we found that the jet velocity (Vj) = V (1-Oh)-1/2, where Oh =μ / (ρ R σ)1/2 , R and V the droplet radius and velocity, ρ, µ and σ indicating the liquid density, viscosity, and interfacial tension coefficient respectively. Within Oh < 0.01, jet velocity is approximately equal to the droplet velocity. With an increase in Weber number (We = ρ V2 R /σ) of the droplet, jet velocity gets increased, and the jet moves in the forward direction penetrating the droplet in a toroidal shape. Furthermore, we analytically predicted the critical Weber number required for the jet to completely traverse the droplet based on an energy analysis of Edgerton's experiment involving a bullet traversing an apple. The critical Weber number for jet formation was found to be approximately 23, which aligns well with our numerical findings. In this case, the jet velocity nearly matches the initial droplet velocity. We also observed that the maximum jet height (Hjmax ≈ 0.056We) and maximum jet radius (Rjmax≈ -0.036We) scale linearly with the Weber number. This linearity phenomenon suggests that the jet becomes narrower and longer as the droplet velocity increases.   

The Dynamics of Secondary Fragmentation of Viscoplastic and Shear-Thinning Droplets

A liquid droplet undergoes secondary breakup under impulsive acceleration when the flow Weber number is greater than critical Weber number (We_cr). For a Newtonian droplet, its We­_cr depends on density ratio (ρ) as well as drop (Oh_d) and ambient (Oh_o) Ohnesorge numbers. However, in many physical applications, the droplet fluid is non-Newtonian in nature. Aerial Firefighting is a prime example of one such application where shear-thinning and viscoplastic fluids such as Xanthan gum and Guar gum solutions are used as fire retardants. Such a change in droplet fluid rheology can have a significant impact on its deformation and breakup as well as its We_cr. Through this work, we explore the role of shear-thinning and viscoplastic rheology on secondary fragmentation using multiphase Direct numerical simulations. To facilitate this exploration, Carreau-Yasuda and Modified Herschel-Bulkley constitutive models for shear-thinning and Viscoplastic rheology respectively are implemented for Volume-of-Fluid Direct numerical simulations and validated against analytical and experimental works. A parameter sweep across Weissenberg number (Wi) and power-law exponent n for some benchmark Newtonian fragmentation cases is performed. Analysis of the simulations reveal the importance of the nominal viscosity and corresponding nominal Drop Ohnesorge number in the droplet's fragmentation dynamics, and its connection to Wi and n is also highlighted.