Session S03: Drops: Instability and Break-Up (5:45pm - 6:30pm CST)

Design and Construction of a Liquid-Fuel Detonation Tube Facility

A new facility is built in order to facilitate the study of multiphase phenomena occurring in liquid-hydrocarbon fueled detonations. The mechanisms behind detonations in this regime are many, and occur over a wide range of time scales. As such, the process of droplet combustion, through breakup, vaporization, and reaction, has yet to be fully characterized. To capture such phenomena, measurements of high temporal and spatial resolution are required. For this purpose, a detonation tube is constructed and fitted with a host of diagnostics. A novel in-situ method of particle sizing is implemented to characterize droplet sizes and particle volume fractions. Further laser-optical systems are introduced for high-resolution imagery and video, Schlieren imagery, and pyrometry. Via these tools, important data on liquid-fuel combustion in the detonation regime, from the individual particle up to jets and sprays, is obtained. Through collaboration with simulation developers, this data will be used to improve and validate simulation capabilities and models, such that multiphase reactions in detonations may be predicted accurately and efficiently.   

Drop-on-demand painting device for highly viscous fluid

A drop-on-demand painting device with a simple structure which ejects highly viscous liquid in the form of microjet is introduced. The novelty of this device is the short nozzle connected to a cylindrical container, instead of a long nozzle used in previous research. An impulsive motion of the device gives rise to eject a microjet. The device can paint letters on a piece of car body plate with car paint of 100 Pas in zero shear viscosity. To understand the liquid jet velocity, we conduct systematic experiment by changing the initial velocity of the container and the ratio between liquid depths in the container and in the nozzle. The results show that the jet velocity increases with the length ratio, up to about 30 times faster than the initial velocity. Nevertheless, a linear relation between the jet velocity and the ratio predicted by the previous model which considers only pressure-impulse, does not hold for high length ratio. This is because the actual position of the stagnation point is significantly different from that predicted by the previous model. Thus, we improve the jet-velocity model by considering mass conservation as well as pressure impulse. This new model successfully predicts the jet velocity in all ranges of length ratio.   

Suppression of drop breakup in a viscoelastic bath

A drop of a Newtonian liquid falling in a bath of another, less-dense and miscible, Newtonian liquid, deforms into a torus which is either stable or subsequently fragments into smaller structures, depending on the relative contributions of diffusive, viscous and convective forces. Here we show that the dynamics of the drop can change significantly when the bath is replaced by a viscoelastic liquid. We investigate two types of viscoelastic baths; aqueous solutions of either highly flexible polyethylene oxide (PEO) chains or stiffer carboxymethyl cellulose (CMC) chains. Remarkably, the critical condition for torus formation and drop breakup, denoted as the Fragmentation number describing the ratio of the convective time scale to the diffusive time scale, increases by more than a factor of four in PEO solutions compared to Newtonian or CMC solutions. Our results demonstrate that the onset of fragmentation is governed by the bath elasticity and the viscosity ratio between the falling drop and the bath.   

Studies on Drop Formation Process under Direct Drop Regime of a Spinning Disc

Wetting issues encountered at low flow-rate in a spinning disc is overcome by placing a wet filter paper on its surface. The periodicity of drop release and progress of drop formation process are probed by high speed imaging. Periodicity of Primary drop formation is reported both at entire disc as well as single site level. An individual drop formation site exhibits aperiodic release of primary droplets. The distribution of overall interval of quiescence is verified to be Poissonian. Based on the observations from a large number of drop detachment events key stages of drop formation process are delineated. Shortly following release of a primary drop (PD) secondary drops (SD) are released from the unstable thread by capillary instability. The remnant of thread gets quickly pulled back for slow formation of a new bulge. Sequential transition of the sinusoidal fresh bulge to triangular shape (TS), inverted U shape (US), and Pear shape (PS) before ultimate release of another primary drop (PD) are time tracked at two rotational speeds. A non-linear relationship between necking time (PS-PD transition time) and disc rotational speed is proposed for drop formation from a spinning disc.   

The break-up of a liquid film caused by drop impact

Liquid films on non-wetting surfaces are unstable at certain thicknesses. They can break up under external disturbance with the formation of dry spots. Although the rupture of liquid films has been intensively studied, the formation of a dry spot under the drop impact has not been considered yet. Therefore, we experimentally studied the break-up of water films on superhydrophobic surfaces caused by the impact of water droplets. We found that the energy of a drop necessary for the liquid film break-up is an order of magnitude more than the estimation of free energy change. A more detailed estimation of the energy required on the formation of a crater with a critical size allows us to predict the necessary droplet energy correctly.   

Measurement of Unsteady Stress Field of Extending Liquid Polymer

Understanding of the behavior of extending liquid polymer is important for various applications such as inkjet printing. The objective of this study is to develop a novel experimental technique to visualize the extensional stress field of extending liquid polymer by utilizing the principles of photoelasticity. The proposed system is a non-contact optical measurement method based on the retardation obtained by the changes of polarization state of the liquid polymer, which results in proportional stress values. A high-speed polarization camera containing an array of micro linear polarizers with four incident angles is used to capture the photoelastic phenomenon at high frame rates. The measuring target is a column of extending liquid polymer. This extension is exerted by a CaBER-Dos (Capillary Breakup Extensional Rheometer Dripping onto Substrate) system, by which it is possible to measure the intensity of extensional stress. The result obtained from the technique, which combines photoelasticity and CaBER-Dos systems, shows an increase of retardation of the liquid polymer as it is extended. Thus, extensional stress field can be visualized experimentally with calibration between the retardation and the extensional stress within an error of ±13.1{\%}.   

Deformation and Burst of a Liquid Droplet with Viscous Surface Moduli in a Linear Flow Field

Suspensions of fluid particles with complex interfacial architecture (for instance, capsules, vesicles, lipid bilayers, and emulsions embedded with certain surface-active agents and surfactants) find an immense number of applications in industry and bioscience. Interfacial rheology plays an essential role in the dynamics of many of these systems, yet little is understood on how these effects alter droplet deformation and breakup. In this study, we present the conditions for the breakup of a single droplet with viscous surface moduli, under the assumption of weak flow and negligible Marangoni forces. The viscous interface is treated as a homogenous fluid obeying the Boussinesq–Scriven constitutive law. We present the drop breakup analysis in Stokes flow in the limit of small droplet deformation using the perturbation theory approach. We examine how the critical capillary number for breakup depends on the interfacial viscosity for different viscosity contrasts between the inner and outer fluid and different flow types. For all the flows considered, we observe that surface dilational viscosity is found to have a destabilizing impact on droplet breakup, whereas surface shear viscosity has a stabilizing effect. We explore the physical picture behind these observations in this work.   

Fluctuation-driven dynamics of nano-threads: Rayleigh-Plateau instability and break-up

Interface dynamics of liquid threads is usually analysed in two stages: (i) the linear Rayleigh-Plateau (RP) instability and (ii) the nonlinear rupture. Both are shown to strongly depend on thermal fluctuations at the nanoscale, which are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). In the linear stage, The classical RP theory is re-evaluated and revised, where MD experiments demonstrate its inadequacy. A new theoretical framework, SLE-RP is developed, which captures nanoscale flow features and highlights the critical role of thermal fluctuations at small scales. For the nonlinear behaviours, a robust numerical scheme is then developed to explore the rupture process and its statistics, where the “double-cone” profile reported by Moseler and Landmann [Science 289, 1165 (2000)] is observed, as well as other distinct profile forms depending on the flow conditions. Comparison to the Eggers’ similarity solution [Phys. Rev. Lett. 89, 084502 (2002)], a power law of the minimum thread radius against time to rupture, shows agreement only at low surface tension; indicating that surface tension cannot generally be neglected when considering rupture dynamics.   

Delayed Singularity Formation in Fiber-Reinforced Dripping Liquids by Hindering Extensional Flow

We study the dripping dynamics of highly viscous liquid cylinders suspended from their upper base. The flow is extensional, gradually accelerates and exhibits a singularity at a finite time. For pure liquids, the necking follows a self-similar dynamics controlled by the balance of gravity and viscous dissipation. Adding dilute rigid fibers in the liquid dramatically modifies the dynamics. Initially, the presence of the fibers hinders the extensional flow and a slow shear-dominated flow gradually separates the fibers. After a delay controlled by the initial configuration of the fibers, the self-similar regime is recovered, as the extensional flow is restored. We present experimental and numerical results supported by scaling analysis.   

The Spatiotemporal Evolution of Antibubbles: Insights from Direct Numerical Simulations

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions (2D and 3D), that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes equations for a binary-fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar order parameter field $\phi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving boundary at the antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with DNS using a sharp-interface Volume-of-Fluid method. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results in particular, the velocity with which the arms of the antibubble retract after breakup scales $\sigma^{1/2}$, where $\sigma$ is the surface tension, which has been been obtained theoretically by Sob\'yanin.   

The Effect of Viscosity Ratio on Inertial Capillary Flow in Long Viscous Filaments.

The effect of viscosity ratio between a long, stationery filament of fluid and a surrounding fluid has been previously studied experimentally and numerically in low Reynolds number flows; we study the influence of inertia for the same problem. Using direct numerical simulation of the two-phase flow and tracking the interface using a level-set function, we study the behavior of the filament in the presence of a dynamically active fluid surrounding it. A long filament of viscous liquid, when surrounded by a dynamically inactive fluid, retracts into a spherical drop by virtue of capillary flow in the absence of inertia. With the inclusion of inertial effects in the capillary flow, the filament shows different modes of behavior - like end pinching, or Rayleigh-Plateau instability, or retraction back into a spherical drop - as a function of initial aspect ratio of the filament and Ohnesorge number. We compare the filament behavior, in the presence of a dynamically active surrounding fluid, with the behavior of an isolated filament.   

Stability of a bounded axisymmetric liquid bridge

This talk examines the stability of a bounded axisymmetric liquid bridge confined between parallel-planar similar substrates by using theory. From classical stability analysis it is now generally understood that stability diagrams for bounded liquid bridges contain; a region of low slenderness where instability is caused by de-pinning; a region of low to large slenderness and small liquid bridge volume where axisymmetric minimum volume instabilities occur; and a low to large slenderness region with large liquid bridge volume where non-axisymmetric maximum volume instabilities are present. Zero-capillary pressure solutions to the Young-Laplace equation for bounded-axisymmetric liquid bridges are analyzed, and their transition, as stability limits. Observable trends show good agreement for critical behavior when comparing experiments and theory in the near hydrostatic limit.   

Energetics of drop and bubble deformation with application to breakup in turbulent flows

Drop breakup in fluid flows is investigated here as an exchange between the fluid's kinetic energy and the drop's surface energy. We show analytically that this energetic exchange is governed only by the action of the rate-of-strain tensor on the surface of the drop, more specifically, by a term analogous to vortex stretching. Our formulation allows to isolate the energetic exchange due to the relaxation of the drop, from the action of velocity fluctuations leading to breakup. We perform direct numerical simulations of single drops in isotropic homogeneous turbulence and show that an important contribution to breakup arises from the stretching of the fluid-fluid interface by velocity fluctuations away from the drop surface. This mechanism is approximately independent of the Weber number, whereas the dynamics inside (and close to) the drop only contribute to breakup for sufficiently large Weber numbers. We discuss the implication of these results for the simplification and improvement of breakup models.   

Simulation of a Shockwave Impacting a Near-critical Fuel Droplet

Shock-droplet interactions occur in a spectrum of high-speed propulsion systems involving liquid fuels. When the combustion chamber pressure nears the critical pressure of the fuel/air mixture, transcritical behavior involving the transition from liquid-like to gas-like states is observed. Our understanding of multiphase-shock interaction is significantly less developed than its gas-phase counterpart and is particularly limited at transcritical conditions. We consider the interaction of a shockwave with a liquid droplet at near-critical conditions. A fully-conservative diffuse-interface framework coupled with the Peng-Robinson equation of state and a vapor-liquid-equilibrium solver is developed to accurately determine the state of the fluid as the shock propagates through the droplet. The thermodynamic state of the droplet changes by the passage of the shock and rarefaction waves causing the droplet interface to transition from a diffusion-controlled mixing that prevails at supercritical conditions to two-phase disintegration as phase separation occurs. The influence of varying the initial temperature of the liquid and the shockwave strength on the droplet breakup and interface transition from supercritical to subcritical (and vice versa) is delineated.   

Droplet generation from jet-like surface waves by a spark-generated underwater bubble

An underwater bubble is generated by electric spark near a free surface, where the inception position of the bubble below the free surface is d and the maximum radius of the bubble is $R_m$. As a result, various jet-like surface waves are observed according to $d/R_m$ and droplets are generated from the perturbed jets. Assuming that the perturbation wavelength is $h-a$ ($h$ is the maximum height of the jet before the generation of droplets and a is the average droplet radius), the droplet-generation mechanism can be successfully explained using the classical Rayleigh-Plateau instability, which has never been applied to the droplet generation by an underwater bubble. It was also experimentally found that there exists a discretely proportional relationship between $h/R_m$ and the number of pinched off droplets ($n$); no droplet ($n = 0$) is generated when $0 < h/R_m < 3.3$; a single droplet ($n = 1$) is generated when $3.3 < h/R_m < 4.4$; two droplets ($n = 2$) when $4.4 < h/R_m < 6.0$; three droplets ($n = 3$) when $6.0 < h/R_m < 7.6$. This relationship is analytically explained using the conservation of mass. Finally, after its generation, the oscillatory motion of a droplet is studied both experimentally and analytically, which shows a good agreement between each other.   

Modeling Droplet Breakup of Viscoelastic Fluids for Mitigation of Viral Particulate Transmission

With infectious disease spread of current global concern, computational modeling of biological fluids provides prediction of viral particulate spread. Nasal and buccal ejected mucus can reach jet velocities up to 100 mph and expel large quantities of droplets at a wide range of diameters. Smaller diameter droplets are subject to escape ejection jet and continue upwards, becoming airborne. A novel approach of altering human saliva viscosity aims to alter droplet properties such that breakup into smaller droplets, thus, limiting dispersion and reducing transmission. This computational of a single droplet subject to relative velocities of a sneezing or coughing jet provides chronological visual of droplet form in time as it leaves the facial cavities and travels out and down. Designs of various saliva viscosity and surface tension values map the droplet breakup forms across ranges of Weber number, a ratio of inertial forces acting on the droplet's surface tension, and of Ohnesorge number, which evaluates the impact of viscosity in that breakup. This map is compared to droplet-scale simulation of a viscoelastic fluid model within the drop fluid's equation of state. The rheology of the fluid is determined based on local shear rate, fluid stress tensor, and relaxation time between short-time reaction akin to solid, and following reaction like fluid. The droplet breakup view provides limits for which fluid viscosity and surface tension properties can be altered to prevent or delay secondary breakup forms into smaller droplets and reduce range of viral particle spread.   

Spray droplet size control using an oil-in-water emulsion

This study examines the effects of using oil-in-water emulsions to control droplet size in flat fan sprays. Using high speed digital inline holography, droplet size, eccentricity, and in-plane velocity measurements were performed at multiple spanwise locations of a flat fan spray of varying pressures. The spray includes water and water mixed with 0.1{\%} volume fish oil. Results show the emulsion initiates hole formation on the lamella at a higher rate than water alone, causing earlier spray breakup and with associated quantitative changes. First, the water only spray size distributions are inherently bimodal, possibly resulting from the two distinct breakup mechanisms, i.e. droplet generated from film and ligament breakup. The addition of oil significantly dampens the smaller droplet mode and the integral droplets size increases significantly due to the earlier breakup and formation of thicker, and thus more stable, ligaments. Second, the eccentricity of the droplets decreases at almost all size ranges for oil-in-water emulsion sprays. This is due to the significant decrease in the characteristic relative velocity for the breakup event due to earlier breakup. Third, the mass flux for small droplets less than 500 $\mu $m decreases with the addition of oil.   

Saliva Content and Viscosity and its Impact on Droplet Formation and Pathogen Transmission

Evidence that SARS-CoV-2 is airborne implies that a host's droplet character is important. Large droplets fall while aerosols remain suspended, hence, aerosols drive airborne transmission. Droplet size relates to airspeed (speech, cough, sneeze), saliva/mucus fluid properties, and content. This work evaluates fluidic drivers and their influence on transmissibility. Saliva is altered with: (1) colloids that increase viscosity/surface tension, and (2) stimulating saliva content. Using experimental and numerical tools, the droplet character, content, and exposure are evaluated. Results indicate that altering the saliva properties impacts the droplet size distribution, aerosols content, and exposure levels. Additionally, it is found that natural human response work with these drivers to potentially mitigate pathogen transmission. Previous studies indicate an increased saliva viscosity from stress and reduced saliva content from either stress or illness. These responses both favorably correspond to reduced transmissibility. The results also indicate a novel approach to alter SARS-CoV-2's transmission pathway and could help to control the COVID-19 pandemic and other pathogens.   

Stability response of liquid bridges to maximum volume asymmetric perturbations

The stability response of a bounded axisymmetric liquid bridge to maximum volume asymmetric perturbations is investigated using theory and experiments. Based on stability theory, a liquid bridge undergoes maximum volume asymmetric instability when the contact angle reaches 180$^{\circ}$, for all radial Bond numbers $Bo_R=\Delta \rho g R^2/\gamma$, where $\Delta \rho$ is the density difference between the bridge liquid and ambient fluid, $g$ the acceleration due to gravity, $R$ the bridge radius, and $\gamma$ the liquid surface tension. The Young--Laplace equation is solved to estimate the maximum stable volume before rotund drop instability occurs for radial Bond numbers in the range $0.1 < Bo_R < 5$. Experiments are performed using water on surfaces with identical chemical signatures on both top and bottom substrates. A needle connected to the bottom substrate is used to increase the bridge volume in small increments to reduce surface waves. The maximum volume theoretical limit of $V_{max}=(2/3)^{1/3}{Bo}^{-2/3}$ is compared with experiments. Deviations in contact angle and volume are explained by comparing experiments with numerical results.   

Hydrodynamic Signatures of Nanoparticle at the viscous micellar solution-water interfaces

Nanoparticles, as emerging materials, are extensively used to stabilize liquid-liquid interfaces in many applications ranging from particle-stabilized emulsions. Structured liquids represent a unique state of matter, where all components are liquids. Conventionally, structured liquids are formed by nanoparticle-surfactant jamming at the oil-water interface where a strong interfacial layer is generated. However, such jamming driven structured liquids lack the multiscale porosity that present in solid hierarchies. In this work, we develop a new approach for the formation of multiscale porous and permeable structured liquids in viscous liquid mediums. We incorporate nanoparticles into spontaneous emulsification systems that results in the formation of a spontaneous bicontinuous system. The generated nano/micro size emulsion droplets at the oil-water interface creates a multiscale porous liquid in liquid configuration. To unravel the role of nanoparticles on inhibiting the plateau Rayleigh instability and formation of liquid columns, we examine the thinning of aqueous liquid filaments in viscous micellar solutions. We find that unlike the breakup of pure water filaments that goes through a number of thinning regimes from viscous (inertia) to viscous-inertia, the breakup of nanoparticle filaments occurs in a single thinning regime. The rapid formation of microemulsions at the oil-water interface increases the viscosity of the oil-water interfacial layer and consequently inhibits the transition of thinning regime from viscous to viscous-inertia.   

Hydrodynamic agitation may naturally disinfect the smallest pathogen-laden aerosols

Lower respiratory tract infections originate from multiple aerosol sources, varying from droplets erupting from bursting bubbles in a toilet or those produced by human speech. A key component of the aerosol-based infection pathway---from source to potential host---is the survival of the pathogen during aerosolization. Due to a rapidly rearranging interface, pinch-off processes occurring during aerosolization have the potential to dissipate energy into these droplets. This dissipated energy can then agitate the fluid, stress objects therein, and if high enough, disrupt biological life within these droplets. However, the extent of the energy dissipated in these droplets is unknown. Here we unlock, using numerical simulations, the spatial and temporal hydrodynamic energy dissipation history within microscale droplets. Our results show that viruses and bacteria likely to reach the lower respiratory tract experience a level of hydrodynamic agitation that has been linked to disinfection of certain pathogens. This introduces a key consideration in determining pathogen transmission, its ability to withstand high levels of agitation. These results suggest that hydrodynamic agitation may be responsible for the viability, and consequently infectivity, differences in aerosolized microbes.   

Droplet size distributions in liquid–liquid semi-batch Taylor-Couette flow

Droplet size distributions in a vertically oriented liquid–liquid Taylor- Couette reactor operated in a semi-batch fashion with continuous feed of the dispersed phase and no feed or removal of the continuous liquid were measured using optical techniques. The effects of both the inner cylinder angular velocity and the dispersed phase inlet flow rate on droplet size distributions were considered. Both the mean droplet diameter and the droplet size distribution were found to depend upon the jet Reynolds number and were independent of cylinder rotation speed up to the largest azimuthal Reynolds number investigated (60 000). The droplet size distribution underwent a transition from a unimodal distribution at low cylinder rotation speeds to a bimodal distribution at intermediate speeds. At the largest rotation speeds considered, the bimodal distribution became right-skewed. These observations suggest that the mean droplet size and droplet size distribution are determined primarily by jet breakage dynamics at the tips of inlet nozzles. Furthermore, the mean droplet size data collected from two geometrically distinct reactors can be collapsed onto a universal curve by plotting the Weber number against the jet Reynolds number.