Session X32: Dynamics and Rupture I

Dilute Oil-in-water Emulsion Promotes Multiple Holes Formation During Bursting of Centimetric Bubble

Bubble bursting and resulting aerosol generation have been extensively investigated due to their direct relevance in varying industrial and environmental settings. Most previous studies focus on water or surfactant-laden bubble, however, under real-world conditions, particles or droplets are inevitably presented. The current experimental study concerns centimetric bubbles containing microscopic solid particles or oil droplets, with sizes relevant to the bubble cap film thickness at breakup. The oil droplets' spreading coefficient varied from 3.6 to 21.3 mN/m. A bubble column array setup has been designed to simultaneously measure bubble lifetime, bubble bursting dynamics, and aerosol formation using both high-speed imaging and digital inline holography. The results show that the dispersed phase in water can significantly affect the bubble lifetime and bubble cap retraction velocity. With the increase of the gas-liquid interfacial spreading coefficient, the average film retraction velocity decreases and the average film thickness increases. In particular, a distinct phenomenon as multiple-hole formation on the bubble cap was documented for bubble bursting in oil-in-water emulsions, due to the perforation of the oil into the air-water interface. The results demonstrate the great impact on bubble bursting dynamics and resulting aerosol generation in real-world contaminated water containing microscopic impurities with varying sizes and concentration.   

Long time dynamics of a finite-size air filament

We conduct a numerical investigation of the long-term dynamic behavior of a quiescent finite-size 3D air filament submerged in a static liquid. Our study focuses on exploring the impact of the Ohnesorge number while maintaining a constant aspect ratio (Γ = 30). At large Oh, the secondary and tertiary breakup behaviors deviate from the regime predicted by the previous phase diagram¹. At low Oh, as the remaining filament evolves towards its final equilibrium state, the presence of short wavelengths on the filament interface leads to a breakup near the center, as waves originating from the left and right tips intersect. For Oh > Oh_lim = 0.018, a long wavelength, similar to those obtained in a Rayleigh-Plateau type instability, forms when the remaining filament is sufficiently long. This long wavelength contributes to a breakup at multiple points corresponding to the number of waves. Additionally, increasing Oh results in a reduction in the number of satellite bubbles, and an increase in the size of generated bubbles.

1. Osama, M., Deng, P., Thoraval, M. J., & Agbaglah, G. G. (2022). Dynamics of finite-size air filaments in a static liquid. Physics of Fluids, 34(6).   

Fully 3-D simulations of bursting bubbles and jet droplets: influence of surface rheology at large Bond number

Aerosol droplets formed by the bursting of bubbles at a liquid-gas interface are at the core of a wide range of natural processes, everyday activities, and high-end applications. In natural flows, these ejected drops carry various contaminants (e.g., biological materials and toxic chemicals) which frequently exhibit surface-active properties and induce complex interfacial phenomena. We study the sub-stages of bubble collapse, jet ascent, and droplet ejection through high-fidelity 3-D numerical simulations that explicitly couple the dynamic transport and exchange of surfactants between the liquid bulk phase and the interface. We specifically focus on a few crucial yet often overlooked aspects of the system, including the individual and combined role of surface viscoelasticity and Marangoni stresses under non-negligible Bond (Bo > 0.1) number conditions. Our results suggest that notable non-axisymmetric flow features develop as capillary waves propagate through the bursting bubble and create the rising jet, highlighting the critical importance of conducting fully three-dimensional simulations for a comprehensive understanding of these systems. Furthermore, we reveal that the influence of gravity extends beyond the equilibrated bubble morphology prior to its collapse, remaining an active element influencing the jet’s dynamics. Finally, we explore in detail the physical mechanisms underlying previously reported events of surfactant-induced wave damping and jet end-pinching suppression.   

Spontaneous Rupture of Thin Films

We explored the lifecycle of freely suspended thin black films - through non-equilibrium molecular dynamics - examining the preparation phase of rupture, subsequent nucleation events characterized by spinodal dewetting, and the growth of individual nuclei leading to coalescence. The absence of surfactants, surface impurities, and external perturbations, allowed us to isolate and investigate the dominating role of thermal fluctuations in the film rupture process. While existing literature attributes complete stochasticity to film rupture, our study uncovers an intriguing short time window during which the future rupture events display deterministic behaviour, eliminating any inherent randomness, both in space, and in time. Findings shed light on the previously unexplored predictability aspects of thin liquid film rupture, and the growth behaviour of nuclei before and beyond coalescence, opening new possibilities for control and manipulation in various nano-fluidic applications.   

Stochastic bubble shape oscillations

In turbulent flows, bubble fate is controlled by the ratio between inertia and capillarity, namely the Weber number, We. There exists a critical Weber number which separates breaking from non-breaking bubbles. However, this limit is only defined in a statistical sense as an a priori stable bubble can encounter a large velocity or pressure fluctuation and break. Using direct numerical simulations of a single bubble in homogeneous and isotropic turbulence, we study bubble shape oscillations as a function of We. We decompose the surface onto the spherical harmonics base and show that the mode stochastic dynamics can be fully described by a damped linear oscillator randomly forced by turbulence. The natural frequency remains unchanged from the quiescent flow case, while the damping factor is significantly larger than in the absence of a surrounding flow. The forcing term is surprisingly independent on We. This model can then be used to predict more accurately bubble lifetimes in turbulent flows.   

Acoustic cavitation, bubble jetting and surface instabilities in a free-falling droplet

We present a study of laser-induced bubble nucleation and dynamics within millimeter-sized liquid droplets in free-fall motion, where the bubbles experience the influence of a free boundary in all directions. The first part of the research focuses on investigating the nucleation of secondary bubbles induced by the rarefaction wave resulting from the reflection of the shock wave emitted by the laser-induced plasma at the droplet's surface. Interestingly, three-dimensional clusters of cavitation bubbles are formed. Direct numerical simulations based on the volume of fluid method allowed us to estimate a cavitation threshold value by comparing the calculated negative pressure distributions with the shape of the clusters.

High-speed recordings of droplet/bubble dynamics are combined with velocity and pressure field simulations under the same initial conditions. The impact of the curved free surface of the drop on the bubble jetting dynamics is qualitatively assessed by classifying cavitation events using a non-dimensional stand-off parameter dependent on the drop size, bubble maximum radius, and relative bubble position inside the droplet. Furthermore, the role of the curvature of the surface is examined through a structural similarity algorithm, comparing bubbles produced near a flat surface to those within the droplet. Remarkably, this quantitative comparison reveals equivalent stand-off distances where bubbles influenced by different boundaries behave similarly. The oscillation of laser-induced bubbles promotes the onset of Rayleigh-Taylor and Rayleigh-Plateau instabilities on the droplet's surface. These are studied by varying the ratio of the maximum radii of the bubble and the drop. Here, specific mechanisms leading to droplet surface destabilization are identified through a detailed analysis of high-speed images and numerical simulations.   

The sound of small bubbles popping in a droplet

        Bubble bursting at the air-liquid interface is an important fluid dynamic process responsible for transport of chemical and biological species across through the interface to the atmosphere. The evolution of daughter droplets from these phenomena has significant influence from ocean mass and heat transport to indoor kitchen air quality. Here, we look at the physics of bubble bursting by placing a droplet of liquid on a superhydrophobic surface (SH), then adding an air bubble and watching it pop. An acoustic microphone and piezoelectric contact microphone system are synchronized with a high speed camera to unravel the physical behavior of the bubble bursting. We observed that the emanating jet length strongly depends on the surface tension of the liquid and bubble size for a fixed droplet volume.  The frequency of the bubble bursting induced capillary wave decreases with decreased surface tension.  At saturated surfactant concentrations (8.1 mM sodium dodecyl sulfate), the capillary wave also propagates slowly, resulting in lower pressure forces. In addition, with increase in bubble size, the frequency of the capillary waves increases for a given volume and type of droplet liquid.   

Equilibrium configurations of two-dimensional bubbles in a channel: N-bubble case

Microfluidic systems often involve flow of droplets or bubbles through narrow channels. How droplets or bubbles arrange in channels influences in turn how they flow. Here the focus is upon bubbles confined in a Hele-Shaw cell. Depending on bubble size relative to channel size, a zig-zag pattern can be adopted with bubbles alternating from side-to-side of the Hele-Shaw channel. Systems with odd numbers of bubbles are of interest as they break topological symmetry, with more bubbles (and hence, in moving systems, more drag) on one side of a channel than the other. Systems with up to N=3 bubbles are dominated by edge effects, with bubbles bulging at the ends of the structure. In systems with N=5 or more bubbles, edge effects remain present, but are weaker: with N=5 or more bubbles, there is at least one bubble confined in the interior of the zig-zag which cannot bulge freely. Edge effects are then defects superposed on a large-N structure. Even weak edge effects are of interest however, since very short bubble films often appear towards edges of structures. These short films represent weak points at which topology of the bubble structure is liable to change. By locating such short films, both maximum and minimum bubble sizes can be obtained to retain a zig-zag pattern.   

The Limits to Bubble Capture Through High Permeability Membranes

The ability to efficiently capture and transport bubbles can have an impact on an array of industries, such as biomanufacturing, electrochemical gas evolving systems, methane capture, and others. Hydrophobic membranes are a common tool used to capture unwanted bubbles. Here, rapid bubble capture on the order of tens of milliseconds is required as longer bubble capture times will lead to bottlenecks. In this work we seek out the mechanisms behind transport of bubbles through hydrophobic membranes of different permeabilities. For this, we designed and fabricated a silicon membrane platform. 

Through bubble evacuation experiments on our membrane platform, we have uncovered three different distinct regimes limiting the bubble evacuation through an aerophilic membrane. Through the use of scaling laws, we can predict the transition between these regimes. These results are then combined on a design map. This design map allows for prediction of the evacuation time of a bubble through a membrane, given a certain set of experimental conditions including radius, a set of viscosities, and a membrane permeability.

At the high end, bubble capture times under 1ms have been recorded for a 3.5mm diameter bubble. As far as the authors are aware, no faster time has been recorded in literature as of July 2023. This work elucidates the limiting factors behind bubble transport through a membrane. Our work can directly be used by anyone requiring bubble evacuation through a membrane driven by Laplace pressure, regardless of the properties of the medium, the bubble, the surface tension, or the membrane. Hence its results can be directly translated to applications where bubble capture is required.   

Effect of Bubbles on Wall Shear in a Horizontal Channel

The effect of bubbles on the wall shear in a horizontal channel is examined by direct numerical simulations. The volume flux is kept constant by dynamically adjusting the pressure gradient and gravity is adjusted to control the average distance of the bubbles from the top wall at steady state. The shear stress at the wall is determined by the velocity gradient at the wall and in turbulent flows the mixing of the low velocity fluid at the wall and the high velocity fluid away from the wall generally changes the velocity profile. Near the wall, mixing in turbulent flow takes place predominantly by vortices oriented in the streamwise direction, resulting from realignment and stretching of spanwise vorticity due to the mean shear. Injecting bubbles into a turbulent boundary layer is known to modify the mixing by disrupting the streamwise vorticity and thus change the velocity profile. Here, the channel Reynolds number is 145 and gravity was chosen to result in a Froude number comparable to that of non-planning vessels. Several bubbles of a diameter of approximately 50 wall units, at We=0.467 and 0.236 were studied, allowing us to examine the effect of bubble deformability on the structure of the flow and the resulting changes in wall stress.   

Oil droplet entrainment from bursting oil-coated bubbles

Compound bubbles with a liquid coating in another continuous immiscible bulk phase are ubiquitous in a wide range of natural and industrial processes. Their formation, rising and ultimate bursting at the air-liquid interface play a crucial role in the transport and fate of both natural organic matters and contaminants. However, the dynamics of compound bubbles have not received considerable attention until recently. Here, we investigate the entrainment of daughter oil droplets in bulk water during oil-coated bubble bursting, inspired by our previous work (Yang et al., Nat. Phys., vol. 19, 2023, 884-890). We document that the size of the entrained daughter oil droplet is determined by the oil coating fraction and the bulk liquid properties. We rationalize this observation by balancing the viscous force exerted by the extensional flow produced by bubble bursting with the capillary force, considering the end-pinching process of the daughter oil droplet formation. The proposed scaling law for the daughter oil droplet size well captures the experimental results for a wide range of oil coating fractions and Ohnesorge numbers of the bulk liquid. Our findings may advance the fundamental understanding of compound bubble bursting, as well as provide guidance and modeling constraints for bubble-mediated contaminant transport in liquids.