Session R02: Bubbles: Dynamics (5:00pm - 5:45pm CST)

On a carpet of microbubbles existing beneath the hydrogen bubbles growing at a microelectrode

Recently, a carpet of microbubbles existing beneath the hydrogen bubble growing at $\diameter$100 $\mu$m microelectrode during water electrolysis was revealed. It was found that the bubble growth is mainly governed by coalescence with this microlayer while the thickness of that increases along with the bubble evolution. The carpet thickness depends sensitively on potential and electrolyte concentration. Upon increasing both parameters, the carpet thickness reduces and a transition from monotonic to oscillatory growth is observed. The oscillatory phenomenon consists of a periodic detachment and reattachment of the bubble while the thickness of the carpet is oscillating in time. During the oscillations, the amplitude and the carpet thickness rise until a critical value is reached, leading to bubble detachment. Although the electric force F$_e$ was shown to be a responsible restoring force, the bubble-carpet interaction needs further consideration. Additionally to that, during recent microgravity experiments in a parabolic flight, a similar behavior was noticed.   

Large Bubbles in Vibrated Liquid Are Levitated by Wall Motions

Experiments have shown that, if a thin slab of liquid confined between vertical transparent walls is vibrated vertically, a large bubble can be stably levitated between the free surface and the bottom [O'Hern et~al., ``Bubble Oscillations and Motion Under Vibration,'' Physics of Fluids 24, 091108 (2012)]. At that time, bubble levitation and stability could not be explained because the downward Bjerknes force is too weak to overcome the upward buoyancy force. However, if wall flexibility is taken into account, the pressure-induced lateral oscillations of the walls lead to a resonance that increases the Bjerknes force. Below resonance, bubbles are driven to the bottom. Above resonance, bubbles are driven to the region of the levitated bubble. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.   

Oscillations of Large Bubbles Due to Sudden Finite Volume Release

The oscillatory behavior of large air bubbles produced from the instantaneous rupture of a submerged, finite volume container is characterized experimentally. Continuous gas release in the form of a unidirectional jet from underwater pipes or geophysical formations has received significant attention in the past, largely focused on the break-up of the gas stream and the size of the resulting bubbles. More recently, so-called `glugging' behavior in constrained systems with very large reservoirs has also been studied, in which bi-directional mass exchange occurs between the liquid and gas phases. In contrast to both of these quasi-steady systems, the finite volume rupture problem depends significantly on the initial transient behavior of the two fluids, due to the bi-directional exchange in a relatively small, fixed, gas reservoir. The resulting gas release produces a similar bubble break-up behavior but with different time and length scales. We present time-resolved pressure and bubble geometry measurements following an instantaneous, underwater volume rupture, identify the relevant scaling behavior for the resulting dynamics, and contrast these measurements with less-constrained release systems.   

Interaction of two non-coalescing bubbles rising in a non-isothermal self-rewetting fluid

The attractive and repulsive behaviours of a pair of initially spherical gas bubbles rising side-by-side in a channel with non-uniformly heated walls containing a self-rewetting liquid are investigated numerically. The surface tension of a self-rewetting fluid exhibits a parabolic temperature dependence with a well-defined minimum, as opposed to linear (common) fluids whose surface tension decreases almost linearly with the increasing temperature. It is found that, for low Reynolds numbers, while in an isothermal medium, two gas bubbles display a repulsive behaviour, they attract in non-isothermal systems. The bubbles in the self-rewetting fluid undergo a plastic collision and show a `squeezing and relaxing' behaviour, whereas they attract and then bounce in the linear fluid. A regime map demarcating the repulsive and attractive behaviours for a self-rewetting fluid is plotted in the Weber number and the dimensionless linear component of the surface tension gradient space. The mechanism underlying the observed phenomenon is elucidated by studying the drag and lift forces acting on the bubbles, their orientations, and the flow field around them.   

Thermal effects in the collapse of a cavitation bubble

Cavitation bubbles play an important role in determining the efficacy and sustainability of a given system in naval hydrodynamics and biomedical applications. The energy concentration and shock emission during collapse are significant damaging mechanisms. Thus, we need to better understand energy concentration efficacy during the collapse. In the present study, energy budgets and energy transfer pathways in the spherical collapse of a gas bubble are investigated with specific consideration of thermal effects. A Rayleigh--Plesset-type equation is solved with taking into account compressibility and heat diffusion. Energy in the liquid-bubble system is partitioned into four components: liquid potential, kinetic and internal energy and bubble internal energy. As a bubble collapses, the initial liquid potential energy is transferred to the liquid kinetic energy and bubble internal energy. In addition, the bubble loses its thermal energy to liquid through heat diffusion, which leads to the increase in the liquid internal energy. At the final stage of collapse, thermal effects play a role in energy concentration due to coupling between heat diffusion and compressibility.   

How Fluid Accumulation Affects the Dynamics~of Bubble Growth and Rearrangements

In dry 2d foams a bubble grows or shrinks according only to its number of sides, dA/dt$=$K$_{\mathrm{o}}$(n-6). This von Neumann law is exact for a purely dry two-dimensional foam with no liquid content, but is increasingly violated for wetter quasi-2d foams where fluid accumulates in Plateau borders and vertices. Accounting for both the overall liquid content of the foam and the size of the Plateau borders extending into a third dimension, we modify von Neumann's law to a generalized coarsening equation where bubble size and shape now matter. To test this experimentally, we measure the growth rate of individual bubbles in quasi-2d foams of variable wetness confined between parallel plates. Interestingly, some 6-sided bubbles grow and others shrink - in direct violation of the usual von Neumann law but in agreement with our prediction. We demonstrate a shape parameter "circularity" is responsible for the violations of von Neumann's law observed in 6-sided and other n-sided bubbles. Additionally, dynamical heterogeneities like T1 events result from coarsening and lead to a relaxation of the foam structure. We present preliminary results on identifying the locations of rearrangements and explore the potential for using softness and machine learning to predict when and where they occur.   

Lift Force Acting on the Trailing Bubble in the Leading Bubble's Wake

We compute the three-dimensional motion of two gravity-driven bubbles, where the bubble is in the other bubble's wake, using an adaptive volume-of-fluid method. In contrast to previous axisymmetric predictions, the numerical results show that the relative motions are collision or escaping from the rising line. This difference depends on the condition of the rising path of a single bubble. The trailing bubble feels a positive transverse force in a stable condition, whereas a negative transverse force is critical. We consider this mechanism is closely related to the relationship between the shear-induced lift force experienced by a spherical-like bubble and the reversal lift force due to the wake instability experienced by an oblate spheroidal-like bubble.   

Hydrodynamics of High Dive and Water Entry Related Injuries.

Diving~is the sport~of jumping or falling into water from a platform, usually while performing acrobatics. For high diving competitions the initial height is 27 meters. From this height, the entry in water occurs at 85 km/h and is very technical to avoid injuries. Several risks come out of the violent impact at the air/water interface if the body is not perfectly vertical and stiffened, and the formation and collapse of the air cavity around the diver. Another issue among diver, underlined by David Colturi, a top level RedBull Cliff Diver, is the injury of adductor muscles due to the spreading of legs underwater, and which limits the number of dives a jumper is able to perform per competition day. In this study, we investigate experimentally the dynamics of the jumper underwater and the hydrodynamics causes of injuries in high diving, both in the field by monitoring several dives of David Colturi during his training and in simplified laboratory experiments in order to understand the underlying physics.   

Cavitation Bubble Growth with Phase Transition near a Rigid Wall

Bubbles grow and cavitate near surfaces during biomedical therapies, such as ultrasound-focused ablation of pathogenic tissues (e.g., kidney stones). The tensile part of the wave can nucleate and rapidly grow the bubble, while the compressive part accelerates its collapse. During these oscillations, liquid evaporates into the gaseous bubble, vapor condenses, and gases dissolve into the liquid. It is known that these dynamics affect the bubble’s growth and collapse dynamics. However, the regimes where phase change plays a significant role on the bubble dynamics under confinement (e.g., near a rigid wall) are not well studied. We investigate these dynamics using the open-source Multi-component Flow Code [Bryngelson et al. Comp. Phys. Comm. (2020)]. The code solves the 3D, compressible Navier--Stokes equations using a 6-equation multiphase numerical model that is adapted to account for heat and mass transfer. Problems involving the growth and collapse of a water vapor bubble in a free field and near a rigid surface are considered. Simulations of the Keller--Miksis equation are used to verify the numerical approach. Results varying driving pressure and bubble stand-off distances will also be presented.   

Experimental study of oil-coated bubble rising dynamics

Bubbles encapsulated by a bulk organic phase are widely present in ocean as well as many industrial processes, such as froth flotation. Despite its central role, their dynamics and the modulation imposed by the oil layer are fundamental multi-phase flow problems far from being well understood. Here, we focus on the coupled dynamics of a water medium and oil-coated bubbles with different oil fractions and viscosity. A combination of particle image velocimetry (PIV) and particle tracking velocimetry (PTV) techniques was used to characterize the flow around the rising bubbles and the 3D trajectories of the bubbles simultaneously. A high-speed stereo camera system with continuous LED light illumination was employed to reconstruct the 3D bubble trajectories; a wavelength filter was used in one of the cameras to isolate the LED illuminated bubbles from the laser-scattered seeding particles. Experiments reveal distinct dynamics of the bubbles dependent on the oil fraction and viscosity. In particular, the bubble trajectories exhibited characteristic features including the onset of path instability, transverse oscillation amplitude and frequency, and unsteady wakes---the results may serve to understand the rising dynamics of bubbles with various coatings.   

Oil-coated bubble formation at coaxial orifices

Dispersions of gas bubbles in liquids are widely present in natural phenomena and various industrial processes, therefore surface phenomena effect on bubble formation in liquids remains as one of the most significant research questions in fundamental multi-phase flows. Here, we document the formation of an oil-coated bubble at coaxial orifices in quiescent liquids. The air bubble is generated inside an oil domain, and then exits into the water with an oil coating under buoyancy. The existence of the oil significantly modified the bubble size, compared with the case of bubble formation in water. We developed a force balance model to predict the oil-coated bubble size, considering the orifice geometry as well as the compound air/oil/water interface. We found that the model agrees well with the experimental results, and we further discussed the dependences of the bubble size on the Bond number, size ratio of the orifices, as well as the interfacial tension ratio of oil/water and oil/air interfaces. Our study contributes to a further understanding on the dynamics of bubbles with a compound interface.   

Time-Resolved X-ray Radiography of Bubble Bifurcation in a Vibrated, Closed, Liquid-Filled Cylinder

Time-resolved quantitative mass distribution measurements were performed on a partially liquid-filled cylinder affixed to a vibration stage using x-ray radiography. A high-flux rotating anode x-ray tube source was used to image the multiphase dynamics inside the polycarbonate cylinder without interruption from the liquid--gas interfaces. The spectral response of the x-ray imaging system (\textasciitilde 5--150 keV) was modeled, and the recorded radiographs were converted to path lengths of the working fluid, PDMS oil. The parameters investigated included oscillation frequency, oscillation amplitude, liquid viscosity, and initial gas volume fraction in the cylinder. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. SAND2020-7887 A   

Acoustic, thermal and chemical response of single bubble collapse at audible frequencies and high amplitudes

Despite its probable feasibility, the use of sound frequencies lower than 20 kHz for acoustic cavitation has been subject to very little examination. In this work, a new formulation for the mass and heat transfer based on a boundary layer method has been coupled to classical hydrodynamic equations in order to model acoustically forced gas/vapor micro-bubbles in water. By accounting for all the critical thermo-mechanical contributions, the proposed model is shown to be robust enough so to be employed in the investigation of a large parameter space (frequency x amplitude $=$[1-100 kHz] x [1-7.5 atm]). Our results in the low frequency range suggest an increasingly important role of water vapor segregation in slowing down the bubble collapse, yielding a remarkably different behavior where the first collapse is not necessarily the strongest one. Moreover, the bubble response in terms of peak temperature and chemical production appears to be comparable to the high-frequency cases, thus casting renewed interest in the study of low frequencies for a variety of engineering applications.   

Inertially collapsing bubbles: a boundary layer approach to mass transfer modelling

Gas-mixture segregation in rapidly collapsing bubbles must be correctly described in order to predict the bubble dynamics around its minimum size, where the excess vapour accumulated in the bubble centre cushions the collapse. Reduced-order models have accounted for segregation of only vapour by approximating the thickness of the diffusion boundary layer to a penetration length, with a somewhat arbitrary upper cut-off for slow oscillations. In this work, a more accurate approach applicable to all the components of the gas mixture is devised. By assuming a concentration radial profile satisfying the boundary conditions, the diffusion-convection equation is employed to derive an expression for the rate of change of the boundary layer thickness. This new equation has been tested for a variety of cases of increasing complexity, from simple diffusion to diffusion-convection with interfacial non-equilibrium phase change. The formulation shows remarkable agreement with results obtained from the numerical solution of the full PDE and provides interesting insights into the mass transfer process in non-linearly oscillating bubbles.   

Application of Koopman theory and dynamic mode decomposition to the analysis of nonlinear bubble dynamics

Volume and shape oscillations of gas bubbles in liquids form a central area of study in multiphase fluids, with important applications to intravenous drug delivery, contrast-enhanced ultrasound imaging, and cavitation-induced flow instabilities and damage in turbomachinery. In this study, we use emerging tools from Koopman theory to analyze an extension of the Rayleigh-Plesset equation governing spherical bubble oscillations and their parametrically-driven nonspherical shape modes. In particular, we apply the dynamic mode decomposition (DMD) and the Hankel alternative view of Koopman (HAVOK) analysis to numerically-generated time series. These methods can extract coherent spatio-temporal structures from data and provide a globally linear representation of strongly nonlinear periodic and even chaotic dynamics. Such a Koopman embedding allows for future state prediction and admits the application of classical control techniques, including optimal control. While the resulting framework is applied to simulated data, it may be equally applied to experimental measurements of encapsulated microbubbles or other systems. The issues of multi-scale dynamics and sampling methods are also explored.   

Not Participating

We show that the Brownian motion of a nanoparticle (NP) can reach ballistic limit when intensely heated to form a supercavitation. As the NP temperature increases, its Brownian motion displays a sharp transition from normal to ballistic diffusion upon the formation of a vapor bubble to encapsulate the NP. Intense heating allows the NP to instantaneously extend the bubble boundary via evaporation, so the NP moves in a low-friction gaseous environment. We find the dynamics of the supercavitating NP is largely determined by the near field effect, i.e., highly localized vapor phase property in the vicinity of the NP.   

Single bubble impacting a curved surface.

Bubbles have played an important role in understanding different applications ranging from chemical processing to ship-turbine manufacturing. In many of these systems, hydrodynamic interactions between bubbles and surfaces are important to understand their performance and efficacy. Here, we investigate the dynamics of a single bubble bouncing and moving along curved surfaces of different radii. Parallel and normal velocities of the bubbles were measured at different bubble speeds to explore their interactions with a curved surface. Their motion will be predicted by considering the inertia, the hydrodynamic drag, and the lubrication film. Finally, based on the kinematics of bubbles, we will briefly discuss its potential applications like cleaning curved surfaces such as fruits.   

Dynamics of a rising bubble through the liquid-liquid interface

The dynamics of a bubble rising in stratified immiscible liquids through liquid-liquid interface is studied experimentally. High-speed imaging and time resolved Particle Image Velocimetry is used to investigate the bubble evolution with liquid-liquid interface. Bubble is released far from the interface to attain terminal condition before approaching the interface. The bubble rises through the lower fluid and then pierces through the interface to enter the upper fluid thereby deforming itself and liquid-liquid interface. Particularly, dependence of the shape and interface deformation, temporal velocity variation and wake dynamics of the bubble on bubble size and physical properties is examined. We identify critical E\"{o}tv\"{o}s number $=$ 5.34 and Galilei number $=$ 0.89 where satellite pinch-off first occurring for high Morton number ( $=$ 245.08) lower fluid and characterize their pinch-off height. By varying the bubble size in the lower liquid, it is observed that, smaller size bubbles are trapped in the liquid-liquid interface as the bubble could not generate enough buoyancy to pierce the interface. It is also found that, film drainage of bubble with satellite pinch-off shows linear bubble velocity variation in transition whereas without pinch-off shows oscillating motion.   

Acoustic Bubble Dynamics in a Yield-stress Fluid

Yield-stress fluids naturally trap small bubbles when their buoyancy applies an insufficient stress to induce local yielding of the material. Under acoustic excitation, trapped bubbles can be driven into volumetric oscillations; they then apply an additional local strain and stress that can trigger yielding and assist their release. We explore different regimes of microbubble oscillation and translation driven by an ultrasound field in a model yield-stress fluid. We first analyze the linear oscillation dynamics of a single bubble and estimate the local, high-frequency viscosity of the fluid. We apply pressure gradients to generate a net acoustic force on the bubble, which allows us to estimate the linear shear modulus of the fluid. We then examine whether bubbles are indeed released under stronger acoustic excitation, i.e. when the stresses associated with bubble oscillation yield the fluid. For large applied pressures, we report bubble shape oscillations and bubble motion becomes erratic, which prevents their release. We compare the observed shape modes and the critical pressure with a recent model. Lastly, we briefly discuss preliminary results on the dynamics of acoustically interacting -- attractive and repulsive -- bubble pairs in yield-stress fluids.