Session A21: Bubbles: Dynamics

A unified relationship for the bubble departure from a wall

Bubble departure is a ubiquitous phenomenon in nature and industry. In addition to the conventional mechanism, i.e., isolated bubble departure driven by buoyancy, coalescence induced bubble departure can be a predominant process while the underlying mechanics remaining unknown. Here, we report a new regime of bubble departure owing to the coalescence of two bubbles, where the departure diameter can be much smaller than the conventional buoyancy limit. We show that the significant reduction of bubble base area promotes the bubble departure, which is governed by two chracterisitic timescales of bubble coalescence. More importantly, using the distribution of bubble nucleation sites, we combine the buoyancy driven and the coalescence induced bubble departure modes and develop a unified relationship between the departure diameter and nucleation site density. This work elucidates how coalescing bubbles depart from a wall and provides design guidelines for achieving efficient bubble departure in applications such as boiling and gas-evolving reactions.   

Direct Numerical Simulation Study of Microbubble Entrapment in Vortical Structures in a Turbulent Channel Flow

We have performed direct numerical simulations of microbubbles in a turbulent channel flow to better understand how bubbles interact with turbulent structures. The flow is simulated using a pseudo-spectral solver, and the bubbles are modeled as massless point particles using modified Maxey-Riley equations. The flow is driven by a constant pressure gradient with no gravity in order to determine if bubbles are preferentially drawn to hairpin vortices found in turbulent wall-bounded flows. Hairpin vortex locations—identified by the λ-2 criterion—are correlated with bubble locations to show the capturing capabilities by different portions of these structures. We explore the statistics of bubble residence times and examine its dependence of the vortex Reynolds number, distance from the wall, and other flow parameters. This is an extension of a previous work which examined bubble entrapment in a Lamb-Oseen vortex (Kelly et al.  Phys. Fluids 33 (6), 061702, 2021); we now seek to understand the nature of temporary, selective entrapment in more complex flows.   

Active control of propagating bubbles in Hele-Shaw channels

We explore the capabilities of active control to stabilise and manipulate propagating bubbles in the confined geometry of a rectangular Hele-Shaw channel. Several steadily-propagating solution branches exist in this system, with only one linearly stable and subsequent branches featuring increasingly deformed bubble shapes and increasing numbers of unstable eigenmodes. Our aim is to use feedback control and control-based continuation to detect and stabilise at least the first of these unstable branches. This system is an appealing prototype for control: the low Reynolds number and strongly confined geometry means the system state is essentially encapsulated in the interface shape, recent experimental realisations of this system are in good agreement with depth-averaged models, and the system responds well to actuation via fluid injection, but nonetheless practical implementation of feedback control presents significant challenges. In this talk, we use a depth-averaged model to illustrate how control would work in this system, including the design of a suitable gain matrix, the impact of control on the bifurcation structure, the complexities of controlling a propagating bubble moving past a fixed array of injection points, and how this simulation relates to experimental reality.   

A backflipping motion of a bubble impacting tilted surfaces

Bubbly flows are ubiquitous in both industrial and natural settings. A recent study [1] showed that forces arising from a bubble impacting a surface in a moderate Reynolds number range can remove active microorganisms or passive beads on the surface. In this work, we experimentally investigate a bubble impacting a tilted glass surface for a bubble diameter range of 1.1< d<1.4. Interestingly, we observe a backflipping-like behavior where the bubble moves backward against the surface slope after its first impact before it starts moving forward. To characterize the backflipping behavior, we find a characteristic backflipping distance for different bubble sizes and surface inclination angles. We find that the backflipping effect is stronger for larger bubbles as the impact velocity is larger. In addition, we find that for each bubble size there is a critical angle for the maximum backflipping effect which varies in the range of 5-10 degrees for bubbles of the current size range. Our PIV measurements indicate that the backflipping strength is directly correlated with the average vorticity around the bubble surface and the resultant lift force. We incorporate the PIV measurements into a simplified force balance model that only considers lift and buoyancy forces, which captures the main essence of the backflipping behavior. In addition, we perform numerical simulations to also consider the thin film pressure during the first impact and compare the numerical backflipping distance with the experiments and the simplified model.

[1] E. Esmaili, P. Shukla, J. Eifert, S. Jung, “Bubble impact on a tilted wall: Removing bacteria using bubbles” Phys. Rev. Fluids, 4, 043603 (2019)   

Dynamics of oil-coated bubbles rising in a quiescent liquid

Compounded bubbles with a liquid phase in another continuous bulk phase are produced in a wide range of natural and industrial processes, such as gas released from natural seeps in the deep sea and froth flotation with oily bubbles. In these configurations, how does the coating influence the bubble rising dynamics remains largely unexplored. Here we take the oil-coated bubble as an example to experimentally investigate its rising dynamics with various oil fractions in a quiescent water medium. We find that the oil coating changes the rising dynamics of the bubble mainly by modifying the bubble surface boundary condition and effective density. A lightly-coated bubble experiences a smaller shape deformation and similar drag coefficient compared to a clean gas bubble, and the increase of oil fraction results in reduced shape deformation and drag coefficient. Estimation of the forces using a Frenet reference frame shows that the wake-induced lift decreased with oil fraction, based on which the effect of oil coatings on the path oscillation frequency and amplitude are further rationalized. Overall, our work contributes to the fundamental understanding of the rising dynamics of oil-coated bubbles with various oil fractions and viscosities.   

Dynamics of a Single Bubble Rising in Confined Stratified Flow

In oceans, density varies with depth due to varying salinity, which captures myriads of pollutants such as plastics, rubber, etc. that drastically affect marine wildlife. The rising motion of a single or cluster of bubbles creates a vertical upflow that can transport the buoyant sediments to the surface for efficient waste removal. To begin realizing this complex multi-phase flow system, we start with a simplified problem of a single millimeter-sized air bubble rising in a 2.5mm confined channel. We performed a time-resolved stereoscopic 2D3C Particle Image Velocimetry (PIV) measurement to characterize the bubble wake. Pure water and varying salt concentration were used to achieve a linear density stratification corresponding to Froude numbers (Fr) ranging from 20-40. Due to the large dynamic velocity range (60) for PIV, we enhance our cross-correlation algorithm with pyramid correlations. The rising bubble generates vortices that shed downstream and decay with varying timescale for different Fr. The wake of the bubble carries the higher density fluid to the top, which later releases from the wake to form the reverse jet. This process enhances the mixing causing destratification. The coherent structures and the jet are characterized as a function of the Froude number.   

Bubble pinch-off in viscoelastic liquids

The formation of gas bubbles in a continuous liquid phase is important in many engineering processes, for instance, to generate foam or to provide agitation and mixing in bubbly flows. A challenge in describing the initial formation of a bubble is that the final pinch-off exhibits a singularity in time and space. Past experiments in Newtonian fluids have shown that the evolution of the neck radius can be captured by a power-law of the time before break-up. The corresponding exponent depends on the viscosity of the continuous liquid, from 1/2 for low viscosity to 1 for large viscosity. However, bubble formation in a dilute polymer solution presenting a viscoelastic behavior remains unclear. In this study, we use high-speed imaging to analyze the pinch-off of air bubbles in a dilute solution of polymers. We characterize the time evolution of the neck radius when varying the characteristic relaxation time and describe the influence of the viscoelasticity on the bubble generation process.   

On the stability of bubble chains in carbonated drinks

Bubbles appear when a carbonated drink is poured in a glass. Very stable bubble chains are clearly observed in champagne, showing an almost straight line from microscopic nucleation sites from which they are continuously formed. In some other drinks such as  soda, such chains are not straight (not stable). Considering  pair interactions  for spherical clean bubbles (Hallez & Legendre JFM 2011), bubble chains should not be stable which contradicts some observations. The aim of this work is to explain the condition of stability of bubble chains. For this purpose, experiments and direct numerical simulation are conducted. The bubble size as well as the level of interface contamination are varied. Both are shown to affect the bubble chain stability. A criteria based on physical arguments is proposed to describe the condition of transition from stable to unstable bubble chain.   

DYNAMICS OF A BUBBLE RISING ON THE VICINITY OF A VERTICAL WALL

An experimental and numerical study on the dynamics of an air bubble rising close of a vertical wall is presented. The problem is characterized by three dimensionless numbers, namely Galileo (Ga), Bond (Bo), and the dimensionless distance between the bubble and the wall, L*. Bubbles are injected in a glass tank 120 cm high with a 15 x 15 cm² cross-section. To vary the control parameters, different liquids and air injectors were employed, and a mobile wall inside the tank let us precisely control L*. We focus on three regimes at high Bo that exhibit different ascending trajectories, i.e. rectilinear, spiral and planar zig-zag. The experiments were recorded with two high-speed cameras moved vertically by a controlled linear motor. The images were processed to obtain the bubble contour, deformation and trajectory. Moreover, unsteady, three-dimensional, incompressible, two-phase flow simulations were performed using Basilisk and spatial Adaptive Mesh Refinement (AMR) technique. The forces acting on the bubbles were obtained, being associated to the bubbles’ dynamics and the topology of the bubbles’ wakes. The study will allow us to determine the effect of a vertical wall on the phase diagram, in the (Bo, Ga) plane, defining the different styles of path exhibited by the bubbles.