Bubble Interaction Research Articles

Clouds of bubbles in a viscoplastic fluid

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$ , the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$ , together with lower and upper estimates.

Cavitation Dynamics and Inertial Cavitation Threshold of Lipid Coated Microbubbles in Viscoelastic Media with Bubble-Bubble Interactions.

Encapsulated microbubbles combined with ultrasound have been widely utilized in various biomedical applications; however, the bubble dynamics in viscoelastic medium have not been completely understood. It involves complex interactions of coated microbubbles with ultrasound, nearby microbubbles and surrounding medium. Here, a comprehensive model capable of simulating the complex bubble dynamics was developed via taking the nonlinear viscoelastic behaviors of the shells, the bubble–bubble interactions and the viscoelasticity of the surrounding medium into account simultaneously. For two interacting lipid-coated bubbles with different initial radii in viscoelastic media, it exemplified that the encapsulating shell, the inter-bubble interactions and the medium viscoelasticity would noticeably suppress bubble oscillations. The inter-bubble interactions exerted a much stronger suppressing effect on the small bubble within the parameters examined in this paper, which might result from a larger radiated pressure acting on the small bubble due to the inter-bubble interactions. The lipid shells make the microbubbles exhibit two typical asymmetric dynamic behaviors (i.e., compression or expansion dominated oscillations), which are determined by the initial surface tension of the bubbles. Accordingly, the inertial cavitation threshold decreases as the initial surface tension increases, but increases as the shell elasticity and viscosity increases. Moreover, with the distance between bubbles decreasing and/or the initial radius of the large bubble increasing, the oscillations of the small bubble decrease and the inertial cavitation threshold increases gradually due to the stronger suppression effects caused by the enhanced bubble–bubble interactions. Additionally, increasing the elasticity and/or viscosity of the surrounding medium would also dampen bubble oscillations and result in a significant increase in the inertial cavitation threshold. This study may contribute to both encapsulated microbubble-associated ultrasound diagnostic and emerging therapeutic applications.

A volume-of-fluid reconstruction based interface sharpening algorithm for a reduced equation model of two-material compressible flow

In this paper we present a numerical method for the simulation of two-material flows governed by the compressible unsteady Euler equations. A system of six equations is used, with a pressure relaxation step which ensures convergence to the equivalent five-equation model. The numerical method employs a volume-of-fluid interface tracking method in order to maintain a sharp interface indefinitely, along with a robust update procedure for interfacial cells which ensures density and internal energy positivity. Numerical results are presented for a range of test cases, including for liquid–gas shock–bubble interaction and cylindrically convergent Richtmyer–Meshkov instability between metal and air. Results are in agreement with theoretical data, and compare well to other approaches designed to sharpen the material interface in the five-equation model.

Boiling crisis due to bubble interactions

The boiling crisis determines the maximum heat flux for the safe operation of boiling equipment, which is widely used in various applications including power generation, thermal management of electronics and water desalination. Here we present a mechanistic and predictive theory for the boiling crisis, combining the thermo-fluidic interaction between bubbles and the stochastic interaction of nucleation sites. Using Rayleigh and Poisson distributions, we demonstrate that the boiling crisis occurs when the population of isolated nucleation sites reaches the maximum. We identified a dimensionless boiling crisis constant 1/πe, which universally relates the bubble base diameter to the isolated nucleate site density during the saturated pool boiling crisis. This finding is supported by our direct numerical simulation as well as by previous numerical and experimental results. Combining the thermo-fluidic and stochastic interaction, quantitative and simultaneous predictions of the critical heat flux (CHF) and the corresponding wall superheat at the CHF were achieved, which agrees with existing experimental data. Our theory thus offers a new avenue for understanding the boiling crisis, and therefore can serve as a guideline for the future boiling enhancement design.

A numerical study of a bubble pair rising side by side in external magnetic fields

The motion of a pair of bubbles rising side by side under the influence of external magnetic fields is numerically examined. Through solving the fully three-dimensional Navier–Stokes equations, the results reveal that the bubble interactions are rather sensitive to the field direction and strength. At first, we identify that, in a hydrodynamic flow, whether the two bubbles will bounce or coalesce depends on the developments of the counter-rotating streamwise vortices during the collision. In particular, for an originally bouncing bubble pair, a streamwise magnetic field tends to promote their coalescence by weakening the strengths of the standing streamwise vortices, and such a weakening effect is caused by the asymmetric distribution of the Lorentz force in the presence of another bubble such that a torque is induced to offset the original streamwise vortices. Under a horizontal magnetic field, on the other hand, the influences are highly dependent on the angle between the bubble centroid line and the field: a transverse field or a moderate spanwise field always leads the bubble pair to coalescence while a strong spanwise field has the opposite effect. This anisotropic effect comes from the Lorentz force induced flow diffusion along the magnetic field, which not only produces two pairs of streamwise vortices at the bubble rear, but also homogenizes the pressure along the magnetic lines. As the competition between the two mechanisms varies with the magnetic direction and strength, the interaction between the bubble pair also changes. We show that the external magnetic fields control the bubble interaction through reconstructing the vortex structures, and hence the core mechanisms are identified.

Numerical Investigation on Combustion-Enhancement Strategy in Shock–Fuel Jet Interaction

Multidimensional numerical simulations are performed to investigate the evolution and formation of unburned fuels for a shock–fuel jet interaction scenario. A full set of Navier–Stokes equations with detailed chemical mechanisms are solved, and the results are analyzed through the Lagrangian method with the goal of improving combustion efficiency in supersonic flows. The flame morphology of a two-dimensional (2-D) non-premixed reactive shock–bubble interaction is first simulated and studied, in which unburned hydrogen is found to prevent efficient combustion. By applying the Lagrangian particle tracking method, most of the unburned hydrogen wrapped into the primary vortex turns out to be initially located upon the symmetry line of the bubble. Motivated by the idea of breaking the primary vortex, this study designs a novel geometry of a concentric bubble, which improves combustion efficiency to 94.4% in contrast to a solid fuel bubble (74%) due to multivortex interaction and a thick bridge structure. With the consistency between qualitative and quantitative 2-D and three-dimensional (3-D) flow dynamics, the idea of a 2-D concentric-bubble configuration is effectively extended to a 3-D coaxial jet interacting with oblique shock despite the existence of Kelvin–Helmholtz instability.

Recent advances in computational fluid dynamics simulation of flotation: a review

AbstractFlotation process is a multi‐phase and multi‐scale complex flow system, in which hydrodynamics plays an indispensable role. In recent years, computational fluid dynamics (CFD) numerical simulation has gradually become a powerful tool for studying flotation. In this review, the theories of CFD numerical simulation in flotation research were reviewed, involving various turbulence models and multi‐phase flow simulation approaches. An attempt has been made to analyze and discuss the characteristics and applicability of different turbulence models and multi‐phase flow simulation approaches in flotation researches in detail. The CFD simulation of two commonly used flotation devices, that is, mechanically agitated flotation machine and flotation column, has been reviewed in detail. The detailed principles, operation, and hydrodynamic of flotation devices were discussed from the viewpoint of CFD. The advances made in CFD simulation for studying flotation process, including particle suspension, bubble dispersion, particle–bubble collision, attachment, and detachment subprocesses have been critically analyzed. Focused analysis was given on the influence mechanism of turbulence on the particle–bubble interactions. Finally, the gaps in the available literature are discussed and potential research directions are also proposed.

Phase portrait analysis of laminar separation bubble and ground clearance interaction at critical (low) Reynolds number flow

Inspiring from nature, flying near the ground surface might increase the aerodynamic performance of Micro Aerial Vehicles (MAVs). Because of the being small in size, these birds have low flight speeds and their operating range is in the low Reynolds flow zone (Re<2.0×105) where a laminar separation bubble (LSB) normally appears on the suction surface of a wing. In this study, the interaction of LSB formed on a full-span wing, with the cross-section of NASA LS (1)-0417, and ground clearance is investigated at the critical Reynolds number (5×104−2×105). The behavioral changes of the separation bubbles in free flow and near the ground surface have been numerically discussed in detail by different distances away from the ground (h/c) and various angle of attack (8°, 12°, 14°, and 16°). Furthermore, the patterns and behavior of multiple flows affected by the interaction of the separation bubble phenomenon with ground effect is discussed from the points of view of vortex fields, phase portrait, frequency analysis, existing stresses, and velocity profiles. The main outcomes reveal that the ground effect's general role does not work in this region of flow, and the aerodynamic performance of the full-span wing is decreased near the ground due to the bubbles. Furthermore, at 0.2<h/c<1, the phase portrait curves have an elliptical shape due to the bursting of the separation bubble.

Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons.

Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted.

Geometry effect in reactive shock-elliptic bubble interactions

Geometry effect in reactive shock-elliptic bubble interactions

An investigation of the gravity effects on pool boiling heat transfer via high-fidelity simulations

Nucleate pool boiling simulations are carried out to study the effects of gravity on the dynamics of bubble formation, bubble departure, and the mutual bubble interactions. We focus on identifying the dominant trends associated with the flow and thermal behavior at different gravity levels using fixed values of wall superheat and liquid subcooling. This is accomplished by measuring the contributions to heat flux associated with turbulent flow resulting from the dynamics of bubble interaction. The time averaged fluctuations of velocity and temperature indicate that the wall heat flux conditioned by the wetted surface area - the liquid heat flux - provides a useful indication of high heat flux hot spots. Furthermore, despite substantial differences in the dynamics of large scale bubbles at different gravity levels, the average heat flux in the liquid region is found to be dominated by the sliding and merger type events associated with small scale bubbles over a wide range of gravity levels. This significance of near-wall, small scale bubble dynamics is reflected in the transition of vorticity structures from hairpin type vortices in the near-wall region to vortex ring patterns away from the wall. While the maximum value of average turbulent fluctuations occurs away from the wall for earth normal gravity, the near-wall peak is only slightly lower and is similar in magnitude to that in the case of low gravity. These observations reveal the significance of small scale dynamics in affecting the heat transfer which was previously thought to be dominated by large scale bubbles, particularly at low gravity levels.

Electrochemically-mediated amine regeneration of CO2 capture: From electrochemical mechanism to bench-scale visualization study

Electrochemically-mediated amine regeneration (EMAR) is a new CO2 capture technology with the potential to exploit the excellent removal efficiencies of thermal amine scrubbers while reducing parasitic energy losses and capital costs. To achieve higher efficiency and explore the industrial application of the promising EMAR system, a home-designed bench-scale modular flowing-through electrolysis cells (MFTECs) is proposed. The MFTECs with MEA solvent is carefully analyzed from electrochemical mechanism to bench-scale demonstration. Firstly, a series of electrochemical experiments were conducted in an H-cell to study the unknown electrochemical behaviors under various complex concentrations and temperatures, which provided a guidance to enhance the electrochemical performance. Subsequently, a visualization study of the CO2 desorption process in MFTECs was conducted at different operating conditions (current, complex concentration, electrode position, and reaction time) to investigate the desorption performance of the proposed MFTECs system. This framework allowed for direct observation and comprehension of the CO2 desorption process, as well as the movement and interaction of CO2 bubbles in MFTECs. Finally, results indicated that the proposed MFTECs enables higher electrode active surface area and lower cell resistance. This will contribute to enhancing the regeneration performance and promoting industrial application of CO2 desorption based on EMAR.

Nonlinear dynamics and acoustic emissions of interacting cavitation bubbles in viscoelastic tissues

The cavitation-mediated bioeffects are primarily associated with the dynamic behaviors of bubbles in viscoelastic tissues, which involves complex interactions of cavitation bubbles with surrounding bubbles and tissues. The radial and translational motions, as well as the resultant acoustic emissions of two interacting cavitation bubbles in viscoelastic tissues were numerically investigated. Due to the bubble–bubble interactions, a remarkable suppression effect on the small bubble, whereas a slight enhancement effect on the large one were observed within the acoustic exposure parameters and the initial radii of the bubbles examined in this paper. Moreover, as the initial distance between bubbles increases, the strong suppression effect is reduced gradually and it could effectively enhance the nonlinear dynamics of bubbles, exactly as the bifurcation diagrams exhibit a similar mode of successive period doubling to chaos. Correspondingly, the resultant acoustic emissions present a progressive evolution of harmonics, subharmonics, ultraharmonics and broadband components in the frequency spectra. In addition, with the elasticity and/or viscosity of the surrounding medium increasing, both the nonlinear dynamics and translational motions of bubbles were reduced prominently. This study provides a comprehensive insight into the nonlinear behaviors and acoustic emissions of two interacting cavitation bubbles in viscoelastic media, it may contribute to optimizing and monitoring the cavitation-mediated biomedical applications.

NNumerical investigation of bubble interaction mechanisms in gas-liquid bubbly flows: Harmonisation of bubble breakup and coalescence effects

Numerical investigation of the dynamics of gas-liquid bubbly flow has been performed by using the population balance approach. Using the homogeneous MUSIG model coupled with the two-fluid model, the evolution of bubble size distribution in vertical pipes has been simulated with appropriate consideration of bubble interaction mechanisms. In particular, the study focuses on harmonising the imbalance often associated with breakup and coalescence rates by performing extensive numerical investigations for the examination and comparison of different model formulations to harmonise the coalescence calibration factor of Prince and Blanch (1990) model. To avoid the fine-tuning procedure of selecting calibration factors to harmonise the breakup and coalescence effects, a breakup calibration factor of 1.0 (default setting in ANSYS CFX) was used and three different expressions area-averaged and included as the coalescence calibration factor for the model of Prince and Blanch (1990) modelled using CFX Expression Language (CEL). The performance of the three different “cases” (modifications) has been investigated, compared with each other and validated against the experimental data reported by Monrós et al. (2013). In general, the comparison has shown that all the “cases” yielded satisfactory results when the numerical results were compared with five primitive experimental parameters, namely: gas volume fraction, interfacial area concentration, Sauter mean bubble diameter, gas velocity and liquid velocity. The encouraging results obtained clearly show the capability of the “cases” modelled in capturing the evolution of the bubble sizes. The agreement with the gas volume fraction profiles indicates a level of confidence in the interfacial force models used. Similarly, the agreement seen with the interfacial area concentration indicates that the “cases” modelled for the birth and death processes are reasonably adequate to describe the bubble dynamics. Overall, the comparison shows that the model labelled as “case 2” presented the best results in most of the experimental conditions simulated.

Stability assessment of the phase-field lattice Boltzmann model and its application to Taylor bubbles in annular piping geometries

This study parametrically assessed the stability of the phase-field lattice Boltzmann model (PFLBM) before applying it to analyze the effect of annular piping geometry on the flow of Taylor bubbles. The impacts of both eccentricity and pipe diameter ratio were examined, providing an insight into the behavior of these bubbles as well as the applicability and shortcomings in current prediction methodologies. A recently developed PFLBM was implemented into the open-source simulation framework, waLBerla, for this analysis. The stability properties of the code were investigated in detail by assessing various lattice discretizations and relaxation kernels applied to the Rayleigh–Taylor benchmark problem and a Rayleigh–Taylor instability in a tubular geometry, with gravitational Reynolds numbers of up to 30 000 and 10 000, respectively. This paper makes three contributions relating to the stability and usage of the PFLBM as well as the flow of Taylor bubbles in annular pipes. First, the work numerically explored the stability properties of the velocity-based, PFLBM and concluded the impact of various collision models and lattice discretizations on simulation results. Second, it provided a flexible open-source code that the interested researcher can use interactively for practical flow problems as well as the analysis of numerical properties of various lattice Boltzmann algorithms. Finally, it quantified the effect of pipe eccentricity and diameter ratio on the propagation of a Taylor bubble inside a water-filled annular pipe, concluding that a previously defined closure model captured the diameter ratio for the cases examined. To extend this work, future studies aim to analytically investigate the stability properties parametrically observed in this study and apply the findings to simulate the interaction of multiple Taylor bubbles.

Dynamic mode decomposition of magnetohydrodynamic bubble chain flow in a rectangular vessel

We demonstrate the first application of dynamic mode decomposition (DMD) to bubble flow with resolved dynamic liquid/gas boundaries. Specifically, we have applied DMD to the output of numerical simulations for a system where chains of bubbles ascend through a rectangular liquid metal vessel. Flow patterns have been investigated in the vessel and bubble reference frames. We show how gas flow rate and applied magnetic affect bubble wake flow and larger-scale flow structures within the liquid metal vessel by examining the velocity field mode statistics over trajectory time and total flow time as well as the computed mode velocity fields. The results of this proof-of-concept study indicate that DMD can yield unique insights into various momentum transfer and bubble interaction mechanisms, and that mode analysis can be used to explain the observed flow patterns. In addition, we showcase our own implementation of DMD that combines resilience to data noise, memory efficiency and special pre-processing for input data.

Multibubble Sonoluminescence from a Theoretical Perspective.

In the present review, complexity in multibubble sonoluminescence (MBSL) is discussed. At relatively low ultrasonic frequency, a cavitation bubble is filled mostly with water vapor at relatively high acoustic amplitude which results in OH-line emission by chemiluminescence as well as emissions from weakly ionized plasma formed inside a bubble at the end of the violent bubble collapse. At relatively high ultrasonic frequency or at relatively low acoustic amplitude at relatively low ultrasonic frequency, a cavitation bubble is mostly filled with noncondensable gases such as air or argon at the end of the bubble collapse, which results in relatively high bubble temperature and light emissions from plasma formed inside a bubble. Ionization potential lowering for atoms and molecules occurs due to the extremely high density inside a bubble at the end of the violent bubble collapse, which is one of the main reasons for the plasma formation inside a bubble in addition to the high bubble temperature due to quasi-adiabatic compression of a bubble, where “quasi” means that appreciable thermal conduction takes place between the heated interior of a bubble and the surrounding liquid. Due to bubble–bubble interaction, liquid droplets enter bubbles at the bubble collapse, which results in sodium-line emission.

Interaction of the galactic-centre super bubbles with the gaseous disc

ABSTRACT The interaction of Galactic centre (GC) super bubbles (GSBs) with the gaseous disc and halo of the Milky Way is investigated using radio continuum, X-ray, H i, and CO line surveys. The radio North Polar Spur (NPS) constitutes the brightest eastern ridge of GSB, brightening towards the galactic plane and reaching l = 22○, b = +2○ at the sharpest end, where it intersects the tangential direction of the 3-kpc-expanding ring and crater. Examination of the spur ridges reveals that the entire GSB, including the NPS and its counter spurs, constitutes a GC-symmetrical Ω/ Ʊ shape. The thickness and gas density of the H i and CO discs are shown to increase sharply from the inside (lower longitude) to the outside the 3-kpc crater. Formation of crater is explained by the sweeping of the upper layer of disc gas by the shock wave from the GC by the explosion ∼10 My ago with the emitted energy of several 1055 erg. Based on the discussion, a unified view on the structure and formation mechanism of GSB is presented.

Numerical study of bubble behaviors and heat transfer in pool boiling of water/NaCl solutions using the lattice Boltzmann method

Through modification of the equation of state applicable to the non-volatile salt solution and characterization of the effect of solute concentration on the physical properties of the solution, a lattice Boltzmann pseudopotential model was developed and used to study the pool boiling processes of pure water and NaCl solutions. The model quantitatively verified the equilibrium vapor pressure reduction and boiling point rise of the NaCl solution with solute concentration. The complete pool boiling curves of pure water and the NaCl solution were simulated, and the differences in bubble behaviors and heat flux evolutions in pure water and the NaCl solution at different superheats were analyzed. The results revealed that the difference of heat flux between water and NaCl solution in the nucleate boiling regime is dominated by the nucleation site density and bubble departure frequency at lower superheats, while dominated by the bubble interactions at larger superheats. As a result, the NaCl solution presents a lower nucleate boiling heat flux than that of water when the imposed superheat is smaller than a critical superheat, while it exhibits a larger heat flux even a higher critical heat flux than water when the superheat is higher than the critical superheat. Furthermore, the lower bubble departure frequency in NaCl solution film boiling was captured by simulation. The simulated film boiling heat flux of the NaCl solution was smaller than that of water, and both the simulated results fitted the Berenson correlation well.

Scaling behavior of density gradient accelerated mixing rate in shock bubble interaction

Variable-density mixing in shock bubble interaction, a canonical flow of Richtermyer-Meshkov instability, is studied by the high-resolution simulation. While the dissipation mainly controls the passive scalar mixing rate, an objective definition of variable-density mixing rate characterizing the macroscopic mixing formation is still lacking, and the fundamental behavior of mixing rate evolution is not yet well understood. Here, we first show that the variable-density mixing of shock bubble interaction is distinctly different from the previous observations in the passive scalar mixing. The widely-accepted hyperbolic conservation of the first moment of concentration in the scalar mixing, i.e., the conservation of the mean concentration, is violated in variable-density flows. We further combine the compositional transport equation and the divergence relation for the miscible flows to provide the evidence that the existence of density gradient accelerated mixing rate, decomposed by the accelerated dissipation term and redistributed diffusion term, contributes to the anomalous decrease or increase of the mean concentration depending on Atwood number. Further analyzing a number of simulations for the cylindrical or spherical bubbles under a broad range of shock Mach numbers, Reynolds numbers, and Peclet numbers, the density gradient accelerated mixing rate exhibits weak dependent on Peclet numbers, and identifies an Atwood number range with high mixing rate, which can be theoretically predicted based on the mode of hyperbolic conservation violation behavior.