Initial Bubble Research Articles

Mathematical modeling of puffing and microexplosion in emulsified fuel droplets containing several bubbles: A case study on n-dodecane/water droplet

This paper presents a theoretical model for microexplosion and puffing in a single isolated emulsion droplet at high ambient temperature and one atmospheric pressure. The model considered transient heating of the droplet, bubble growth dynamics, bubble motion, and bubble interactions (e.g., bubble coalescence). The bubble growth is determined by solving a modified Rayleigh equation which considered bubble interactions. The model considered multiple bubbles inside a fuel droplet which were not accounted for in the models proposed in previous studies. The model is applied to simulating the microexplosion of n-dodecane/water droplets. The simulated microexplosion delay times are compared with the experimental data from the literature, with good qualitative and quantitative agreements obtained. Results show that microexplosion delay time diminished by 40% and 50% for a 10-times increase in the initial bubble diameter and changing the bubble location from droplet center to 0.4 times the droplet radius, respectively. For multiple bubbles inside the droplet, the microexplosion delay time converges to a minimum threshold value without further changing the bubble number. The simplified model bears practical potential in enabling spray combustion modeling of water-emulsified fuels with considerably reduced computational costs.

Theoretical Study of Supercavitation Bubble Formation Based on Gillespie’s Algorithm

Understanding the creation and development of a supercavitation bubble is essential for the design of supercavitational underwater vehicles and applications. The pressure field of the supercavitation bubble is one of the most significant factors in these processes, and it should be taken into account in the analysis. The underwater vessel is surrounded by a supercavitation bubble which is, in fact, an inhomogeneous fluid containing cavities (also described as microbubbles). The distribution of the cavities in the supercavitation volume dictates the pressure field and thus determines the stresses and forces that act on the vessel and affect its motion and stability. In this research, we suggest a new approach to studying the bubbles’ formation and learning about the cavities’ distribution in the low-pressure volume that envelops the underwater vehicle. We used Logvinovich’s principle to describe a two-dimensional ring of fluid that is created at the front edge of the supercavitation body and moves downstream along the vessel. To describe the distribution of the cavities we used Gillespie’s algorithm, which is usually used to describe biological and chemical systems. The algorithm succeeded in describing the random movement of the cavities in the cross-section under various conditions and also in describing their distribution and effects on the macroscopic system. A few factors of the physical characteristics of the fluid and the flow conditions were examined (the initial bubble supply, and the rate coefficients of creation and collapse). The results led to the conclusion that with an examination of those factors and using Gillespie’s algorithm, predictions of the distribution and thus the development of supercavitation could be achieved. The main finding of the analysis was that asymmetric development of the bubbles took place, in spite of the symmetry of the physical problem, as observed in high-resolution experiments.

Effect of Coarse Aggregate Content on Bubble Formation Behavior in Corundum Permeable Brick for Tundish

Herein, corundum porous permeable bricks with different coarse aggregate contents are prepared using particle packing method. Based on the similarity principle, a local water model of a tundish is designed to investigate the bubbling behavior in porous permeable bricks at various argon flow rates. Through dimensionless analysis, empirical formulas of bubbling region diameter and initial bubble size in porous permeable bricks are proposed. The results show that an increasing aggregate content can increase the apparent porosity and the proportion of large pores, reduce the surface fractal dimension of the porous permeable bricks, and obtain a higher gas permeability. With the increase of argon flow rate and the decrease of gas permeability, the internal pressure gradient in porous permeable bricks increases. The larger the argon flow rate and the gas permeability value, the more beneficial it is to activate more pores and form a larger bubbling region on the upper surface of porous permeable bricks. The Sauter mean diameter of bubbles and the initial velocity of gas plumes are inversely correlated with the content of coarse aggregate; that is, the porous permeable brick with a higher content of coarse aggregate is beneficial to generating much more small bubbles.

Bubble Coalescence During Pool Boiling with Different Surface Characteristics

This work investigates the bubble dynamics during pool boiling from isolated cavities on a horizontal silicon substrate with three surface coatings, silicon oxide, Perfluorodecyltrichlorosilane, and silica nanoparticles. The experiments were conducted with FC-72 under various superheat degrees. In the case of vertical coalescence, coalescences at the boundary between the departed bubble and the subsequent nucleated bubble were observed and analyzed. Vertical coalescence appears with lower superheat degrees on Perfluorodecyltrichlorosilane coated surfaces due to the faster initial bubble growth than on the other surfaces. However, the vertical coalescence has a limited effect on the bubble departure diameter, which is nearly kept constant at around 0.6 mm. In the case of horizontal coalescence, bubbles growing on the silica nanoparticles coated surface are able to coalesce for small cavity spacing with lower superheat degree than other surfaces. Coalescing bubbles from cavities spaced 0.50 mm apart can detach just after coalescence, while for a shorter spacing of 0.25 mm, bubbles remain attached to the surface and further growth is needed for their detachment. Based on the analysis of energy removal per unit of area, the optimal heat transfer performance may be achieved when the cavities spacing is approximate to the single bubble departure diameter.

Effects of N-Alkanol Adsorption on Bubble Acceleration and Local Velocities in Solutions of the Homologous Series from Ethanol to N-Decanol

The influence of n-alkanol (C2-C10) water solutions on bubble motion was studied in a wide range of concentrations. Initial bubble acceleration, as well as local, maximal and terminal velocities during motion were studied as a function of motion time. Generally, two types of velocity profiles were observed. For low surface-active alkanols (C2-C4), bubble acceleration and terminal velocities diminished with the increase in solution concentration and adsorption coverage. No maximum velocities were distinguished. The situation is much more complicated for higher surface-active alkanols (C5-C10). In low and medium solution concentrations, bubbles detached from the capillary with acceleration comparable to gravitational acceleration, and profiles of the local velocities showed maxima. The terminal velocity of bubbles decreased with increasing adsorption coverage. The heights and widths of the maximum diminished with increasing solution concentration. Much lower initial acceleration values and no maxima presence were observed in the case of the highest n-alkanol concentrations (C5-C10). Nevertheless, in these solutions, the observed terminal velocities were significantly higher than in the case of bubbles moving in solutions of lower concentration (C2-C4). The observed differences were explained by different states of the adsorption layer in the studied solutions, leading to varying degrees of immobilization of the bubble interface, which generates other hydrodynamic conditions of bubble motion.

Dynamics of an oscillating microbubble in a blood-like Carreau fluid.

A numerical model for cavitation in blood is developed based on the Keller-Miksis equation for spherical bubble dynamics with the Carreau model to represent the non-Newtonian behavior of blood. Three different pressure waveforms driving the bubble oscillations are considered: a single-cycle Gaussian waveform causing free growth and collapse, a sinusoidal waveform continuously driving the bubble, and a multi-cycle pulse relevant to contrast-enhanced ultrasound. Parameters in the Carreau model are fit to experimental measurements of blood viscosity. In the Carreau model, the relaxation time constant is 5-6 orders of magnitude larger than the Rayleigh collapse time. As a result, non-Newtonian effects do not significantly modify the bubble dynamics but do give rise to variations in the near-field stresses as non-Newtonian behavior is observed at distances 10-100 initial bubble radii away from the bubble wall. For sinusoidal forcing, a scaling relation is found for the maximum non-Newtonian length, as well as for the shear stress, which is 3 orders of magnitude larger than the maximum bubble radius.

Double-pulse laser ablation in liquids: nanoparticle bimodality reduction by sub-nanosecond interpulse delay optimization

Applications of nanoparticles (NPs) in medicine, energy, catalysis, or additive manufacturing demand the development of NP production methods that are offering material and solvent versatility, high purity, morphology, and size control, together with industrial-scale production capabilities. Pulsed laser ablation in liquids (PLAL) is a technique that comes close to meeting these demands; however, NP size control remains a challenge. To reduce the characteristic bimodality in NPs synthesized by high-intensity PLAL, a double pulse configuration with inter-pulse delays between 300 ps and 1200 ps is proposed. In this temporal delay window, the plume and initial bubble are still flat so that shielding of the second laser pulse by the cavitation bubble is avoided; minimizing pulse shielding that could reduce NP productivity. At a pulse delay of 600 ps, a (9 ± 1) wt% reduction of the large NP fraction is demonstrated (at the expense of mass yield), showing the possibility of modifying the NP size distribution produced in PLAL by temporal pulse shaping.

An ammonia flash break-up model based on bubble dynamics with force and energy analysis on droplet

Ammonia flash break-up model was developed using bubble dynamics based on force analysis of surface tension and pressure forces in this study. The initial bubble radius was calculated by modifying bubble number density equation considering the superheat degree with assuming a single bubble in the droplet. The Rayleigh–Plesset equation with compressibility factor was employed to calculate bubble growth in the liquid ammonia droplet. Droplet disintegration was predicted by force analysis. The velocity change by flash break-up was assumed to be a product of the surplus energy between the surface-energy change and the pressure work, and the bubble growth rate. The simulation results were compared to results in a previous experimental study of ammonia spray behavior. The time constant of the thermodynamic breakup model was added to simulate the flash boiling condition that induces rapid spray changes. In this study, the time constant 12 is used through the verification process. Compared with previous experimental results of ammonia flash boiling spray, the proposed flash breakup model was superior in predicting radial spray development by the flash boiling compared to the conventional aerodynamic breakup model.

Investigation on the cavitation bubble collapse and the movement characteristics near spherical particles based on Weiss theorem.

In this paper, the cavitation bubble dynamics near two spherical particles of the same size are investigated theoretically and experimentally. According to the Weiss theorem, the flow characteristics and the Kelvin impulse are obtained and supported by the sufficient experimental data. In terms of the initial bubble position, the bubble size and the distance between the two particles, the collapse morphology and the movement characteristics of the bubble are revealed in detail. The main findings include: (1) Based on a large number of experimental results, it is found that the Kelvin impulse theoretical model established in this paper can effectively predict the movement characteristics of the cavitation bubble near two particles of the same size. (2) When the initial bubble position is gradually away from the particles along the horizontal symmetry axis near two particles of the same size, the movement distance of the bubble centroid in the first period increases first and then decreases. (3) When the initial position of the bubble centroid is at the asymmetric position near the two particles, the movement direction of the bubble centroid is biased towards the particle closer to the bubble, but not towards the center of this particle.

Nucleation and bubble growth during puffing and micro-explosions in composite droplets

Heating of droplets composed of water and fuel is known to lead to internal nucleation and bubble growth that can eventually lead to their puffing and to micro-explosions. The time to puffing/micro-explosions includes times spent on: heating (time to nucleationPleasestriketheSymbolt_Nfromtheabstract), bubble growth Pleasestrike:tgrfromtheabstract. In the present paper, we examine the effect of different aspects of bubble growth on the puffing and micro-explosions. Specifically, we address the effects of nucleation temperature and the relative positions of the inner water sub-droplet and the bubble within it. The nucleation temperature of the water sub-droplet is higher than its normal boiling temperature yet lower than its spinodal temperature in most realistic cases. The degree of superheating and the nucleation time depend on the heating rate and the nucleation site density. Higher nucleation temperatures imply larger driving force for the bubble growth. Bubble growth rate is dominated by the degree of superheating, while growth time is dominated by both the degree of superheating and the location of the bubble with respect to the inner and outer interfaces of the composite droplet. It is found that the inertial bubble growth regime is dominant for micron-sized droplets, and thus sensitivity to the modelling of the inertial regime can be of crucial importance to the evaluation of the breakup time for the droplets. The model for puffing and micro-explosion presented in the paper considers an isolated bubble growing at the water/fuel interface at various degrees of superheating, and for a wide range of Jakob numbers. This analysis allows us to assess the sensitivity of bubble growth time to the initial bubble location, and to generalise the previously developed model of the phenomenon taking into account the effect of finite time of bubble growth during the development of puffing/micro-explosion.

Numerical study of dynamics of cavitation bubble collapse near oscillating walls

This paper presents a numerical study of the dynamics of an initially spherical bubble collapse near an oscillating rigid wall with a large amplitude; the wall oscillating amplitude is greater than 1% of the initial maximum bubble radius. Numerical simulations were conducted using a compressible two-phase flow model and the volume of fluid (VOF) interphase-sharpening technique on a general curvilinear moving grid. The numerical results for bubbles in the free field and near a wall were computed and compared with published experimental data. To study the effects of the oscillating wall on bubble collapse, a sinusoidal function was used for wall oscillation. The initial bubble conditions were set as a Rayleigh bubble located above the rigid wall at a dimensionless bubble-boundary distance with initial phases of 0° and 180°. During bubble collapse, the interface deformation, jetting behavior, bubble collapse time, and bubble migration were determined. Violent collapse of the bubble, jetting behavior, and shock propagation from the significant effects of the oscillating wall were observed in simulation cases with different wall motions. The effects of the non-dimensional amplitude scale and non-dimensional period timescale were considered with the initial phases in the problem. The trend lines of typical characteristics and critical points of bubble collapse were determined.

Design Exploration of Initial Bubbles for Higher-Speed Laser-Induced Microjets

Laser-induced microjets are advantageous for yielding high-speed and convergent microjets shape. However, owing to the need for high-power laser devices, reducing the required laser power is a prerequisite for convenience in practical use. This study aimed to optimize initial multiple bubbles design and find the dominant parameters for efficient microjet generation. For this purpose, the bubble design was optimized using an evolutionary algorithm—the covariance matrix adaptation evolutionary strategy. In addition, the dataset of solutions obtained through the optimization process was analyzed via principal component analysis (PCA). The optimization and analysis revealed that a higher microjet velocity could be obtained when a single bubble was generated near the tube wall, and an optimal total bubble volume was observed corresponding to this optimization. In addition, this approximate optimal solution we obtained was confirmed to reduce 88% of total initial energy compared to that of the typical solution. The result shows possibility to improve the efficiency of microjet generation and reducing the laser power.

Investigation of cavitation bubble dynamics near a solid wall by high-resolution numerical simulation

We investigate dynamics of a single cavitation bubble in the vicinity of a horizontal wall throughout expansion and collapse using a sharp–interface level-set method. The numerical scheme is based on a finite-volume formulation with low-dissipation high-order reconstruction schemes. Viscosity and surface tension are taken into account. The simulations are conducted in three-dimensional axi-symmetric space. A wide range of initial bubble wall standoff distances is covered. We focus, however, on the near-wall region where the distance between the bubble and the wall is small. We reproduce three jetting regimes: needle, mixed, and regular jets. The needle jets impose a significant load on the solid wall, exceeding the force induced by the collapse of the pierced torus bubble. For intermediate standoff distances, the large delay time between jet impact and torus bubble collapse leads to a significant decrease in the imposed maximum wall pressure. A liquid film between bubble and wall is observed whenever the bubble is initially detached from the wall. Its thickness increases linearly for very small standoff distances and growths exponentially for intermediate distances leading to a significant increase in wall-normal bubble expansion and bubble asymmetry. For configurations where the torus bubble after jet impact reaches maximum size, the collapse time of the cavitation bubble also is maximal, leading to a plateau in the overall prolongation of the cycle time of the bubble. Once the initial bubble is attached to the solid wall, a significant drop of all macroscopic time and length scales toward a hemispherical evolution is observed.

Dynamics of bubbles spontaneously entering into a tube.

When an open tube of small diameter touches a bubble of a larger diameter, the bubble spontaneously shrinks and pushes a soap film into the tube. We characterize the dynamics for different bubble sizes and number of soap films in the tube. We rationalize this observation from a mechanical force balance involving the Laplace pressure of the bubble and the viscous force from the advancing soap lamellae in the tube. We propose a numerical resolution of this model, and an analytical solution in an asymptotic regime. These predictions are then compared to the experiments. The emptying duration is primarily affected by the initial bubble to tube diameter ratio and by the number of soap films in the tube.

NUMERICAL INVESTIGATION OF BUBBLE CLOUD FORMATION BY HIGH-INTENSITY FOCUSED ULTRASOUND USING THE GHOST FLUID METHOD COUPLED WITH BUBBLE DYNAMICS

In this study, numerical simulations were conducted to investigate the growth of bubble nuclei and the corresponding bubble cloud formation in a pressure field given by high-intensity focused ultrasound (HIFU) backscattered from the bubble interface. A multiscale numerical method was developed to simulate the corresponding experiment, in which the overall pressure fields obtained by HIFU were solved using the ghost fluid method coupled with the bubble dynamics in the microscopic field. The validity of the present method was confirmed by the growth of a single bubble nucleus placed on the HIFU propagation axis. The formation of a cone-shaped bubble cloud that consisted of multiple layers of bubbles observed in the experiment was simulated successfully under the random distribution of initial bubble nuclei. The influence of the initial distribution of bubble nuclei on the cone-shaped bubble cloud formation was also investigated. The results showed that the shape of each bubble layer affects the final form of the bubble cloud since the negative pressure due to backscattering from the HIFU is dependent on the shape of each bubble layer. A final bubble cloud shape was predicted by averaging the void fractions in all of the bubble nuclei distribution cases. The results showed that the averaged final shape of the bubble clouds matched the results observed in the experiment: the distances between the first cavitation inception point and the laser-induced bubble interface and between the bubble layers in the cloud were in quantitative agreement with the experiments.

Simulation of vapour bubble condensation using a 3D method

In this work, simulation of a rising vapour bubble condensation in subcooled boiling flow conditions was performed using an interface tracking method, called the InterSection Marker (ISM) method which was previously developed by the authors to track the bubble interface. The rising bubble was condensing under the influence of the buoyancy and the surface tension forces. Immersed boundary method was used as a coupling mechanism between the ISM method and an in-house variable-density and variable-viscosity single-fluid flow solver. To imitate the condensation (i.e., heat and mass transfers from the vapour bubble), the source terms were modelled in the Computational Fluid Dynamics (CFD) governing equations. During the simulation, the condensing bubble properties such as bubble size, shape, and velocity were predicted for various initial bubble sizes and liquid subcooling values. The numerical results compared well against the past works, and the ISM method established itself to be an efficient, reliable, and viable alternative numerical tool for multiphase flow simulations involving heat and mass transfers across the interface.

Fabrication of gold nanoparticle decorated surfaces for controlled nucleation of plasmonic microbubbles

Plasmonic bubbles produced by water-immersed gold nanoparticles (GNPs) under a laser irradiation are of great relevance in numerous applications. Normally, plasmonic bubbles are produced on a well-fabricated GNP decorated sample surfaces, which rely on expensive devices and complex fabrication processes. In this study, we systematically investigate the fabrication of GNP decorated sample surfaces for optimized production of plasmonic bubbles. Sample surfaces are fabricated by thermal dewetting of a gold film coated on fused silica substrates under an annealing temperature up to 1200 °C. Both the size and density of GNPs can be well tuned by adjusting gold film thickness and annealing temperature. The optical absorption of sample surfaces is also experimentally and numerically investigated, from which the optimal parameters of fabrication are determined. More importantly, for the first time, we find that the high annealing temperature leads to the formation of nanoindents beneath GNPs, resulting in the partial enwrapment of GNPs into fused silica substrates. This helps to stabilize GNPs on sample surfaces. With the fabricated sample surfaces, the nucleation and growth dynamics of giant initial bubbles and ordinary plasmonic bubbles can be well tuned. No apparent damage has been observed on the sample surfaces after the violent bubble nucleation. The increased stability of GNPs is important for plasmonic bubble related applications.

A mathematical model for single CO2 bubble motion with mass transfer and surfactant adsorption/desorption in stagnant surfactant solutions

Gas absorption into a liquid is an effective means of reducing the emission of environmentally unfavorable gases. The efficiency of the gas absorption is determined by the gas–liquid mass transfer. In this study, a mathematical model coupling gas–liquid mass transfer and surfactant adsorption/desorption with CO2 bubble motion in a bubble column is proposed. The kinetics of surfactant adsorption and desorption on the bubble surface are represented by two model parameters. To obtain the model parameters, we measured the eccentricity, rising velocity and volume of bubbles in a diameter range of 1.96–0.59 mm in stagnant surfactant solutions using high-speed photography. The instantaneous mass transfer coefficient is derived from the variation of the bubble volume with time. The effect of the accumulation of surfactant on the bubble shape, rising velocity, and mass transfer coefficient is discussed. The mathematical model is able to calculate the variation trends of the CO2 bubble diameter and rising velocity with an initial bubble diameter d less than 2 mm in surfactant solutions, which are consistent with the experimental results.

Numerical modeling of methane pyrolysis in a bubble column of molten catalysts for clean hydrogen production

Methane pyrolysis using molten catalysts in a bubble column reactor (BCR) has recently been proposed to produce hydrogen with separable carbon particles as byproducts. In this study, a numerical model of the BCR of molten catalysts for methane pyrolysis was developed and validated using experimental data. Based on a non-isothermal 1-D simplification, continuous liquid and discrete bubble phases were considered by incorporating submodels for bubble behaviors, catalytic and homogeneous reactions, heat/mass transfer, and a submerged orifice for methane supply. The initial bubble diameter was predicted using the correlation derived from measurements. When applied to experiments with Ni(27)Bi(73) and mixtures of KCl–MnCl2, the model accurately reproduced the methane conversion at different temperatures and column heights. Furthermore, detailed information on the key phenomena was acquired, including the profiles of the bubble diameter, rise velocity, reaction rates, temperature, and gas composition. A sensitivity analysis confirmed that the uncertainties regarding the physical properties of molten catalysts had a negligible impact. A comparison of the performances of Ni(27)Bi(73) and KCl(50)MnCl2(50) under the same reaction conditions revealed a favorable influence of the catalyst density on methane conversion because of the increased pressure. The proposed model would be useful in reactor optimization and scale-up with high hydrogen productivity.

Wall wettability effect on process of collapse of single cavitation bubbles in near-wall region using pseudo-potential lattice Boltzmann method

This study investigates the effect of wall wettability on cavitation collapse based on a large-density-ratio lattice Boltzmann method (LBM) pseudo-potential model. The validity and superiority of the proposed model in simulation of cavitation under complex conditions are confirmed by comparing with theories, experiments, and numerical results by other models. Our simulations indicate that wall wettability has a significant influence on near-wall cavitation of an order no less than the effect of the initial bubble distance. A criterial initial distance exists in near-wall cavitation within which the micro-jet will direct toward the wall. This criterial distance is shown to be positively correlated with the contact angle by a cosine function. Within this distance, the lifetime of the bubble decreases by up to 50%, and the increase of the maximum micro-jet velocity and collapse pressure are up to 131% and 65%, respectively, when the contact angle increases from the hydrophilic 53° to the hydrophobic 113°. Without considering the shock-wave mechanism, the impact pressure transmitted to the hydrophilic wall is of the same order as the maximum collapse pressure while the impact velocity is an order smaller than the maximum micro-jet velocity. Wall wettability affects collapse through the Bjerknes force and the pressure around the bubble. Preliminary analysis also suggests that the relation between the pressure difference and the intensity of collapse exhibits more patterns than we have assumed, which fits a logistic curve well, and appears not changing with the contact angle or the initial bubble distance.