Control of bubble ζ-potentials to improve the kinetics of bubble-particle interactions
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Engineering↗
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Effect of pores and He bubbles on the thermal transport properties of UO 2 by molecular dynamics simulation
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Lee, C. -W.↗
Experimental study on bubble dynamics and wall heat transfer arising from a single nucleation site at subcooled flow boiling conditions – Part 2: Data analysis on sliding bubble characteristics and associated wall heat transfer
In this second of two companion papers presents an analysis of sliding bubble and wall heat transfer parameters measured during subcooled boiling in a square, vertical, upward flow channel. Bubbles were generated only from a single nucleation site for better observation of both the sliding bubbles’ characteristics and their impact on wall heat transfer through optical measurement techniques. Specific interests include: (i) bubbles departure and subsequent growth while sliding, (ii) bubbles release frequency, (iii) coalescence of sliding bubbles, (iv) sliding bubbles velocity, (v) bubbles size distribution and (vi) wall heat transfer influenced by sliding bubbles. Our results showed that sliding bubbles involve two distinct growth behaviors: (i) at low mass fluxes, sliding bubbles grew fast near the nucleation site, subsequently shrank, and then grew again, (ii) as mass flux increased, however, sliding bubbles grew more steadily. The bubbles originating from the single nucleation site coalesced frequently while sliding, which showed close relation with bubbles release frequency. The sliding bubble velocity near the nucleation site consistently decreased by increasing mass flux, while the observation often became reversed as the bubbles slid downstream due to the effect of interfacial drag. The sliding bubbles moved faster than the local liquid (i.e., ur<0) at low mass flux conditions, but it became reversed as the mass flux increased. The size distribution of sliding bubbles followed Gaussian distribution well both near and far from the nucleation site. The standard deviation of bubble size varied insignificantly through sliding compared to the changes in mean bubble size. Lastly, the sliding bubbles enhanced the wall heat transfer and the effect became more noticeable as inlet subcooling/mass flux decreased or wall heat flux increased. Particularly, the sliding bubble characteristics such as bubble growth behavior observed near the nucleation site played a dominant role in determining the ultimate level of wall heat transfer enhancement within the test channel.
42 ENGINEERING↗
Equation of state for He bubbles in W and model of He bubble growth and bursting near W{100} surfaces derived from molecular dynamics simulations
Abstract Molecular dynamics (MD) simulations are performed to derive an equation of state (EOS) for helium (He) bubbles in tungsten (W) and to study the growth of He bubbles under a W(100) surface until they burst. We study the growth as a function of the initial nucleation depth of the bubbles. During growth, successive loop-punching events are observed, accompanied by shifts in the depth of the bubble towards the surface. Subsequently, the MD data are used to derive models that describe the conditions that cause the loop punching and bursting events. Simulations have been performed at 500, 933, 1500, 2000, and 2500 K to fit the parameters in the models. To compute the pressure in the bubble at the loop punching and bursting events from the models, we derive an EOS for He bubbles in tungsten with an accompanying volume model to compute the bubble volume for a given number of vacancies ( $$N_\text {V}$$ N V ), He atoms ( $$N_\text {He}$$ N He ), and temperature ( T ). To derive the bubble EOS, we firstly derive the EOS for a free He gas. The derived free-gas EOS can accurately predict all MD data included in the analysis (which span up to 54 GPa at 2500 K). Subsequently, the bubble EOS is derived based on the free-gas EOS by correcting the gas density to account for the interaction between He and W atoms. The EOS for the bubbles is fitted to data from MD simulations of He bubbles in bulk W that span a wide range of gas density and sizes up to about 3 nm in diameter. The pressure of subsurface bubbles at the loop punching events as calculated using the bubble-EOS and the volume model agrees well with the pressure obtained directly from the MD simulations. In the loop punching model, for bubbles consisting of $$N_\text {V}$$ N V vacancies and $$N_\text {He}$$ N He helium atoms, the $$N_\text {He}/N_\text {V}$$ N He / N V ratio that causes the event, the resulting increase in $$N_\text {V}$$ N V , and the associated shift of the bubble depth are formulated as a function of $$N_\text {V}$$ N V and T . In the bursting model, a bubble must simultaneously reach a certain depth and $$N_\text {He}/N_\text {V}$$ N He / N V ratio in order to burst. The burst depth and $$N_\text {He}/N_\text {V}$$ N He / N V are also modeled as a function of $$N_\text {V}$$ N V and T . The majority of the loop punching events occur at bubble pressures between 20 and 60 GPa, depending on the bubble size and temperature. The larger the bubble and the higher the temperature, the lower the bubble pressure. Furthermore, our results indicate that at a higher temperature, a bubble can burst from a deeper region.
36 MATERIALS SCIENCE↗
Propagation of positive discharges in an air bubble having an embedded water droplet
Low temperature plasmas generated inside gas bubbles immersed in water is an effective method of rapidly transferring plasma generated reactive species to the water for applications in biomedicine, agriculture and environment. Reactive species are generally produced in the gas phase plasma and then solvate into the liquid. The large surface-to-volume ratio (SVR) of the bubble accelerates this process. In generating bubbles in water, aerosols and droplets are also contained within the bubble. These droplets also have a large SVR and so can be rapidly plasma activated. However, the presence of the droplets can also impact the propagation of the plasma in the bubble. In this paper, results are discussed from computational and experimental investigations of the formation and evolution of discharges in an air bubble immersed in water with an embedded water droplet. The computations were performed with a two-dimensional plasma hydrodynamics model. Experiments were performed with a quasi-2D bubble apparatus. In bubbles having a droplet, a plasma filament typically bridges from the powered electrode to the droplet, and then from the droplet to the bubble surface. A surface-hugging streamer also occurs on the inner bubble surface and on the surface of the droplet. Both surface streamers result in part from surface charge accumulation and can dominate the formation of reactive species that transport into the droplet. Increasing droplet conductivity suppresses propagation of the surface discharge and leads to a lower density of aqueous reactive species. Increasing conductivity of the surrounding water does not change the overall structure of the discharge but does slightly elevate the discharge intensity. Finally, the size and shape of the embedded droplet can significantly affect the formation and propagation of the streamer.
2D fluid modelling↗
Remobilizing the Interface of Thermocapillary Driven Bubbles Retarded By the Adsorption of a Surfactant Impurity on the Bubble Surface
Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow that propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillary to direct the movement of bubbles in space is the fact that surfactant impurities, which are unavoidably present in the continuous phase, can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. (This can also be the case if kinetic desorption of surfactant at the back end of the bubble is much slower than convection.) For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like and bubbles translate as solid particles). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature-induced tension gradient, and can decrease to near zero the bubble's thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have be retarded by the adsorption onto the bubble surface of a surfactant impurity. Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble surface much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition, the rapid kinetic exchange and high bulk concentration maintain a saturated surface with uniform surface concentrations. This prevents retarding surface tension gradients and keeps the thermocapillary velocity high. In our reports over the first 2 years, we presented numerical simulations of the bubble motion and surfactant transport which verified theoretically the concept of remobilization, and the development of an apparatus to track and measure the velocity of rising bubbles in a glycerol/water surfactant solution. This year, we detail experimental observations of remobilization. Two polyethylene oxide surfactants were studied, C12E6 (CH3(CH2)11(OCH2)6OH) and C10E8 (CH3(CH2)4(OCH2CH2)8OH). Measurements of the kinetic exchange for these surfactants show that the one with the longer hydrophobe chain C12E6 has a lower rate of kinetic exchange. In addition, this surfactant is much less soluble in the glycerol/water mixture because of the shorter ethoxylate chain. As a result, we found that C12E6 had only a very limited ability to remobilize rising bubbles because of the limited kinetic exchange and reduced solubility. However, C10E8, with its higher solubility and more rapid exchange was found to dramatically remobilize rising bubbles. We also compared our theoretical calculations to the experimental measurements of velocity for both the non-remobilizing and remobilizing surfactants and found excellent agreement. We further observed that for C10E8 at high concentrations, which exceeded the critical micelle concentrations, additional remobilization was measured. In this case the rapid exchange of monomer between micelle and surfactant provides an additional mechanism for maintaining a uniform surface concentrations.
Palaparthi, Ravi↗
Single Bubble Sonoluminescence in Low Gravity and Optical Radiation Pressure Positioning of the Bubble
Several groups of researchers have demonstrated that high frequency sound in water may be used to cause the regular repeated compression and luminescence of a small bubble of gas in a flask. The phenomenon is known as single bubble sonoluminescence (SBSL). It is potentially important because light emitted by the bubble appears to be associated with a significant concentration of energy within the volume of the bubble. Unfortunately, the detailed physical mechanisms causing the radiation of light by oscillating bubbles are poorly understood and there is some evidence that carrying out experiments in a weightless environment may provide helpful clues. In addition, the radiation pressure of laser beams on the bubble may provide a way of simulating weightless experiments in the laboratory. The standard model of SBSL attributes the light emission to heating within the bubble by a spherically imploding shock wave to achieve temperatures of 50,000 K or greater. In an alternative model, the emission is attributed to the impact of a jet of water which is required to span the bubble and the formation of the jet is linked to the buoyancy of the bubble. The coupling between buoyancy and jet formation is a consequence of the displacement of the bubble from a velocity node (pressure antinode) of the standing acoustic wave that drives the radial bubble oscillations. One objective of this grant is to understand SBSL emission in reduced buoyancy on KC-135 parabolic flights. To optimize the design of those experiments and for other reasons which will help resolve the role of buoyancy, laboratory experiments are planned in simulated low gravity in which the radiation pressure of laser light will be used to position the bubble at the acoustic velocity node of the ultrasonic standing wave. Laser light will also be used to push the bubble away from the velocity node, increasing the effective buoyancy. The original experiments on the optical levitation and radiation pressure on bubbles in water by Unger and Marston noted above were carried out using a continuous wave (CW) beam of an Argon laser. For lateral stability the beam had a intensity minimum along its axis. Calculations of the optical radiation force on an SBSL bubble indicate that ion laser technology is a poor choice for providing the magnitude of the average optical radiation force required. Consequently it is necessary to examine various diode-pumped solid state laser technologies. The approach for this part of the research will be to achieve optical levitation of a quiescent bubble based on contemporary laser technology and then to strobe the laser synchronously with the SBSL bubble oscillations.
Thiessen, D. B.↗
Remobilizing the Interfaces of Thermocapillary Driven Bubbles Retarded by the Adsorption of a Surfactant Impurity on the Bubble Surface
Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is applied to the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow which propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillarity to direct the movement of bubbles in space is the fact that surfactant impurities which are unavoidably present in the continuous phase can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature tension gradient, and decreases to near zero the thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have been retarded by the adsorption onto the bubble surface of a surfactant impurity, Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition the rapid kinetic exchange and high bulk concentration maintain a saturated surface with a uniform surface concentrations. This prevents retarding surface tension gradients and keeps the velocity high. In our first report last year, we detailed experimental results which verified the theory of remobilization in ground based experiments in which the steady velocity of rising bubbles was measured in a continuous phase consisting of a glycerol/water mixture containing a polyethylene glycol surfactant C12E6 (CH3(CH2)11(OCH2CH2)6OH). In our report this year, we detail our efforts to describe theoretically the remobilization observed. We construct a model in which a bubble rises steadily by buoyancy in a continuous (Newtonian) viscous fluid containing surfactant with a uniform far field bulk concentration. We account for the effects of inertia as well as viscosity in the flow in the continuous phase caused by the bubble motion (order one Reynolds number), and we assume that the bubble shape remains spherical (viscous and inertial forces are smaller than capillary forces, i e. small Weber and capillary numbers). The surfactant distribution is calculated by solving the mass transfer equations including convection and diffusion in the bulk, and finite kinetic exchange the bulk and the surface. Convective effects dominate diffusive mass transfer in the bulk of the liquid (high Peclet numbers) except in a thin boundary layer near the surface. A finite volume method is used to numerically solve the hydrodynamic and mass transfer equations on a staggered grid which accounts specifically for the thin boundary layer. We present the results of the nondimensional drag as a function of the bulk concentration of surfactant for different rates of kinetic exchange, from which we develop criteria for the concentration necessary to develop a prescribed degree of remobilization. The criteria compare favorably with the experimental results.
Palaparthi, Ravi↗
Area of bubble influence due to sliding bubbles in subcooled boiling flow
The heat transfer effect of sliding bubbles is discussed in two aspects based on new experimental findings: (i) the area of bubble influence and (ii) bubble sliding characteristics influencing the degree of wall heat transfer. One notable finding was that the bubble sliding behavior, characterized by sliding trajectories, played a crucial role in determining the area of bubble influence and the bubble influence factor (K). Also, such sliding characteristic was observed strongly dependent on the sliding bubble size. An empirical model has been proposed based on this finding to evaluate the bubble influence factor (K) for the sliding bubbles. Another experimental finding was that the bubble sliding characteristic, represented by bubble spreading factor (S), had a significant impact on the degree of wall heat transfer induced by sliding bubbles. This is due to the fact that the bubbles spread across the heater width as they slid downstream, which reduced the effective frequency of sliding bubbles per unit wall area. These new findings not only improve our understanding of the heat transfer associated with sliding bubbles, but also are expected to contribute to improving the insight in the existing CFD boiling heat transfer models.
42 ENGINEERING↗
Evaluation of bubble-induced turbulence using direct numerical simulation
Not Available
Feng, Jinyong↗
Phase-field simulations of fission gas bubbles in high burnup UO2 during steady-state and LOCA transient conditions
To improve the economics of commercial nuclear energy generation, U.S. utilities are currently seeking licensing approval to operate UO2 fuel to higher burnups. One significant safety issue that must be addressed to obtain approval is the potential for fine fragmentation/pulverization of the fuel during a loss-of-coolant accident (LOCA). It has been hypothesized this is caused by the rapid increase of pressure in fission gas bubbles in the high burnup region of the fuel. To better understand this phenomenon, a novel phase-field model of the fission gas bubble microstructure in UO2 has been developed and implemented in Idaho National Laboratory's Marmot application for phase-field simulation of nuclear materials. Simulations of bubble growth in the high burnup region during steady-state conditions showed that initially overpressurized bubbles decreased in pressure during growth, but still remained above equilibrium pressure. During a LOCA transient, simulations of bubbles in the high burnup region showed that bubble size did not change significantly, and the pressure increase due to the transient was calculated and passed to a phase-field model of fracture.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Void fraction, bubble size and interfacial area measurements in co-current downflow bubble column reactor with microbubble dispersion
Micro-bubbles dispersed in bubble column reactors have received great interest in recent years, due to their small size, stability, high gas-liquid interfacial area concentrations and longer residence times. The high gas-liquid interfacial area concentrations lead to high mass transfer rates compared to conventional bubble column reactors. In the present work, experiments have been performed in a down-flow bubble column reactor with micro-bubbles generated and dispersed by a novel mechanism to determine the gas-liquid interfacial area concentrations by measuring the void fraction and bubble size distributions. Gamma-ray densitometry has been employed to determine the axial and radial distributions of void fraction and a high speed camera equipped with a borescope is used to measure the axial and radial variations of bubble sizes. Also, the effects of superficial gas and liquid velocities on the two-phase flow characteristics have been investigated. Further, reconstruction techniques of the radial void fraction profiles from the gamma densitometry's chordal measurements are discussed and compared for a bubble column reactor with dispersed micro-bubbles. The results demonstrate that the new bubble generation technique offers high interfacial area concentrations (1,000 to 4,500 m 2 /m 3 ) with sub-millimeter bubbles (500 to 900 µm) and high overall void fractions (10% – 60%) in comparison with previous bubble column reactor designs. The void fraction data was analyzed using slip velocity model and empirical correlation has been proposed to predict the Sauter mean bubble diameter.
09 BIOMASS FUELS↗
Atomistic simulations of thermodynamic properties of Xe gas bubbles in U10Mo fuels
Not Available
Hu, Shenyang (ORCID:0000000271873082)↗
Bubble Formation and Lattice Parameter Changes Resulting from He Irradiation of Defect-Fluorite Gd2Zr2O7
Pyrochlores have long been considered as potential candidates for advanced ceramic waste-forms for the immobilization of radioactive waste nuclides. This work provides evidence that Gd2Zr2O7, often considered the most radiation tolerant pyrochlore, could be susceptible to radiation damage in the form of bubble nucleation at the highest He doses expected over geological time. Ion irradiations were utilized to experimentally simulate the radiation damage and He accumulation produced by ..alpha..-decay. Samples were pre-damaged using 7 MeV Au3+ to induce the pyrochlore to defect-fluorite phase transformation, which would occur due to ..alpha..-recoil damage within several hundred years of storage in a Gd2Zr2O7 waste-form. These samples were then implanted to various He concentrations in order to study the long-term effects of He accumulation. Helium bubbles 1-3 nm in diameter were observed in TEM at a concentration of 4.6 at.% He. Some bubbles remained isolated, while others formed chains 10-30 nm in length parallel to the surface. GIXRD measurements showed lattice swelling after irradiating pristine Gd2Zr2O7 with 7 MeV Au3+ to a fluence of 2.2 x 1015 Au/cm2. An increase in lattice swelling was also measured after 2.2 x 1015 Au/cm2 + 2 x 1015 He/cm2 and 2.2 x 1015 Au/cm2 + 2 x 1016 He/cm2. A decrease in lattice swelling was measured after irradiation with 2.2 x 1015 Au/cm2 + 2 x 1017 He/cm2, the fluence where bubbles and bubble chains were observed in TEM. Bubble chains are thought to form in order to reduce lattice strain normal to the surface, which is produced by the Au and He irradiation damage.
36 MATERIALS SCIENCE↗
A improved equation of state for Xe gas bubbles in gamma U-Mo fuels
A monolithic fuel design based on a U-Mo alloy has been selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). An issue with U-Mo monolithic fuel is the large amount of swelling that takes place during operation. The accurate prediction of fuel evolution under irradiation requires implementation of correct thermodynamic properties into mesoscale and continuum level fuel performance modeling codes. However, the thermodynamic properties of the fission gas bubbles (such as the relationship among bubble size, equilibrium Xe concentration, and bubble pressure) are not well known. This work studies Xe bubbles in ?U-Mo from a diameter of 3 nm up to 8.5 nm and from 400 K up to 700 K. The energetic relationship of Xe bubbles with regard to voids and Xe substitutional atoms is described. The transition is also determined for when a bubble becomes over-pressurized. Finally, an equation of state is fit to the pressure as a function of molar volume and temperature.
Beeler, Benjamin↗
The spectrum and morphology of the Fermi bubbles
The Fermi bubbles are two large structures in the gamma-ray sky extending to 55° above and below the Galactic center. We analyze 50 months of Fermi Large Area Telescope data between 100 MeV and 500 GeV above 10° in Galactic latitude to derive the spectrum and morphology of the Fermi bubbles. We thoroughly explore the systematic uncertainties that arise when modeling the Galactic diffuse emission through two separate approaches. The gamma-ray spectrum is well described by either a log parabola or a power law with an exponential cutoff. We exclude a simple power law with more than 7σ significance. The power law with an exponential cutoff has an index of 1.9 ± 0.2 and a cutoff energy of 110 ± 50 GeV. We find that the gamma-ray luminosity of the bubbles is 4.4{sub −0.9}{sup +2.4}×10{sup 37} erg s{sup –1}. We confirm a significant enhancement of gamma-ray emission in the southeastern part of the bubbles, but we do not find significant evidence for a jet. No significant variation of the spectrum across the bubbles is detected. The width of the boundary of the bubbles is estimated to be 3.4{sub −2.6}{sup +3.7} deg. Both inverse Compton (IC) models and hadronic models including IC emission from secondary leptons fit the gamma-ray data well. In the IC scenario, synchrotron emission from the same population of electrons can also explain the WMAP and Planck microwave haze with a magnetic field between 5 and 20 μG.
79 ASTRONOMY AND ASTROPHYSICS↗
Alma observations of massive molecular gas filaments encasing radio bubbles in the Phoenix cluster
We report new ALMA observations of the CO(3-2) line emission from the $2.1\pm0.3\times10^{10}\rm\thinspace M_{\odot}$ molecular gas reservoir in the central galaxy of the Phoenix cluster. The cold molecular gas is fuelling a vigorous starburst at a rate of $500-800\rm\thinspace M_{\odot}\rm\; yr^{-1}$ and powerful black hole activity in the form of both intense quasar radiation and radio jets. The radio jets have inflated huge bubbles filled with relativistic plasma into the hot, X-ray atmospheres surrounding the host galaxy. The ALMA observations show that extended filaments of molecular gas, each $10-20\rm\; kpc$ long with a mass of several billion solar masses, are located along the peripheries of the radio bubbles. The smooth velocity gradients and narrow line widths along each filament reveal massive, ordered molecular gas flows around each bubble, which are inconsistent with gravitational free-fall. The molecular clouds have been lifted directly by the radio bubbles, or formed via thermal instabilities induced in low entropy gas lifted in the updraft of the bubbles. These new data provide compelling evidence for close coupling between the radio bubbles and the cold gas, which is essential to explain the self-regulation of feedback. As a result, the very feedback mechanism that heats hot atmospheres and suppresses star formation may also paradoxically stimulate production of the cold gas required to sustain feedback in massive galaxies.
79 ASTRONOMY AND ASTROPHYSICS↗
Dynamics of Vapour Bubbles in Nucleate Boiling: Basic Equations of Bubble Evolution - 1
We consider the behaviour of a vapour bubble formed at a nucleation site on a heated horizontal wall. There is no forced convection of an ambient liquid, and the bubble is presumably separated from the wall by a thin liquid microlayer. The energy conservation law results in a variational equation for the mechanical energy of the whole system consisting of the bubble and liquid. It leads to a set of two strongly nonlinear equations which govern bubble expansion and motion of its centre of mass. A supplementary equation to find out the vapour temperature follows from consideration of heat transfer to the bubble, both from the bulk of surrounding liquid and through the microlayer. The average thickness of the microlayer is shown to increase monotonously with time as the bubble meniscus spreads along the wall. Bubble expansion is driven by the pressure head between vapour inside and liquid far away from the bubble, with due allowance for surface tension and gravity effects. It is resisted by inertia of liquid being placed into motion as the bubble grows. The inertia originates also a force that presses the bubble to the wall. This force is counteracted by the buoyancy and an effective surface tension force that tends to transform the bubble into a sphere. The analysis brings about quite a new formulation of the familiar problem of bubble growth and detachment under conditions of nucleate pool boiling.
Buyevich, Yu A.↗