Dynamics Of Bubble Formation Research Articles

A non-spherical model for bubble formation with liquid cross-flow

A non-spherical model for bubble formation at an orifice with liquid cross-flow has been developed. The interface element approach is applied to describe the dynamics of bubble formation. The effect of liquid cross-flow on the bubble formation process is modelled by a combination of tilting of the bubble axis and liquid pressure analysis of each element on the bubble interface. Model predictions compare well with the experimental results available in the literature for different conditions of gas flow rate, orifice diameter and liquid cross-flow velocity. Simulated bubble shapes are highly non-spherical, especially at high liquid velocities, and bear a striking resemblance with the experimental high-speed video sequences.

Chaotic behavior in bubble formation dynamics

We constructed an experimental apparatus to study the dynamics of the formation of air bubbles in a submerged nozzle in a water/glycerin solution inside a cylindrical tube. The delay time between successive bubbles was measured with a laser-photodiode system. It was observed bifurcations, chaotic behavior, and sudden changes in a periodic regime as a function of the decreasing air pressure in a reservoir. We also observed dynamical effects by applying a sound wave tuned to the fundamental frequency of the air column above the solution. As a function of the sound wave amplitude, we obtained a limit cycle, a flip bifurcation, chaotic behavior, and the synchronization of the bubbling with sound wave frequency. We related some of the different dynamical behaviors to coalescent effects and bubble sizes.

Starting mechanisms and dynamics of bubble formation induced by a Ho:Yttrium aluminum garnet laser in water

The starting mechanisms and dynamics of laser-induced bubble formation at a submerged fiber tip in distilled water were experimentally investigated using pressure measurements and fast flash videography. A fiber guided Ho:YAG laser operating in the free running (τ=200 μs) and Q-switched (τ=45 ns) mode at a wavelength of λ=2.12 μm was used as a light source. It is shown that the beam profile at the distal fiber tip (multimode fiber d=300 μm) exhibits hot spots that result in an inhomogeneous temperature distribution in the heated water volume. Depending on the laser irradiance, three different bubble formation processes are distinguished: bubble formation by heating, by rarefraction (cavitation), and by a combination of these two processes. For laser irradiances of less than 0.5 MW/ cm2 bubble formation takes place at temperatures near the critical point of water (T=280 °C). A rapid decrease in the threshold temperature for bubble formation was found for laser irradiances between 0.5 and 1 MW/cm 2. At laser irradiances higher than 3 MW/cm2, microbubbles with radii of up to 20 μm were formed at the front of the laser pulse even though the average water temperature was far below 100 °C. The water temperature distribution during the laser pulse was determined by numerical simulation. Simultaneous pressure measurements revealed that each subablative laser spike induces a bipolar pressure transient. The onset of the bubble expansion was found to be correlated with a characteristic pressure increase that can be used for on-line monitoring of the ablation process. The distortion of the temporal profile of the pressure wave is shown to be an effect of diffraction. The reduction of pressure by the negative part of the bipolar pressure transients leads to a lowering of the evaporation pressure and therefore to the initiation of bubbles by cavitation. With increasing irradiance this mechanism becomes more efficient.

Boiling Nucleation on a Very Small Film Heater Subjected to Extremely Rapid Heating. (Effect of Ambient Pressure on Bubble Formation by Fluctuation Nucleation).

The effect of ambient pressure on the dynamics of bubble formation in liquid heated rapidly to the limit of superheat is investigated by heating a fine film heater immersed in ethyl alcohol at a high rate of temperature rise up to 20×106K / s. The heater surface temperature at boiling incipience increases with the increase of the rate of temperature rise and saturates at the rate higher than about 5×106K / s. The saturated temperature agrees well with that of homogeneous nucleation in an ambient pressure range from 0.1 to 2.0 MPa. The nucleated bubbles become smaller to coalesce with the increase of ambient pressure and the measured number density of them reaches 7.0×1010l / m2 for the maximum. The increase of the number density versus the surface temperature agrees qualitatively with that predicted by the fluctuation nucleation theory. As the result, the bubble formation observed at a higher rate of temperature rise is concluded to be due to fluctuation nucleation.

Ultrafast dynamics of Rydberg states in the condensed phase

We report on the ultrafast dynamics of bubble formation following excitation of the A 2 Σ + 3s σ( ν = 0) Rydberg state of the NO molecule trapped in Ar matrices. The investigation is carried out by means of a femtosecond pump-probe technique. The detected signal is the depletion of Rydberg fluorescence induced by Rydberg-Rydberg transitions. Our results suggest that the bubble is formed on a timescale of a few picoseconds.

Dynamics of cavitation bubble induced by 193 nm ArF excimer laser in concentrated sodium chloride solutions

Cavitation bubbles were generated by the 193 nm argon fluoride excimer laser delivered with a specially designed tip into absorbing NaCl solution. The dynamics of bubble formation and collapse have been studied using fast flash photomicrography. The bubble dimensions were measured at different time delays as a function of the tip exit diameter, the energy fluence of the laser, and the NaCl concentration. The dynamics of the cavitation bubble created on the tip is compared with the well-studied dynamics of bubbles resulting from dielectric breakdown near a boundary.

Infrared multiwavelength laser system for establishing a surgical delivery path through water

A multiwavelength laser system designed for precise and efficient tissue ablation under water was realized by simultaneously coupling radiation of a holmium:YAG laser, emitting at a wavelength of 2.12 μm and an erbium: YSGG laser at 2.79 μm into the same zirconium fluoride (ZrF4) fiber. The beam paths of the two lasers were collinearly combined taking advantage of the dispersion of an Infrasil prism. Fast video flash photographs and laser induced pressure transients simultaneously recorded with a PVDF pressure transducer were used to study the dynamics of bubble formation at the submerged fiber tip. The bubble size and the bubble lifetime were determined as a function of the wavelength and the delay time between the two different laser pulses. The results indicate that the combination of 2 and 3 μm radiation takes specific advantage of both wavelengths and strongly enhances the ablation efficiency of tissue under water.

Applied Research in Critical Heat Flux

Critical heat flux (CHF) in boiling water and pressurized water reactors is investigated using a three-pronged approach. First, a physically realistic and mathematically rigorous computational model is developed to describe and simulate the transitions between flow regimes. This is called the dynamic flow regime model (DFRM). Second, extensive reanalysis of the Columbia University CHF experimental data is performed to shed light on the processes at work. This analysis indicates that the mechanism for wall drying may not follow conventional wisdom. The DFRM has therefore been supplemented with a semiempirical liquid entrainment model, which accounts for the dynamics of bubble formation. The model produces CHF predictions that agree with the Columbia data slightly better than the Columbia correlation function. Third, to develop a mechanistic understanding of the empirical model, detailed microscale simulations of boiling are performed using the EITACC computer code. EITACC solves the Navier-Stokes equations for three-dimensional two-phase flow using a finite difference method. EITACC has been used to produce time-lapse images of bubble formation at a wall during subcooled boiling. These images provide insight into the mechanisms of bubble separation from the wall, bubble collapse due to condensation, wall drying, and liquid entrainment. This insight is used to improve and validate the DFRM.

Positron annihilation in simple condensed gases

The angular-correlation technique of positron annihilation has been used to detect and measure the localized bubble state of positronium (Ps) in liquid Ne, Ar, Kr, H2, and N2 and in liquid and solid He at various pressures and temperatures. No bubble state was seen in liquid O2 or in solid Ne and Ar. The dynamics of bubble formation is not yet understood. In the cases where theoretical calculations, and adequate data, exist, viz. He, Ar, and H2, there is reasonable agreement for the momentum of the photons from the annihilation of positrons with the outer electrons of these atoms. The Ps annihilations from the self-trapped bubble state are reasonably well described in terms of a simple finite potential-well model.

Marangoni effects under electric fields

An electric field when applied across liquid-liquid interface was found to cause, due to different susceptibilities of the two phases, what the authors would term as Marangoni “type” of instabilities, that resulted in the generation of bubbles/drops and caused the movement of the interface countering gravity. Thus “mixing” of the two phases would occur and in systems involving mass transfer, enhanced rates of transfer could be expected. Equations for the bubble formation involving parameters such as electrostatic pressure, surface tension, gravity force have been derived. In the case of non-gravitational or weak-gravitational fields such as obtainable in space, the separation of two liquids one below the other, as obtaining on the earth, exhibiting an interface may well nearly be impossible. Under such conditions recourse may have to be taken to super-imposition of other fields as a tool for obtaining the necessary contacting/separation. The dynamics of bubble formation etc. under these contexts are theoretically analysed.

Mathematical Model of Bubble Formation at the Tuyeres of a Copper Converter

Based on earlier observations that gas discharges from the tuyeres of a non-ferrous converter as discrete bubbles, a mathematical model has been developed to describe the dynamics of bubble formation in copper converting. The bubbles have been assumed to be spherical in shape and to grow at the tuyere tip under conditions of constant flow. The model incorporates the effects of heat transfer to the bubble, chemical reaction between the bubble and the bath and co flowing bath circulation. The model has been used to predict the concentrations of O2 and SO2, temperature, volume and rise velocity for the bubble as a function of time, while imposition of a detachment condition has permitted the prediction of the bubble frequency. Thus it has been shown that the oxidation reactions have little effect on the bubble formation while convective heat transfer and bath circulation have a large influence. Bath velocity acts to increase the bubble frequency while heat transfer has the opposite effect. Depending on the value of the heat-transfer coefficient employed, the model predicts the velocity of bath circulation in the vicinity of the tuyere to be between 120 and 260 cm/s. For a given bath velocity, the bubble frequency decreases with increasing air input rate. The implications of these predictions for copper converting are discussed, and it is suggested that present converter operation may be “bubble-volume“ limited. Résumé En se fondant sur les observations anterieures que le gaz qui s' échappe des tuyères d'un convertisseur de métaux non-ferreux est sous forme de bulles séparées, nous avons développé un modèle mathématique pour décrire la dynamique de formation des bulles dans le convertissage du cuivre. Nous avons supposé que les bulles ont une forme sphérique et qu'elles croissent à l'extrémité de la tuyère dans des conditions d' écoulement constant. Le modèle incorpore les effets du transfert de chaleur à la bulle, de la réaction chimique entre la bulle et le bain, et la circulation du bain. Le modèle a été utilisé pour prédire les concentrations de O2 et SO2, la température, le volume et la vitesse de montee des bulles en fonction du temps, alors que l'introduction d'une condition de séparation a permis de prédire la fréquence des bulles. Ainsi nous avons montré que les réactions d'oxydation ont peu d'effet sur la formation des bulles alors que le transfert de chaleur par convection et la circulation du bain ont une grande influence. La vitesse du bain accroît la fréquence des bulles alors que le transfert de chaleur a l'effet opposé. Dépendant de la valeur du coefficient de transfert de chaleur employé le modèle predit que la vitesse de circulation du bain dans le voisinage de la tuyère est comprise entre 120 et 260 cm/s. Pour une vitesse donnée du bain, la fréquence des bulles décroît lorsque l'on augmente le taux d'arrivée d'air. Les implications de ces predictions pour le convertissage du cuivre sont discutées et nous suggérons que l'opération actuelle des convertisseurs pourrait être limitée par le volume des bulles.

Mechanisms of Rapid Cooling and Their Design Considerations in Underwater Welding

Rapid cooling is an inherent problem in underwater welding. This paper discusses the basic understanding of cooling mechanisms during underwater welding and the effectiveness of various methods of reducing the cooling rate. Numerical results obtained from a computer analysis are used to discuss the design criteria and the effect of various parameters on the cooling rate. Introduction During the last several years, systematic research efforts on underwater welding have been made at the Dept. of Ocean Engineering of the Massachusetts Inst. of Technology. Most of the research programs were funded by the National Sea Grant Office of the National Oceanic and Atmospheric Admin. Some of the reports, theses, and papers have been published. The research programs have covered various subjects including basic research on mechanisms of underwater welding as well as development of new, improved processes. This paper discusses one subject: rapid cooling during underwater wet arc welding.* This paper has been prepared primarily from results obtained in research by Tsai.The major portion of Tsai's research is composed of extensive mathematical analyses of heat flow during underwater wet arc welding. A series of mathematical equations has been developed to analyze all pertinent phenomena involved: dynamics of bubble formation, heat-loss mechanisms, etc. Experiments were made to examine the validity of the analyses. Studies were made to investigate effects of various parameters (welding conditions, plate thickness, etc.) on cooling rates in weldments, especially in the heat-affected zone (HAZ). Studies also were made to evaluate the effectiveness of various methods of reducing the cooling rate.Since details of analytical and experimental results are included in Ref. 4, this paper presents a brief summary of the analysis and some experimental results. The emphasis of this paper is placed on information of practical importance. Brief Summary of Cooling Mechanisms in Underwater Welding The mode of heat transfer in underwater welding is quite different from that in air welding. The existence of dynamic bubbles during underwater welding induces a flow field around the welding arc. This water flow along with the agitation of bubbles carries the heat away quickly from the base material and causes the rapid cooling phenomenon. In this section, buble dynamics and heat-loss mechanisms are discussed. Underwater Bubble Dynamics Bubble generation due to the high concentration of heat in the arc and its departure and final collapse during the underwater arc welding process in the wet condition was investigated by a high-speed cinematography study at the Massachusetts Inst. of Technology. JPT P. 1825＾

Gas-bubble formation in liquid layer

The dynamics of bubble formation and breakaway when a gas issues into a liquid is considered. The different modes of gas-bubble formation in a liquid layer are indicated. The results of analytic investigation are compared with experimental data.

The dynamics of bubble formation and growth in magmas: A review and analysis

The mechanisms of bubble formation and the dynamics of bubble growth in common magmas have been investigated. Experimental and theoretical data suggest that the levels of volatile supersaturation pressure required for nucleation are low (< 10 bars) due to the occurrence of surface active components in common magmas. The growth history is, moreover, insensitive to the assumptions made on nucleation, except during early stages of growth. Nucleation theory indicates that there is a minimum diameter of bubble that can be preserved in tephra which is of the order of a few microns. A numerical method has been developed to determine bubble growth rates during volcanic eruptions of basaltic and rhyolitic magmas. The numerical solutions consider both diffusional and decompressional growth and the effects of magma ascent rates (0–400 cm s −1), magma viscosity (10 2 to 10 8 poise), gas solubility, gas content (0.25–5%) and gas diffusivity (10 −6 to 10 −9 cm 2 s −1) on growth rates. Bubbles are predicted to grow to between 5.0 and 0.1 cm diameter in typical basaltic explosive eruptions (Strombolian type) and between 200 and 10 μm in typical rhyolitic explosive eruptions (plinian and ignimbrite type). The smaller bubble sizes in rhyolitic tephras is shown to be due to the lower diffusivity of H 2O in acid melts and the generally higher rates of eruption in plinian and ignimbrite type eruptions rather than to the high viscosity. Non-equilibrium effects produce excess internal pressures within growing bubbles. These are a static surface tension pressure and dynamic pressure terms due to viscous resistance of the liquid to growth and the inertia of the liquid. These pressure terms are shown to be small compared to supersaturation pressures driving growth in freely growing bubbles in magmas with viscosities up to 10 7 poise and magma ascent velocities up to 400 cm s −1. For viscosities of 10 8 poise and above the viscous pressure term is calculated with values of tens of bars and has a major role in inhibiting growth. It is proposed that most bubbles cease growth well before explosive disruption of the magmatic froth. This is postulated to occur at volume ratios of gas bubbles to liquid of the order 3:1 to 5:1. At this stage bubbles cannot expand further because of the increasing viscosity of the melt as exsolution takes place and because high viscosity liquid has to be forced along very thin paths between closely spaced neighbouring bubbles. Vesicle walls are sufficiently thin that pressures close to equilibrium between gas bubble pressure and the vapor pressure of the gas dissolved in the liquid are established before the magma is disrupted. Equilibrium partitioning of gas between vesicles and liquid produces gas pressures of tens to hundreds of bars. The disruption of the magma is proposed to occur by bursting of the larger bubbles within the froth at the free surface of the magma due to a pressure difference across this interface.