Initial Bubble Size Research Articles

Isothermal foam growth in polymer matrices

A theoretical model is discussed to analyze the growth kinetics of gas bubbles in isothermal viscous polymer solutions. This model obtained by grafting the Tri Diagonal Matrix Algorithm (Patankar, Ref. [1]) into the cell model (Amon and Denson, Ref. [2]), eliminates many of the assumptions introduced in the previously reported mathematical models. Neglect of the convection term in the transient diffusion equation results in significant error in the prediction of the bubble growth. Assumption that diffusion of volatile solute is confined within a thin layer around the gas-liquid interface is also proved to be unrealistic when diffusion coefficient is relatively high. Physical parameters for expansion of nitrogen bubbles in vinylidene chloride-acrylonitrile copolymer at 100° (Barlow and Langlois, Ref. [3]) are taken to investigate the applicability of the model. Effect of initial bubble size on the growth behavior lasts a long time. Increase of diffusion coefficient and decrease of external pressure and viscosity of polymer solution enhance greatly the rate of bubble growth, whereas surface tension affects it only slightly.

Hot‐stage Microscopy of Cake Batter Bubbles during Simulated Baking: Sucrose Replacement by Polydextrose

ABSTRACTA hot‐stage video microscopical technique was developed to study the effects of sucrose replacement by polydextrose (weight for weight basis) on the foam characteristics of cake batters, before and during heating. Polydextrose substitution increased the mean size of air‐bubbles in the cake batter and introduced a larger variation in bubble size distribution than the sucrose batter. The differences between sucrose and polydextrose batters on initial bubble size distribution were reflected in expansion rates of bubble populations during heating. The lack of uniformity in the bubble distribution of batters containing polydextrose increased the rate of gas diffusion from small bubbles to larger ones. On heating, the bubble population of sucrose batters expanded more than that of polydextrose substituted batters.

The influence of fluid properties and pulse amplitude on bubble dynamics in the field of a shock wave lithotripter

This study concerns the radial dynamics of a bubble driven by pulsed ultrasound of the type generated during extracorporeal shock wave lithotripsy. In particular, a numerical model has been used to examine the sensitivity of the bubble oscillations to changes in both the amplitude of the driving field and the physical conditions of the fluid surrounding the bubble: viscosity, surface tension, temperature and gas content. It is shown that, at high negative pressures (p-=10 MPa) as in lithotripsy, the timing and amplitude of bubble collapses have a considerably reduced sensitivity to the initial bubble size and all fluid parameters, except gas content, compared with those expected in lower-amplitude fields (p-=0.2 MPa). This study indicates that, in the lithotripsy fields, the differences in the viscosity, surface tension and temperature of body fluids and the initial bubble size will have little effect on bubble dynamics compared with those expected in water.

Interaction of lithotripter-generated shock waves with air bubbles

The shock wave-induced collapse and jet formation of pre-existing air bubbles at the focus of an extracorporeal shock wave lithotripter is investigated using high-speed photography. The experimentally obtained collapse time, ranging from 1 to 9 μs for bubbles with an initial radius R0 of 0.15 to 1.2 mm, agrees well with numerical results obtained using the Gilmore model. The collapse time is not linearly dependent on the initial bubble diameter since the temporal profile of the lithotripter wave contains a stress wave. The bubbles, positioned below a thin plastic foil, show strong jet formation in the direction of wave propagation with peak velocities of up to 770 m/s at the moment of collapse. Bubbles of initial radii between 0.3 and 0.7 mm always induce perforation of the foil by the jet (hole diameter 80–300 μm). Averaging the jet flow speed over 5 μs immediately after the collapse results in velocities from nearly zero up to 210 m/s, depending on the initial bubble size, with a maximum at R0=550 μm. This maximum is related to the temporal profile of the shock wave and to the effective cross section of the bubble for shock wave energy transfer. As cavitation bubbles are generated in the focal region of the lithotripter, the results are discussed with respect to the processes in a cavitation bubble field, which are of importance in cavitation erosion as well as in extracorporeal shock wave lithotripsy.

The radial oscillations of a gas bubble in a surfactant solution

In a surfactant solution, a gas bubble can be covered by an adsorbed film of surfactant. When the bubble is excited into radial oscillations by a sound field, the surface concentration of the surfactant varies with the surface area and the mass interchange between the surface and the bulk liquid. As a result, the surface tension becomes a function of the bubble radius. Previous theoretical work on this subject [R. E. Glazman, J. Acoust. Soc. Am. 74, 980–986 (1983)] will be commented on and the equations governing the radial oscillations for this kind of gas bubble will be discussed. By numerically solving the equation under different initial bubble sizes, sound pressures, and driving frequencies, one can determine the effects of variable surface tension, surface viscosity, and surface mass transfer on the motions of the gas bubble. Thresholds of transient cavitation will also be estimated by including these effects. [Work supported by NASA through JPL, Contract No. 958722.]

Measurement of air bubble size using densitometer

AbstractA simple mass‐transfer model is derived which gives the initial air bubble size distributions in a dispersion of air bubbles in water from the density/time responses to a step increase of pressure. Bubble size distributions from the model showed reasonable agreement with direct optical measurements. This work is applicable to dilute dispersions of bubbles which experience a sufficiently large increase in pressure such that the resulting solution is unsaturated with air.

Pressure effects on the hydrodynamic behavior of gas-liquid-solid fluidized beds

Basic hydrodynamic behavior of a gas-liquid-solid fluidized bed at elevated pressures up to 1 MPa was studied by measurement and visualization techniques in a specially constructed rectangular column. Conditions of gas and liquid velocities, particle size, distributor type, and pressure were varied in the apparatus, which was designed to allow operation in both two- and three-dimensional modes. Visualization in two-dimensional operation and measurement in three-dimensional operation were combined to provide a unique tie point between the two modes. The study indicated that bubble size decreases, bubble size distribution narrows, and gas holdup increases with increasing pressure. The type of distributor was found to have a marked impact on bed behavior, including bulk circulation, bubble coalescence, and gas holdup. Possible mechanisms for the observed pressure effects on the hydrodynamic behavior are also discussed, combined with available experimental observations. Analysis indicates that initial bubble size and maximum stable bubble size should decrease with increasing pressure due to changes in interfacial physical properties as well as in gas density

Air bubble interaction with a submerged, axisymmetric water jet.

Individual air bubbles were released from a vertical, blunt-tipped, 20-gauge hypodermic needle. They rose and collided with an axisymmetric, horizontal water jet submerged in a water-filled tank. Acoustic emissions resulting from bubble–jet interaction were studied. High-speed video analysis was also employed to visually determine bubble behavior (e.g., extent of shear-induced bubble distortion and/or bubble breakup, etc.). Parameters which were varied included the downstream location of the bubble–jet collision, the flow characteristics (Reynolds number, laminar versus turbulent flow, etc.), and the initial bubble size. Results to be discussed will include the sound produced when the bubbles break up and when they do not. The role played by the flow characteristics in determining the acoustical bubble response will also be considered. [Worked supported by ONR, ONT, and DTRC.]

Collapse and rebound of a gas-filled spherical bubble immersed in a diagnostic ultrasonic field

This work is concerned with the influence of the finite-amplitude distortion of a driving diagnostic ultrasonic field on the collapse and rebound of a gas-filled spherical microbubble, present in the exposed compressible liquid. Such an analysis is especially important since one of the mechanisms for cavitation damage comes from the very large gas pressures generated at bubble collapse and in the subsequent pressure wave formed by bubble rebound. Gilmore's model [F.R. Gilmore, "The growth or collapse of a spherical bubble in a viscous compressible liquid," Hydrodynamics Lab. Rep. No. 26-4, California Institute of Technology, Pasadena, CA (1952)] for bubble dynamics is used to obtain the motion of the bubble interface when subjected to a pulsed diagnostic ultrasonic field of large amplitude. Knowledge of the bubble motion allows one to derive the pressure distribution around the bubble. Numerical results over a range of initial bubble sizes, acoustic pressures, and frequencies relevant to medical use show that the strength of the pressure spikes radiated by the rebounding bubble depends upon (i) the acoustic frequency (f), (ii) the initial bubble size (R0), and (iii) the magnitude of the pressure amplitude of the fundamental (PF) in a Fourier series description of the distorted pulse. As the pressure spikes propagate outward from the bubble wall, their strength is attenuated as the reciprocal of the distance from the center of collapse.

Dissolution of an oxygen bubble in blood.

The equation of motion for the dissolution of an oxygen bubble in blood is derived by combination of an equation of motion for the bubble in Casson fluids taking into consideration the effect of hematocrit and an approximate solution of diffusion equation. According to computational analyses, the effects of hematocrit Hct, the ratio ƒ of the initial dissolved O2 concentration to the cencentration at saturation, and the initial bubble size on the process of dissolution of an O2 bubble in human blood are made clear. It is found that the dissolution of an O2 bubble in blood is strongly influenced by hematocrit. The completely dissolved time T of the bubble is the least at Hct=40∼50 which is the value of hematocrit for a healthy body.

Mass transfer phenomena and hydrodynamics in agitated gas—liquid reactors and bubble columns at elevated pressures: State of the art

All important studies on the influence of pressure on mass transfer phenomena in gas—liquid systems and reactors are reviewed critically. Points of agreement and conflict are indicated and discussed. It is concluded that: (1) the initial bubble size at a single orifice decreases with increasing pressure; (2) the gas-phase mass transfer coefficient k G is inversely proportional to the pressure to the power n, where n depends on the mass transfer mechanism; (3) the liquid-phase mass transfer coefficient k L is not influenced by pressure; (4) the gas hold-up ε G in bubble columns increases with increasing pressure. However, insufficient data on the influence of the operating pressure on the interfacial areas in gas—liquid contactors are available.

Prediction of oxygen transfer and total dissolved gas pressure in airlift pumping

The results of an experimental study to determine the oxygen transfer properties of a 38 mm diameter airlift pump are presented. The effects of varying initial bubble size, flow rate, flow pattern, and water quality on oxygen transfer were examined. Pumping efficiencies of the airlift pump were found to be as high or higher than centrifugal pumps and oxygen transfer efficiencies as high or higher than fine bubble diffuser aeration systems. Generalized predictive equations for oxygen and nitrogen transfer and supersaturation in airlift pumping are presented

Bubble properties in large-particle fluidized beds

Bubble properties were studied in a two-dimensional bed and a square bed 1.2m wide fluidized with large particles (1 mm average diameter). Horizontal and vertical arrays of optical probes were used to measure the bubble characteristics. The velocity of a bubble depends on the proximity of bubbles above it; the average velocity is closely approximated by the Davidson and Harrison expression. At high flow rate, the initial bubble size is closely estimated by a Froude number correlation. The rate of bubble coalescence is well-correlated by the void fraction of bubbles in the bed and can be predicted by allowing for the random spatial distribution of bubbles. A one-dimensional model for the bubble growth is presented.

Bubble Migration and Coalescence during the Solidification of Basaltic Lava Flows

The initial size distribution of gas bubbles in lava flows is modified by bubble rise and coalescence during post eruptive cooling and crystallization. A simple model which computes the effects of rise and coalescence accounts for observed features and may provide a means whereby the initial bubble size distribution can be inferred. A model lava flow of assumed thickness, viscosity, and volume percentage of gas bubbles is given an initial bubble size distribution. Bubbles coalesce due to differences in their relative rise velocities. Using a gravitational collection kernel, the process may be modeled by numerical integration of the stochastic collection equation, which yields the change in the number density spectrum of the population from the number densities of all pairs of bubbles and their probabilities of collision. Bubbles rise and coalesce within a fluid interior sandwiched between fronts of crystallization that advance inward from top and bottom. Bubbles that are overtaken by the crystallization fronts cease to migrate. The model predicts the formation of upper and lower vesicle-rich zones separated by a vesicle-free interior. The upper zone is broader, more vesicular, and has larger bubbles than the lower zone. Increasing the initial average bubble size in the model results in a stratigraphically lower and thinner lower vesicular zone, a thicker vesicle-free central region, and a higher and more vesicular upper zone.

Homogeneous nucleation of gas bubbles in vivo.

Several current theories of decompression sickness (DCS) presume the preexistence of gas bubble nuclei in tissue, because the de novo nucleation of gas bubbles in the body is thought to be theoretically impossible. Reexamination of nucleation theory reveals the overwhelming importance of two parameters: gas supersaturation and tissue surface tension (gamma). For the high gamma of pure water nucleation theoretically requires more than 1,000 ATA supersaturation. Lower values of gamma allow nucleation to occur with vastly smaller supersaturations. Application of homogeneous nucleation theory can provide reasonable fits to both rat and human pressure-reduction data with values of gamma within the range reported for biological fluids (below 5 dyn/cm). The initial bubble sizes predicted are 0.1 micron or less. The presence of heterogeneous sites, for example crevices and lipid surfaces, makes nucleation even more likely.

Gas-liquid mass transfer in rotating perforated-disc contactors

This paper presents a numerical model for predicting the performance of liquid-gas mass transfer in a rotating perforated-disc type contactor. The device consists of a cylindrical section situated between two 45-degree conical sections. A liquid flows downward by gravity while a stream of air moves upward by buoyancy thus forming a counter-current flow situation in the contactor. A gas dissolved in the liquid transfers into air bubbles which are sheared to a tiny size as they rise through the perforations on the rotating disc. Both laminar and turbulent flows are treated. Utilizing the velocity distribution [10,11] and bubble trajectory [12] as the basis, the interphase mass transfer performance of carbon dioxide in the water-air system is numerically determined. It is disclosed that in both laminar and turbulent flow cases, the rate of interphase mass transfer increases significantly with a reduction in bubble size. Rotational speed does not affect mass transfer in laminar flow but causes an exponential mass transfer enhancement in higher turbulent flows. There exists an optimum through-flow rate of the liquid for the best mass transfer performance depending on the initial bubble size and disc speed. Test results [9] provide a qualitative confirmation of the theory.

Effect of distributor design on heat transfer from an immersed horizontal tube in a fluidized bed

Experiments have been carried out to examine the effect of distributor design on the total heat transfer coefficient between a 12.7 mm diameter electrically heated copper tube and a square fluidized bed (0.305 m × 0.305 m) of glass beads ( d p = 265, 357 and 427 μm). The distributors are two perforated plates of different open area with a cloth sandwiched between them. The effect of distributor design on the total heat transfer coefficient is explained on the basis of its effect on the initial bubble size and frequency.

The effect of initial bubble size distribution on the interbubble gas diffusion in foam

The changes in bubble size produced by the titled effect are computed in detail from theory and mutually compared. The results show a marked effect on the increases in the various averages of bubble size with time, but a much smaller effect on the fractional decrease in the overall surface of the bubbles.

Effect of distributor design on heat transfer from an immersed horizontal tube in a fluidized bed

Experiments have been carried out to examine the effect of distributor design on the total heat transfer coefficient between a 12.7 mm diameter electrically heated copper tube and a square fluidized bed (0.305 m × 0.305 m) of glass beads ( d p = 265, 357 and 427 μm). The distributors are two perforated plates of different open area with a cloth sandwiched between them. The effect of distributor design on the total heat transfer coefficient is explained on the basis of its effect on the initial bubble size and frequency.

Acoustic cavitation prediction

In the course of preparing a chapter on “Acoustic Cavitation” for a volume on “Ultrasonics” for the series Methods of Experimental Physics [edited by P. Edmonds, Academic, New York], I noticed that the question of what type of acoustic cavitation occurs for a given set of circumstances could be displayed in a simple manner in a series of graphs. The ordinate scale of these graphs is the ratio of a particular bubble radius (see below) and the radius at which a bubble is resonant at a given frequency. The abscissa is the ratio of acoustic pressure amplitude to ambient pressure. Five relevant bubble radii are plotted: The radius associated with (1) nucleation, (2) the rectified diffusion threshold, (3) inertially limited growth, (4) the maximum size of a transient bubble, and (5) the initial size of a transient bubble that will assure supersonic collapse. When these are plotted on a single graph for a given frequency and equilibrium gas saturation pressure, regions are defined which allow one to predict under what conditions a given type of cavitation will exist and, for transient cavitation, whether it will be violent. [Work supported by Physics Program, U. S. Office of Naval Research.]