Minimum Bubble Radius Research Articles

A new optical instrument for the study of bubbles at high void fractions within breaking waves

An optical imaging system (BubbleCam) has been tested for the quantification of bubble distributions at high void fractions formed beneath breaking waves. The instrument consists of a CCD video camera, stroboscopic light source, and optics allowing adjustable magnification, a fixed imaging volume, and the resolution of bubbles 3 pixels in radius and larger (equivalent to a minimum bubble radius of about 200 /spl mu/m in the test configuration). BubbleCam has been deployed in a shore-based configuration (data and power supplied via shore-connected cables) as well as an autonomous device in the open sea with its own power supply and data storage. The resulting images are processed using a variant of the Hough transform which allows computer-automated counting and measurement of the bubbles within the video frames. In addition, images can be qualitatively examined to provide insights into bubble plume evolution and creation mechanisms.

Nonequilibrium Plasma Theory of a Cavitation Bubble Containing Xenon Gas.

The behavior of a single xenon bubble in an adiabatic compression process was investigated theoretically. Rayleigh's equation for the bubble dynamics was coupled with the detailed collisional and radiative processes for xenon plasma to obtain plasma conditions in a bubble. A two-temperature model for electrons and heavy particles was adopted to estimate the luminescence property from a spherical bubble. For the conditions of initial bubble radius of 10 to 150 μm and pressure change of 200 to 800 kPa, the maximum electron temperature ranged from 5000 to 15000 K and electron number densities about 1017 to 1020 cm-3 at the minimum bubble radius. The plasma in a bubble was in thermally nonequilibrium state during the compression process, and generally the maximum electron temperature was significantly lower than the heavy particle one. The emission intensity from cavitation bubbles was sensitive to the change rate of pressure and the bubble radius.

The influence of liquid temperature on the sonoluminescence hot spot

An explanation is provided for the influence of relatively small changes in liquid temperature on the hot spot within a sonoluminescence bubble. This influence derives from a change in the (stable) equilibrium mass of the bubble due to a variation of the gas solubility in the liquid with temperature. If the acoustic drive amplitude is held constant, a change in the liquid temperature has a large or small effect depending on the variability of the solubility with temperature. For a gas like xenon, which has rapidly decreasing solubility in water with increasing temperature, a decrease in water temperature shifts the stable mass exchange equilibrium to a smaller bubble size. This increases the ratio of maximum to minimum bubble radius over an acoustic cycle, resulting in a much higher hot spot temperature. In contrast helium has very little variation of solubility with temperature near room temperature; therefore the hot spot temperature is relatively insensitive to variations in the liquid temperature outside a helium bubble.

Theory of sonoluminescence in single bubbles: Flexoelectric energy contribution

An equation of motion for a cavitating gas bubble immersed in a liquid is introduced which includes a flexoelectric energy term. This energy is deduced from the electric field produced by the bubble wall acceleration (pressure gradient) in the fluid (the flexoelectric effect). We show that under conditions of sonoluminescence, this electric field reaches values typical of the electric breakdown field in water. Our theoretical results are consistent with the duration of light emission, minimum bubble radius, and energy release as measured in sonoluminescence experiments in water.

The acoustic emissions from single-bubble sonoluminescence

Detailed measurements of the acoustic emissions from single-bubble sonoluminescence have been made utilizing both a small 200-μm aperture PVDF needle hydrophone, and a focused 10-MHz transducer. Signals obtained with the needle hydrophone show a fast (5.2 ns), probably bandlimited rise time and relatively large pulse amplitude (≈1.7 bar). Below the sonoluminescence threshold, the emissions are observable, but considerably smaller in amplitude (≈0.4 bar). Several signals are observed with the 10-MHz transducer and correspond to acoustic emissions from the bubble during the main collapse, as well as from the rebounds. Experiments reveal that the acoustic emissions occur at or near the minimum bubble radius. Calculations of the peak pressures and pulse widths are compared with experimental data.

Pulsed Mie Scattering Measurements of the Collapse of a Sonoluminescing Bubble

Measurements of light scattered off a bubble that is illuminated by a train of short pulses enables one to resolve the strongly supersonic collapse of a sonoluminescing bubble. We find that the collapse is faster than Mach 4 (relative to the ambient speed of sound of the gas in the bubble) and that the flash of sonoluminescence is emitted within 500 ps of the minimum bubble radius, at about which time the bubble's acceleration is greater than ${10}^{11}\phantom{\rule{0ex}{0ex}}\mathrm{g}$.

Respiratory support, surface activity and protein content during nosocomial infection in preterm neonates.

Small volume bronchoalveolar lavages from 10 infants (26.6 +/- 0.4 weeks gestational age) during postnatal nosocomial infection were fractioned by differential centrifugation into large (LA) and small (SA) surfactant aggregates. Before deterioration of the clinical status, the surface tension at minimum bubble radius (gamma min), as measured in a pulsating bubble surfactometer, was reduced to about 14 mN/m by LA and to about 22 mN/m by the corresponding SA. The gamma min of both LA and SA increased during clinical deterioration, was highest at the worst clinical state and returned during recovery to values in the range before deterioration. Respiratory support significantly correlated to gamma min at all times. In contrast, no correlation was observed for total protein or albumin content of the LA or SA fractions. The SA fraction was characterized by a 10-fold higher protein content than LA. These data demonstrate functional impairment of surfactant in subfractions during mechanical ventilation and nosocomial infection in preterm neonates that are not fully explained by inhibition with increasing amounts of total protein.

On the surface activity of surfactant-associated protein C (SP-C): effects of palmitoylation and pH.

The effect of palmitoylation on the surface activity of bovine surfactant-associated protein C (SP-C) in lipid mixtures was investigated. Native and chemically depalmitoylated SP-C were reconstituted with dipalmitoylphosphatidylcholine/egg phosphatidylglycerol (7:3) using two different procedures, one of which included lyophilization and sonication. When tested using a pulsating bubble surfactometer, no significant changes in the surface activity of these mixtures were observed upon the hydrolysis of the palmitates. Since the purification and deacylation procedures of SP-C included the use of acid and alkali, the effect of pH was examined. The surface activity of the mixtures was found to vary with pH. At low pH values (approx. 2.5), surface tensions between 3 and 10 mN/m at minimum bubble radius were reached within 5 pulsations, while at neutral and slightly alkaline pH, surface tension reduction was much slower and near zero (< 5 mN/m) values at minimum bubble radius were not reached by the fiftieth pulsation. Protein-free lipid samples that were exposed to acid exhibited enhanced surface activity over similar non-treated samples. It is therefore concluded that low surface tension measurements recorded for acidic samples are secondary to a pH effect and do not reflect the surface activity at physiological conditions.

Toward a hydrodynamic theory of sonoluminescence

For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.

Light scattering measurements of the repetitive supersonic implosion of a sonoluminescing bubble.

Light scattering is used to measure the dynamics of the repetitive collapse of a sonoluminescing bubble of gas trapped in water. It is found that the surface of the bubble is collapsing with a supersonic velocity at about the time of light emision which in turn precedes the minimum bubble radius by about 0.03% of the period of the acoustic drive. These observations suggest that the shedding of an imploding shock mediates between the bubble collapse and light emission

The role of palmitic acid in pulmonary surfactant: enhancement of surface activity and prevention of inhibition by blood proteins

The surface activity of two surfactant preparations, Lipid Extract Surfactant (LES) and Survanta, was examined during adsorption and dynamic compression using a pulsating bubble surfactometer. At low surfactant phospholipid concentrations (1–2.5 mg/ml), Survanta reduces surface tension at minimum bubble radius faster than LES: however, with continued pulsation LES obtains a lower surface tension. Addition of surfactant-associated protein A (SP-A) to LES significantly reduces the time required to reduce surface tension. Survanta is completely unresponsive to the addition of SP-A in that no further reduction of surface tension is observed. Addition of various blood components has been previously shown to inactivate surfactants in vitro. Addition of fibrinogen to Survanta causes an increase in surface tension when measured in the absence of calcium. When assayed in the presence of calcium, inhibition by fibrinogen is not observed possibly due to aggregation of this protein. Albumin and α-globulin strongly inhibit Survanta at physiological serum concentrations both in the presence and absence of calcium. The surface activity of Survanta is also inhibited by lysophosphatidylcholine (lyso-PC). The role of palmitic acid in the surface activity of pulmonary surfactant was examined by adding palmitic acid to LES. At low phospholipid concentrations addition of palmitic acid (10% w/w of the surfactant phospholipid) greatly enhances the surface activity of LES. Maximal enhancement of surface activity and adsorption was observed at or above 7.5% added palmitic acid (w/w of surfactant lipid). LES supplemented with palmitic acid is more resistant to inhibition by fibrinogen, albumin, α-globulin and lyso-PC than LES alone, however, the counteraction of blood protein inhibition is not as pronounced as that observed with SP-A.

Low-molecular-weight hydrophobic proteins from bovine pulmonary surfactant

Pulmonary surfactant stabilizes the lung by reducing the surface tension in the terminal air spaces. Lipid extract surfactant contains approx. 1% (w/w) low-molecular-weight hydrophobic proteins SP-B (15 kDa: nonreduced) and SP-C (3.5 kDa) and with the remainder being mainly phospholipids. The hydrophobic proteins were purified from bovine lipid extract surfactant using delipidation by phospholipase C digestion followed by hydroxyapatite chromatography. The phospholipase C step removed most of phosphatidylcholine resulting in a 10-fold enrichment of hydrophobic proteins relative to phospholipid. Chromatography of this preparation on a hydroxyapatite column resulted in the elution of phospholipids followed by SP-C and then SP-B. The column chromatography was repeated to remove residual phospholipids and yield purified SP-B and SP-C. The final recovery of SP-B from the lipid extracts was about 15–20% and that of SP-C was 5–10%. The bovine surfactant proteins were reconstituted with phospholipids and examined for their ability to lower the surface tension with a pulsating bubble surfactometer. Reconstituted surfactant preparations containing SP-B and dipalmitoylphosphatidylcholine plus dioleoylphosphatidylglycerol were capable of reducing the surface tension to near zero values at minimum bubble radius while the reconstitutes with SP-C only lowered the surface tension to approx. 20 mN/m. A more rapid decrease in surface tension was observed with reconstituted samples containing both hydrophobic proteins. These results indicate that both SP-B and SP-C can promote the adsorption and spreading of surfactant lipids at the air/liquid interface. In addition, SP-B appears to facilitate the squeeze-out of unsaturated phospholipids leading to an enrichment of dipalmitoylphosphatidylcholine in the monolayer.

Comparative studies on the biophysical activities of the low-molecular-weight hydrophobic proteins purified from bovine pulmonary surfactant

Two low-molecular-weight hydrophobic proteins with nominal molecular weights M r = 15000 and M r = 3500 have been isolated from the lipid extracts of bovine pulmonary surfactant by several methods, including (a) dialysis plus silicic acid chromatography, (b) elution from Waters SEP-PAK silica cartridges with a variety of solvent mixtures, and (c) ultrafiltration. As detailed in the text, these proteins have been designated surfactant-associated protein-BC (SP-BC) (15 kDa: nonreduced), and SP-C (3.5 kDa). The biophysical activities of reconstituted surfactant containing these proteins and the phospholipids present in lung surfactant have been compared with the biophysical activities of bovine lipid extract surfactant on a pulsating bubble surfactometer using a phospholipid concentration of 10 mg/ml. At this concentration, unmodified lipid extract surfactant reduces the surface tension of the pulsating bubble to near 0 within 10 pulsations at 20 cycles per min. Similar biophysical properties were observed with modified lipid extract surfactant in which the relative concentration of hydrophobic protein had been reduced from 1 to 0.4% (w/w) of the phospholipids by addition of dipalmitoylphosphatidylcholine (DPPC) or DPPC plus phosphatidylglycerol. Reconstituted surfactants, which contained partially delipidated SP-BC (15 kDa: nonreduced) obtained by method (a) at a relative concentration of 0.1%, were also capable of reducing the surface tension to near 0 mN/m. Preparations of SP-BC (15 kDa: nonreduced) obtained by method (b), which had been subjected to very low pH levels during isolation and were extensively delipidated, exhibited full biophysical activity only at higher protein concentrations and with prolonged pulsation. Extensively delipidated samples of SP-BC obtained by method (c) exhibited impaired biophysical activities, even when prepared with neutral organic solvents. Reconstituted surfactant samples containing SP-C (3.5 kDa) obtained by any of the methods listed above were only able to reduce the surface tension at minimum bubble radius to approx. 20 mN/m. The biophysical activity of SP-C (3.5 kDa) was not significantly affected by low pH or extensive delipidation. Reconstituted samples containing mixtures of SP-BC (15 kDa: nonreduced) and SP-C (3.5 kDa) were more effective than samples containing either protein alone. Furthermore, with samples containing both hydrophobic proteins the final surface tensions at maximum bubble radius were attained within a few bubble pulsations. These studies demonstrate that SP-BC (15 kDa: nonreduced) is important for the complete biophysical activity observed with lipid extracts of pulmonary surfactant, but a cooperative effect may exist between this protein and SP-C (3.5 kDa), which is the major low-molecular-weight hydrophobic protein present in bovine surfactant.

Calcium interactions in pulmonary surfactant

The surfactant properties of natural bovine pulmonary surfactant, its lipid extracts and acetone precipitates of lipid extracts have been examined with an artificial alveolus model, the pulsating-bubble surfactometer. At bulk concentrations of 0.4% (wt/vol.) phospholipid in saline, all three preparations exhibited surfactant activity i.e., were capable of reducing the surface tension of the pulsating bubble to approx. 27 dynes/cm at maximum bubble radius and to near zero at minimum bubble radius. At a concentration of 0.1% (wt./vol.) in saline, only natural surfactant was effective. Acetone-precipitated surfactant at 0.1% (wt./ vol.) achieved these criteria in the presence of 5 mM calcium, but 15–20 mM calcium was required to restore the surfactant activity of lipid extract surfactant. Chemical analysis revealed that lipid extraction decreases the protein content but does not alter the endogenous calcium levels. A calcium requirement for natural surfactant could only be demonstrated after repeated treatment with chelators for divalent cations. Surfactant activity was restored by low levels of calcium or high levels of magnesium. Paradoxically, a calcium requirement could not be demonstrated by treating acetone-precipitated lipid extract with chelators. The subtle differences noted between natural, lipid extract and acetone-precipitated lipid extract surfactant with the pulsating-bubble assay show that the latter preparations do not represent simplified model systems for the natural product.

Effect of a dense gas equation of state on the expansion and contraction of an underwater gas bubble

At the high pressure believed to occur in underwater explosion gases, and in cavitation gas bubble collapse, deviations from an ideal gas must be considered. A theoretical investigation into the effect of a simplified dense gas equation of state on underwater gas bubble dynamics is presented. Our approach is to make a direct comparison between ideal and dense gas results. First, the lossless, incompressible liquid case is analyzed. The requirement of a realistic equation of state yields some startling results, placing severe bounds on some of the key parameters: the peak bubble pressure, the maximum bubble wall velocity, and the minimum bubble radius. Next, nonviscous energy losses are discussed. A generalization of the Herring method is used for approximate evaluation of the radiation‐loss integral derived from the Kirkwood–Bethe equation. These calculations appear to give physically reasonable loss estimates under both the ideal and dense gas assumptions. Also, an often‐quoted formula for the acoustic radiation loss has been found to be in error and has been corrected. For ease in calculation of some of the important quantities of interest, useful graphs and formulas have been presented.Subject Classification: 30.60, 30.75; 25.60.

Effect of a dense gas equation of state on the expansion and contraction of an underwater gas bubble

At the high pressure believed to occur in underwater explosion gases, and in cavitation bubble collapse, deviations from an ideal gas much be considered. A theoretical investigation into the effect of a simplified dense gas equation of state on underwater gas bubble dynamics is presented. Our approach is to make a direct comparison between ideal and dense gas results. First, the lossless, incompressible liquid case is analyzed. The requirement of a realistic equation of state yields some startling results, placing severe bounds on some of the key parametrs: the peak bubble pressure, the maximum bubble wall velocity, and the minimum bubble radius. Next, nonviscous energy losses are discussed. A generalization of the Herring technique is used for approximate evaluation of the radiation loss integral derived from the Kirkwood-Bethe equation. These calculations appear to give physically reasonable loss estimates under both the ideal and dense gas assumptions. Also, an oft-quoted formula for the acoustic radiation loss has been found to be in error and has been corrected.

Finite and Small Amplitude Underwater Gas Bubble Oscillations Compared

Bubble oscillation is well described by the nonlinear Keller-Kolodner equation. Although compressibility effects, which strongly influence the motion, are considered, analysis starts with incompressible approximation. The key parameter is p1/p0, the ambient/bubble pressure ratio. This ranges from zero to unity; near the lower limit finite amplitude pulsations occur; near the upper, simple harmonic motion ensues. The equation determining the maximum and minimum bubble radii, with p1/p0 as parameter, is graphed; these endpoints coalesce at a level where p1/p0 = 1. Further, taking compressibility into account, at each depth the end-points also converge to an equilibrium radius. T̄ has a simple power law dependence on p1/p0; this is generally not true for the finite amplitude period T1. The curves for T̄ and T1, as calculated from the Willis formula, cross; hence the actual T1 vs depth may be inferred. The shape of the bubble radius vs time curve changes from pulsation to simple oscillation with depth; this is asymptotically correct at any level, since T1 → T̄.