Mean Bubble Radius Research Articles

How robust are gravitational wave predictions from cosmological phase transitions?

Abstract Gravitational wave (GW) predictions of cosmological phase transitions are almost invariably evaluated at either the nucleation or percolation temperature. We investigate the effect of the transition temperature choice on GW predictions, for phase transitions with weak, intermediate and strong supercooling. We find that the peak amplitude of the GW signal varies by a factor of a few for weakly supercooled phase transitions, and by an order of magnitude for strongly supercooled phase transitions. The variation in amplitude for even weakly supercooled phase transitions can be several orders of magnitude if one uses the mean bubble separation, while the variation is milder if one uses the mean bubble radius instead. We also investigate the impact of various approximations used in GW predictions. Many of these approximations introduce at least a 10% error in the GW signal, with others introducing an error of over an order of magnitude.

Memory-friendly fixed-point iteration method for nonlinear surface mode oscillations of acoustically driven bubbles: from the perspective of high-performance GPU programming

A fixed-point iteration technique is presented to handle the implicit nature of the governing equations of nonlinear surface mode oscillations of acoustically excited microbubbles. The model is adopted from the theoretical work of Shaw [1], where the dynamics of the mean bubble radius and the surface modes are bi-directionally coupled via nonlinear terms. The model comprises a set of second-order ordinary differential equations. It extends the classic Keller–Miksis equation and the linearized dynamical equations for each surface mode. Only the implicit parts (containing the second derivatives) are reevaluated during the iteration process. The performance of the technique is tested at various parameter combinations. The majority of the test cases needs only a single reevaluation to achieve 10-9 error. Although the arithmetic operation count is higher than the Gauss elimination, due to its memory-friendly matrix-free nature, it is a viable alternative for high-performance GPU computations of massive parameter studies.

The Effects of Viscosity and Capillarity on Nonequilibrium Distribution of Gas Bubbles in Swelling Liquid–Gas Solution

A detailed statistical description of the evolution of supersaturated-by-gas solution at degassing has been presented on the basis of finding the time-dependent distribution in radii of overcritical gas bubbles. The influence of solution viscosity and capillarity via internal pressure in the bubbles on this distribution has been considered until the moment when the gas supersaturation drops due to depletion and stops nucleation of new overcritical gas bubbles. This study is based on our previous results for the nonstationary growth rates of overcritical bubbles depending on gas supersaturation, diffusivity and solubility in solution, solution viscosity, and surface tension on bubble surface. Other important factors are linked with the initial rate of homogeneous gas bubble nucleation and coupling between diffusivity and viscosity in the solution. Here, we numerically studied how all these factors affect the time-dependent distribution function of overcritical bubbles in their radii, maximal and mean bubble radii, and the time-dependent swelling ratio of a supersaturated-by-gas solution in a wide range of solution viscosities.

Passive Acoustic Determination of Spectral Wave Breaking Dissipation

Abstract When a wave breaks, it produces bubbles whose sizes depend on the breaking severity. This paper attempts to estimate wave breaking dissipation through a passive acoustic method. Initially, regular waves were forced to break in a flume. The breaking energy loss (severity) and the underwater acoustic noise were recorded. Two kinds of thresholds, in terms of sound wave amplitude and the ratio of sound wave height to period, respectively, were used together to identify the sound waves generated by newly formed bubbles. The frequencies of these sound waves are connected with the bubble sizes. Thus, a relationship between the mean bubble radius and the breaking severity was established and found to be linear. This laboratory relationship was then applied to Lake George data to study the breaking dissipation rate across the spectrum. An average acoustic spectral density threshold was proposed to identify breaking events from acoustic records in the field. The sound waves associated with bubble formation were selected by means of the same two kinds of threshold as used in the laboratory. Thus, the mean bubble radius of each breaking event was obtained and translated into the breaking severity. The values of experimental dissipation were compared with previous relevant results obtained through different methods as well as the wave breaking dissipation source terms ST6 (WAVEWATCH-III model) and are in good agreement with both of them.

Time-resolved rheometry of coarsening foams using three-dimensionally printed fractal vanes

Aqueous foams are useful in several applications, especially to reduce liquid loading in the oil and gas industry. The rheology of these foams evolves rapidly, and suitable constitutive models are required to describe the resulting multiphase flow. We describe a new experimental setup for advanced rheometry involving 4-arm and 12-arm vane-in-textured-cup toolsets. The cup was designed to provide in situ foaming to minimize injection times and flow-history artifacts before measurement, while the 12-arm vane was selected to eliminate slip and generate a homogeneous stress field in a weak foam. Using these tools, we measure the decay of linear viscoelasticity and yield stress and link the rheological evolution to optical measurements of the bubble size distribution. Time-resolved rheological measurements of the full flow curve of an aging foam are performed and used to construct a rheological master curve. Measurements of the transient linear viscoelastic response and observations of the bubble size distribution show that foams, after an initial induction period, experience an increase in the Sauter mean bubble radius that scales as t1/2. Using the well-known Princen and Kiss model as a framework, we define a single unique time-dependent shift factor that varies with the Sauter mean bubble radius and enables us to use the rheological master curve to predict the temporal evolution of the foam's elastic and steady-state viscoplastic properties.

Effects of anti-clay agents on bubble size distribution and stability of aqueous foam under pressure for earth pressure balance shield tunneling

The earth pressure balance (EPB) shield inevitably encounters heavy clay soils during tunneling, which form mud cakes on the cutter head. To prevent this, it is necessary to add anti-clay agents to foam agents. However, the effect of anti-clay agents on foam properties and its optimal concentration under different conditions remain unknown. In this study, the bubble size distribution and half-life of foam produced by foam agents and anti-clay agents under pressure were measured and analyzed. The results show that the mean bubble radius decreases with the addition of anti-clay agents at 0 bar but increases at a pressure of 1 bar or 2 bar. The anti-clay agents weaken the stability of foam, and optimal concentrations of anti-clay agents for different test pressures are proposed. The test results obtained provided guidance for selection of the optimal concentration of anti-clay agents to be used in EPB shield tunneling.

Quantitative measurement of bubble textures in pumice clasts using a digital stereo microscope with low-angled ring illumination

Quantitative analysis of bubble textures in a large number of volcanic pyroclasts is critical to investigating the eruption dynamics in a volcanic conduit. Here, we used a digital stereo microscope with low-angled ring illumination (DSM-LaRI) to measure bubble textures on unpolished cutting surfaces of pumice clasts. As the DSM-LaRI enhances brightness contrast between the bubbles (pores) and the matrix, we easily obtained the two-dimensional data on the size and shape of bubbles by image analysis. The DSM-LaRI imaging provided the distributions of size and shape of bubbles at least 50 µm across. We applied the DSM-LaRI to analyze more than 1000 pumice clasts from the 232 AD Taupo eruption and measured the mean bubble radius (overline{R}) and the mean deformation degree (overline{D}) in the individual clasts. The distribution of overline{R} and overline{D} in each layer showed a distinctive difference between the fallout and the flow deposits. These quantitative data are consistent with a qualitative classification in a previous study. Although the new DSM-LaRI method has the disadvantage of the low spatial resolution, it allows for the analysis of a large number of pumice clasts in a short time, which can address larger scale heterogeneity, by efficiently generating a large representative suite of bubble size and shape data to link bubble textures to conduit processes. This provides vital information for quantitatively modeling eruption dynamics.

Shape stability of a gas bubble in a soft solid.

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.

On the theory of bubble coarsening in metals

A comprehensive analysis of simulation results obtained recently by the authors in modeling of gas bubble evolution driven by the Ostwald ripening process in irradiated metals has been carried out. Relevant experimental data characterized by a relatively small mean bubble radius measured in a range of about 1–5 nm in stainless steel specimens containing 100 appm He and annealed at 1023 K have also been used in this study. A comparison of both the experimental and simulation data with analytical estimations predicted by the original theory at the late stage of bubble coarsening was considered unsatisfactory. To overcome this inconsistency, a new approach has been applied assuming that bubbles evolve at significantly different rates at either earlier or later stages of the process. Despite the difference of the rates in these cases, a complete similarity of corresponding asymptotic bubble size distributions has been detected. Experimentally observable time dependences of bubble density and mean bubble radius agree well with the recent modeling and our present analysis results. This indicates that Ostwald ripening provides a reasonable explanation for bubble evolution during annealing. Unlike the conventional interpretation of bubble coarsening, growing bubbles attain chemical equilibrium with interstitial gas emitted by shrinking bubbles. It is this assumption which allows for getting the asymptotic bubble size distribution function similar to that given by the classical theory of Ostwald ripening.

Observing patchy reionization with future CMB polarization experiments

We study the signal from patchy reionization in view of the future high accuracy polarization measurements of the Cosmic Microwave Background (CMB). We implement an extraction procedure of the patchy reionization signal analogous to CMB lensing. We evaluate the signal to noise ratio (SNR) for the future Stage IV (S4) CMB experiment. The signal has a broad peak centered on the degree angular scales, with a long tail at higher multipoles. The CMB S4 experiment can effectively constrain the properties of reionization by measuring the signal on degree scales. The signal amplitude depends on the properties of the structure determining the reionization morphology. We describe bubbles having radii distributed log-normally. The expected S/N is sensitive to the mean bubble radius: R̄=5 Mpc implies S/N ≈ 4, R̄=10 Mpc implies S/N ≈ 20. The spread of the radii distribution strongly affects the integrated SNR, that changes by a factor of 102 when σlnr goes from ln 2 to ln 3. Future CMB experiments will thus place important constraints on the physics of reionization.

Ultrasonic investigation of the effects of composition on the volume fraction of bubbles and changes in their relative sizes in non-yeasted gluten-starch blend doughs

Interactions between water, gluten and starch during dough mixing alter the aeration properties of dough. Effects of composition on dough gas volume fraction and relative changes in bubble sizes of non-yeasted gluten-starch (G-S) blend doughs were investigated using density measurements and an ultrasonic transmission technique, respectively. At fixed water content, greater gluten content increased the air volume fraction, while frequency-dependent ultrasonic attenuation coefficient and phase velocity measurements indicated that the bubble sizes in the G-S doughs were larger. The latter outcome may be due to mixing to optimal conditions such that shorter mixing times for doughs of high gluten content lessened the number of bubble subdivision events during mixing. The effect of increased water content on the attenuation coefficient implied a decrease in mean bubble radius as elucidated using an ultrasonic model. Time evolutions of attenuation coefficient and phase velocity for G-S blend doughs had a similar trend to those of non-yeasted wheat flour doughs. However, the shifts in the frequency of the peaks observed in the ultrasonic parameters were noticeably slower for G-S blend doughs, implying that G-S blend doughs were more stable against disproportionation.

Point-source imbibition into dry aqueous foams

We use experiments, modeling and numerics to study the imbibition dynamics from a point source into a homogeneous dry aqueous foam. A distinctive feature of foams compared to solid porous material is that imbibition occurs in the liquid microchannels of the foam called Plateau borders, which have a volume varying in space and time. Dynamics is driven by the capillary pressure and resisted by the viscous and gravity forces in the liquid microchannels. Assuming a constant pressure in the imbibing liquid reservoir, we show that the imbibition front advances and flattens out in time due to gravity, the effect of which is quantified by introducing the Bond number B, which compares the gravitational effects to the capillary pressure using the mean bubble radius as the characteristic length. This evolution describes both miscible and immiscible imbibing liquids. For the latter, we introduce the idea of an effective interfacial tension to take the oil-water interfacial energy into account. The details of the imbibition process are confirmed by experiments and numerics using foams with tangentially immobile interfaces in the channel-dominated model.

Propagation of ultrasound in aqueous foams: bubble size dependence and resonance effects

We report experimental results on the propagation of ultrasonic waves (at frequencies in the range of 40 kHz) in aqueous foams. Monitoring the acoustics of the foams as they age, i.e. as the mean bubble radius increases by coarsening, we recover at short times some trends that are already known: decrease of the speed of sound and increase of attenuation. At long times, we have identified, for the first time, robust non-monotonic behaviors of the speed of sound and attenuation, associated with a critical bubble size, which decreases at increasing frequency. The experimental features appear to be surprisingly reminiscent of the Minnaert resonance known for a single isolated bubble in a fluid. Transposing the Minnaert theoretical framework to the limit of a dense packing of bubbles gives some qualitative agreement with the data, but still cannot explain quantitatively the measured properties.

Rheology of Milk Foams Produced by Steam Injection

Rheology of milk foams generated by steam injection was studied during the transient destabilization process using steady flow and dynamic oscillatory techniques: yield stress (τ(y) ) values were obtained from a stress ramp (0.2 to 25 Pa) and from strain amplitude sweep (0.001 to 3 at 1 Hz of frequency); elastic (G') and viscous (G″) moduli were measured by frequency sweep (0.1 to 10 Hz at 0.05 of strain); and the apparent viscosity (η(a) ) was obtained from the flow curves generated from the stress ramp. The effect of plate roughness and the sweep time on τ(y) was also assessed. Yield stress was found to increase with plate roughness whereas it decreased with the sweep time. The values of yield stress and moduli-G' and G″-increased during foam destabilization as a consequence of the changes in foam properties, especially the gas volume fraction, ϕ, and bubble size, R(32) (Sauter mean bubble radius). Thus, a relationship between τ(y) , ϕ, R(32) , and σ(surface tension) was established. The changes in the apparent viscosity, η, showed that the foams behaved like a shear thinning fluid beyond the yield point, fitting the modified Cross model with the relaxation time parameter (λ) also depending on the gas volume fraction. Overall, it was concluded that the viscoelastic behavior of the foam below the yield point and liquid-like behavior thereafter both vary during destabilization due to changes in the foam characteristics. Studying the transient rheology of milk foams during destabilization contributes to our knowledge of the relationships between the changes in foam properties: texture and mouth feel during the consumption of hot foamed beverages.

“Compression-only” behavior: A second-order nonlinear response of ultrasound contrast agent microbubbles

Oscillating phospholipid-coated ultrasound contrast agent microbubbles display a so-called "compression-only" behavior, where it is observed that the bubbles compress efficiently while their expansion is suppressed. Here, a theoretical understanding of the source of this nonlinear behavior is provided through a weakly nonlinear analysis of the shell buckling model proposed by Marmottant et al. [J. Acoust. Soc. Am. 118, 3499-3505 (2005)]. It is shown that the radial dynamics of the bubble can be considered as a superposition of a linear response at the fundamental driving frequency and a second-order nonlinear low-frequency response that describes the negative offset of the mean bubble radius. The analytical solution deduced from the weakly nonlinear analysis shows that the compression-only behavior results from a rapid change of the shell elasticity with bubble radius. In addition, the radial dynamics of single phospholipid-coated microbubbles was recorded as a function of both the amplitude and the frequency of the driving pressure pulse. The comparison between the experimental data and the theory shows that the magnitude of compression-only behavior is mainly determined by the initial phospholipids concentration on the bubble surface, which slightly varies from bubble to bubble.

Segregating gas from melt: an experimental study of the Ostwald ripening of vapor bubbles in magmas

Diffusive coarsening (Ostwald ripening) of H2O and H2O-CO2 bubbles in rhyolite and basaltic andesite melts was studied with elevated temperature–pressure experiments to investigate the rates and time spans over which vapor bubbles may enlarge and attain sufficient buoyancy to segregate in magmatic systems. Bubble growth and segregation are also considered in terms of classical steady-state and transient (non-steady-state) ripening theory. Experimental results are consistent with diffusive coarsening as the dominant mechanism of bubble growth. Ripening is faster in experiments saturated with pure H2O than in those with a CO2-rich mixed vapor probably due to faster diffusion of H2O than CO2 through the melt. None of the experimental series followed the time1/3 increase in mean bubble radius and time−1 decrease in bubble number density predicted by classical steady-state ripening theory. Instead, products are interpreted as resulting from transient regime ripening. Application of transient regime theory suggests that bubbly magmas may require from days to 100 years to reach steady-state ripening conditions. Experimental results, as well as theory for steady-state ripening of bubbles that are immobile or undergoing buoyant ascent, indicate that diffusive coarsening efficiently eliminates micron-sized bubbles and would produce mm-sized bubbles in 102–104 years in crustal magma bodies. Once bubbles attain mm-sizes, their calculated ascent rates are sufficient that they could transit multiple kilometers over hundreds to thousands of years through mafic and silicic melt, respectively. These results show that diffusive coarsening can facilitate transfer of volatiles through, and from, magmatic systems by creating bubbles sufficiently large for rapid ascent.

Reconstructing patchy reionization from the cosmic microwave background

We introduce a new statistical technique for extracting the inhomogeneous reionization signal from future high-sensitivity measurements of the cosmic microwave background (CMB) temperature and polarization fields. If reionization is inhomogeneous, then the optical depth to recombination will be a function $\ensuremath{\tau}(\stackrel{^}{\mathbf{n}})$ of position on the sky. Anisotropies in $\ensuremath{\tau}(\stackrel{^}{\mathbf{n}})$ alter the statistics of the observed CMB via several physical mechanisms: screening of the surface of last scattering, generation of new polarization via Thomson scattering from reionization bubbles, and the kinetic Sunyaev-Zel'dovich effect. We construct a quadratic estimator ${\stackrel{^}{\ensuremath{\tau}}}_{\ensuremath{\ell}m}$ for the modes of the $\ensuremath{\tau}$ field. This estimator separates the patchy reionization signal from the CMB in the form of a noisy map, which can be cross correlated with other probes of reionization or used as a standalone probe. A future satellite experiment with sufficient sensitivity and resolution to measure the lensed $B$ modes on most of the sky can constrain key parameters of patchy reionization, such as the duration of the patchy epoch or the mean bubble radius, at the $\ensuremath{\sim}10%$ level.

CRYSTAL GROWTH LIMITATION IN AQUEOUS FOAM CRYSTALLIZATION

We present results concerning the limitation of maximum crystal size by pre-foaming an aqueous supersaturated solution, followed by its crystallization. Foams are generated by adding specific surface active agents to the solution and by air injection under continuous high shear agitation, leading to a gas-liquid stable dispersion having polyhedral internal structures with thin separating liquid films. This spatial dispersion structuration, by locally reducing the amount of solute available for each crystal growth, permits the limitation of the resulting crystal sizes. It is shown that, under these conditions, the initial film thickness and mean bubble radius, obtained for a given volume fraction of gas in the foam, can control the final crystal size distribution. The foam expansion ratio thus appears to be a new operating parameter for crystal growth limitation when using a foam crystallization technique.

Is the yield stress of aqueous foam a well-defined quantity?

Dimensional arguments suggest that the yield stress of aqueous foams and emulsions, for a given volume fraction of the dispersed phase, should scale as the ratio of surface tension and a length scale, such as the mean bubble radius. We show that yield stress data from the literature and from our experiments follow this scaling only in a very rough approximation. We present new experimental evidence that clarifies the role of shear banding in this context and we discuss the robustness of the yield stress with respect to changes of flow geometry and experimental technique. Finally, we show that scaling oscillatory yield stress data by the elastic shear modulus at small amplitude provides a master curve when plotted versus the volume fraction of the dispersed phase.

Drag force acting on a bubble in a cloud of compressible spherical bubbles at large Reynolds numbers

We have derived the expressions for the viscous forces acting on a bubble in a cloud of bubbles by using the approach by Levich. To obtain the dissipation function, an approximate expression for the velocity potential calculated previously by the authors up to order β 3 has been used. Here β = b ¯ / d is a small dimensionless parameter, b ¯ is the mean bubble radius and d is the mean distance between bubbles.