On an inhomogeneous coagulation model with a differential sedimentation kernel

Time-resolved tomographic particle tracking velocimetry (TR-3D-PTV), also called 4D-PTV, is used here to obtain the instantaneous 3D liquid flow field information in the wake of a single rising bubble in water. Simultaneously, the bubble shape, size and velocity are determined by tomographic reconstruction of the 3D bubble shape. Both, tracer particles for PTV and bubbles, are imaged in a shadow mode with background illumination. The Lagrangian method used in this paper, especially combined with the shake the box algorithm, has big advantages compared to particle image velocimetry, in situations, where only low particle per pixel values can be obtained. In this research, single air bubbles of different sizes, with diameters of around 2.4 mm, 4.0 mm, 6.0 mm and 9.6 mm, were injected into stagnant de-ionized water. Their shape was reconstructed in 3D, and an equivalent bubble diameter was determined from this reconstruction. Compared to conventionally used 2D shadow imaging, this diameter is about 13% smaller. The 3D bubble trajectory can be analysed and decomposed into a sinusoidal function curve lateral projection and an ellipsoidal shape vertical projection. As the bubble diameter increases, the radius of the spiral trajectory is decreasing as well as the amplitude of vertical sinusoidal oscillation. The wake structure in the liquid behind the bubbles is also changing with bubble size: from simple vortex pairs for smaller bubbles to an intertwined structure of several twisted vortices for the bigger ones.Graphical abstractThree-dimensional bubble reconstruction (grey surface) and liquid stream lines coloured with velocity magnitude around an ascending air bubble in de-ionized water.

Nuclear magnetic resonance has been used to determine the mean radius of air bubbles in distilled water that has stood for a long time and the volume concentration of these “reduced to mean radius” bubbles. It is shown that the kinetics of the change in the concentration of these bubbles can be observed from the change in the spin-spin relaxation time.

Hydrophobicity and Rupture of Thin Aqueous Films

The dissolution rates for 20‐ to 500‐μm‐diameter air bubbles in water and seawater at 50% and 100% air saturation are presented. The data indicate a dissolution rate that is independent of diameter for bubbles larger than ∼70 μm but is strongly dependent on diameter for smaller bubbles. Rise velocity data from a companion study were used in conjunction with Levich's “dirty bubble” formula to predict dissolution rates for the bubbles. There is good agreement with theory for bubbles in saturated liquids and for bubbles with diameters larger than 70 μm. Agreement is fair for smaller bubbles in 50% saturated water and seawater.

The optical glory, which is related to a weak focusing of backscattered light, is known to exist for spherical bubbles.1 This caustic, however, is affected by small deviations from sphericity. Hydrodynamics causes freely rising air bubbles in pure water to become slightly spheroidal if the bubble diameter ≳ 250 μm. We modeled and photographed the near backward scattering from slightly spheroidal horizontally illuminated bubbles. Spherical bubbles produce backward-directed glory wavefronts having the local shape of a circular torus. Our model introduces the leading perturbation of those wavefronts resulting from a small deviation from sphericity. The cross-polarized scattering from a sphere1 has a fourfold symmetric sin22φ azimuthal dependence where φ denotes the azimuthal angle. For the spheroids, both the model and the observation give a twofold symmetric pattern. Detailed features of the modeled patterns are confirmed by the observations. This gives a specific example of broken symmetry resulting in an unfolding of a caustic which would otherwise have an infinite codimension.2

The objective of this research was to gain fundamental knowledge of the drag and lift forces on ellipsoidal air bubbles in water in a turbulent flow. This was accomplished by employing a cinematic two-phase particle image velocimetry (PIV) system to evaluate bubbly flow in a two-stream, turbulent, planar free shear layer of filtered tap water. Ellipsoidal air bubbles with nominal diameters from 1.5 to 4.5 mm were injected directly into the shear layer through a single slender tube. The cinematic PIV allowed for high resolution of the unsteady liquid velocity vector field. Triple-pulsed bubble images were obtained in a temporal sequence, such that the bubble size and bubble trajectory could be accurately determined. The bubble’s oscillation characteristics, velocity, acceleration, and buoyancy force were obtained from the trajectory data. A bubble dynamic equation was then applied to allow determination of the time-evolving lift and drag forces acting upon bubbles within the shear layer. The results indicate that for a fixed bubble diameter (and fixed Bond and Morton numbers), the drag coefficient decreases for an increasing Reynolds number. This is fundamentally different than the increasing drag coefficient trend seen for ellipsoidal bubbles rising in quiescent baths for increasing diameter (and increasing Bond number), but is qualitatively consistent with the trend for spherical bubbles. A new empirical expression for the dependence of the drag coefficient on Reynolds number for air bubbles in tap water for both quiescent and turbulent flows is constructed herein. Finally, the instantaneous side forces measured in this study were dominated by the inherent deformation-induced vortex shedding of the bubble wake rather than the inviscid lift force based on the background fluid vorticity.

Systematic and extensive evidence for the existence of multiple, complete, huge stop bands in the band structure for three-dimensional (3D) cubic arrays of air bubbles in water is reported. A Fourier series expansion method, which does not require matching of the messy boundary conditions, is used to investigate all three important 3D geometries such as face-centered cubic (fcc), body-centered cubic (bcc), and simple-cubic (sc) arrangements. The lowest stop bands are largest for a volume fraction f≤10%, with a gap/midgap ratio of ≊1.8 for all three geometries. Surprising but rigorously justifiable is the fact that the low-frequency flat passbands for the perfectly periodic systems correspond to the discrete modes of a single bubble. This is an artifact of the low-filling fraction and huge density contrast in air and water. It is emphasized that such a simple inhomogeneous system made up of air bubbles in water can exhibit the widest stop bands ever reported for elastic and/or dielectric periodic composites.

This work reports systematic and extensive evidence for the existence of complete, multiple, huge stop bands in the band structures for cubic arrays of air bubbles in water. All three important structures: face-centered cubic (fcc), body-centered cubic (bcc), and simple-cubic (sc) arrangements are investigated using the Fourier-series expansion (of position dependent density and elastic constant) method. It is noteworthy that this formulation does not require matching of the messy boundary conditions. The lowest stop bands are largest for a volume fraction f≤10%, with a gap/ midgap ratio of 1.8, for all three geometries. It is found that the low-frequency, flat passbands for the perfectly periodic systems correspond to the discrete modes of a single bubble. This is an artifact of the low filling fraction and huge density contrast in air and water. It is stressed that such a simple inhomogeneous system as made up of air bubbles in water gives rise to the largest stop bands ever reported for elastic/acoustic as well as dielectric composites—save the similar 2D composites discussed in the preceding work. [This work was partially supported by CONACyT grant No. 28110E.]

A systematic and extensive evidence is presented for the existence of complete, multiple, huge stop bands in the band structure for cubic arrays of air bubbles in water. This has been demonstrated by investigating face-centered cubic (fcc), body-centered cubic (bcc), and simple-cubic (sc) arrangements using the Fourier series expansion methodology, which does not require matching of the messy boundary conditions usually needed for the inhomogeneous composite systems. The lowest stop bands are largest for a volume fraction f≤10%, with a gap/midgap ratio of ≊1.8 for all the three geometries. Surprisingly interesting but rigorously justifiable is the fact that the low-frequency flat passbands for the perfectly periodic systems correspond to the discrete modes of a single bubble. This is an artifact of the low filling fraction and huge density contrast in air and water. It is stressed that such a simple inhomogeneous system as made up of air bubbles in water exhibits the widest stop bands ever reported for phononic as well as photonic crystals. Some conclusive remarks will also be made on the reverse situation, where one can investigate the periodic system of water balloons in air.

<p>Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.</p>

Sound isolation from cubic arrays of air bubbles in water

The properties of light scattering from air bubbles in water have recently attracted considerable attention, but in practical applications such as in underwater detection, submarine imaging etc., we must take account of light scattering from various sizes of particles suspended in water. The situation of air bubbles and particles co-exist in water was studied in the first time. It is known that an air bubble in water is an example of a scatterer for which the refractive index of core (gas) is less than that of surroundings, which differs significantly from that for particles in water. Consequently, the forward light scattering characteristics of both air bubbles and typical particulate assemblages in the ocean are estimated with Mie theory, the result are analyzed and compared to validate the influence of particles on forward light scattering of air bubbles in the ocean. A preliminary laboratory experiment is also carried out to investigate the properties of forward light scattering (scattering angle less than 4 degrees) caused by particles and air bubbles and to illustrate the differences of light scattering between them.

Chapter 6 - Introduction to Bubble Dynamics and Cavitation

The air side of the water‐air interface is the most hydrophobic surface known. In quantitative terms the water‐air interface is about 30% more hydrophobic than the surfaces of nonpolar condensed‐phase compounds or materials such as octane or Teflon. The hyperhydrophobicity of the air side of the water‐air interface is the main cause of the large increase in contact angle of drops of water deposited upon rough surfaces of apolar materials, as compared with the water contact angle on smooth surfaces of the same materials. A water drop supported on a very porous fractal surface, encountering only about 1% solid support and 99% air, can reach a contact angle of 174°, which is exceedingly close to the (albeit unattainable) maximum of 180°. The water‐air interface hydrophobically attracts completely apolar molecules, as well as the apolar side of amphiphilic molecules (such as surfactants). Thus, for instance, dissolved surfactant molecules aggregate at a high concentration at the water‐air interface when dissolved in water. On the other hand, the water‐air interface repels dissolved hydrophilic (or near‐hydrophilic) solutes, such as sugars and polysaccharides, mainly via net repulsive van der Waals forces. Thus, the water‐air interface is depleted of such hydrophilic (or near‐hydrophilic) solutes, leaving a significantly higher concentration of these solutes in the bulk of the aqueous medium than at its air interface. As both of these contrasting phenomena result in strongly anisotropic concentration distributions in liquid drops and as contact angle determinations depend on a known and homogeneous free energy of cohesion of the liquid throughout the drop, one should never measure contact angles on solid surfaces for the purpose of measuring their surface thermodynamic properties by using aqueous solutions, mixtures, or solutions in or mixtures of other polar or partly polar liquids. Finally, the peculiar properties of the water‐air interface give rise to what at first sight appears to be paradoxical behavior of air bubbles in water: in pure deionized water, air bubbles attract one another and coalesce. On the other hand, upon the addition of salt (e.g., NaCl), air bubbles repel each other and thus do not coalesce, all in apparent contradiction of the classical rules governing the stability or instability of colloidal suspensions in water.

The optical glory, which is related to a weak focusing of backscattered light, was observed for bubbles in water. This caustic is affected by small deviations from sphericity. Hydrodynamics causes freely rising bubbles in pure water to become slightly spheroidal if their diameter ≳ 250 μm. We modeled and photographed the near backward scattering from spherical and slightly spheroidal horizontally illuminated bubbles. Spherical bubbles produce backward-directed glory wavefronts having the local shape of a circular torus [D. S. Langley and P. L. Marston, Phys. Rev. Lett. 47, 913–916 (1981)]. Our model introduces the leading perturbation of those wavefronts resulting from a small deviation from sphericity. The cross-polarized scattering from a sphere has a fourfold symmetric azimuthal dependence; the patterns for spheroids are typically twofold symmetric. Detailed features of the modeled patterns are confirmed by the observations. This gives a specific example of broken symmetry resulting in an unfolding of a caustic which would otherwise have an infinite co-dimension. Related unfoldings should occur in certain acoustical scattering problems. [Work supported by ONR.]