Bubble Compressibility Research Articles

Numerical investigation of acoustic droplet vaporization and tissue deformation

Acoustically-triggered droplet vaporization (ADV) and tissue deformation are numerically analyzed by extending a numerical model for ADV process based on a level-set method, which considers multiple interfaces between bubble, droplet and ambient water regions, bubble compressibility and droplet-bubble phase change, to include nearby tissue deformation using a full Eulerian formulation. The tissue is assumed to be a viscoelastic neo-Hookean material to properly handle large deformation. The numerical results show that droplet vaporization causes greater tissue deformation than isothermal bubble growth under the same acoustic and initial size conditions. The computations of ADV near a deformable solid demonstrate various bubble-tissue interactions such as mushroom-shaped bubble formation near an elastic tissue, tissue compression due to high-speed liquid jet, and large tissue deformation and perforation caused by the non-spherical bubble re-expansion and bubble entrapment. The effects of droplet-tissue distance and elastic shear modulus on the tissue deformation and perforation are investigated.

Acoustic waves in saturated porous media with gas bubbles.

The present framework employs various interface characteristics of gas bubbles into a continuum description of acoustics in porous media. It first extends the bubble compressibility in classic models by surface tension and higher-order curvature effects. This modelling extension is significantly relevant to estimate the impact of interface effects, e.g. on emerging nano-scale bubbles or pickering emulsions. The gas bubble dynamics is then homogenized to derive a manageable set of continuum equations. Respective assumptions and limitations are summarized in this process to provide a quick reference when choosing the compromise between a model's complexity and applicability. The acoustic response of a water-saturated sandstone with gas bubbles is finally evaluated with respect to the practical importance at ambient and reservoir conditions. The shape of the bubble-size distribution is represented in the evolution of the inverse quality factor but less distinct in the dispersion of the phase velocity. The presented, rigorous framework thus allows to predict what frequencies and acoustic properties relate to specific gas bubble sizes and whether respective signals may be detected with current apparatus. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Numerical investigation of acoustic vaporization threshold of microdroplets

A numerical model is presented for the acoustic vaporization threshold of a dodecafluoropentane (or perfluoropentane) microdroplet. The model is based on the Rayleigh-Plesset equation and is improved by properly treating the supercritical state that occurs when a bubble collapses rapidly and by employing the van der Waals equation of state to consider the supercritical state. The present computations demonstrate that the microdroplet vaporization behavior depends intricately on bubble compressibility, liquid inertia and phase-change heat transfer under acoustic excitation conditions. We present acoustic pressure-frequency diagrams for bubble growth regimes and the ADV threshold conditions. The effects of acoustic parameters, fluid properties and the droplet radius on the ADV threshold are investigated.

벽 근처에서 안티버블 거동에 관한 수치모사

Numerical study is conducted for the acoustically-driven oscillation of an antibubble, which is a composite of droplet core and surrounding bubble. The interfaces between the droplet, bubble and surrounding liquid regions are calculated by two level-set functions. The conservation equations in the three regions are solved by using the ghost-fluid method to treat the interface conditions and the semi-implicit pressure correction method to consider the bubble compressibility effect. The numerical results for antibubble oscillation compare well with the theoretical predictions when the antibubble is far from the wall. The presence of wall inhibits the antibubble oscillation and reduces its resonance frequency. The effects of wall, acoustic amplitude and droplet-bubble volume ratio on the antibubble oscillation are investigated.

Numerical investigation of acoustically-triggered droplet vaporization in a tube

Acoustically-triggered droplet vaporization (ADV) in a tube is numerically studied by extending a level-set method to determine the bubble-droplet interface as well as the droplet-ambient liquid interface and to include droplet evaporation and bubble compressibility effects. The Rayleigh-Plesset equation for ADV in a tube is improved by correctly evaluating the transition from spherical to tube flows. The computations of ADV show that the liquid pressure variation along the tube caused by droplet vaporization and bubble condensation is an important factor determining bubble survival and growth. The influence of tube radius on bubble growth in ADV is quantified in various acoustic amplitude and frequency conditions. Computations are also performed to investigate bubble-bubble interaction in acoustic vaporization of two droplets.

Surfactant stabilized bubbles flowing in a Newtonian fluid

Bubbles suspended in a fluid cause the suspension to have different rheological properties than the base fluid. In general, the viscosity of the suspension increases as the volume fraction of the bubbles is increased. A current application, and motivation for this study, is in wellbore cements used for hydrocarbon extraction and carbon sequestration. In these settings, the gas bubbles are dispersed into the cement to reduce the density as well as improve the properties for specific conditions or wellbore issues. In this paper, we use Stokesian dynamics to numerically simulate the behavior of a large number of bubbles suspended in a Newtonian fluid. Going beyond prior work on simulating particles in suspension, we account for the nature of bubbles by allowing for slip on the bubble surface, the deflection on the bubble surface, and a bubble–bubble pairwise interaction that represents the surfactant physics; we do not account for bubble compressibility. We incorporate these interactions and simulate bubble suspensions of monodisperse size at several volume fractions. We find that the bubbles remain better dispersed compared with hard spherical particles that show a greater tendency to structure or cluster.

Numerical study of droplet vaporization under acoustic pulsing conditions

Bubble growth and collapse in acoustic droplet vaporization (ADV) are numerically studied by employing the level-set interface tracking method, which is extended to examine bubble compressibility, phase change, and multiple interfaces between bubble–droplet and droplet–ambient liquid phases. Numerical results on the vaporization of dodecafluoropentane droplets show that the acoustic pressure amplitude and frequency considerably affect bubble survival and collapse in the ADV process, whereas the number of acoustic cycles exerts minimal influence on it. The effects of acoustic pulsing conditions on the vaporization of droplets with high surface tension are also quantified.

INFLUENCE OF SURFACE PROPERTIES ON AXISYMMETRICAL OSCILLATIONS OF A CYLINDRICAL BUBBLE

We consider the oscillations of an oblate gas bubble in the vibrational field with the emphasis placed on the interplay between the bubble compressibility and the contact line motion. The bubble is surrounded by an incompressible fluid and is bounded in the axial direction by two parallel solid surfaces. The velocity of the contact line is assumed to be proportional to the deviation of the contact angle from the equilibrium value. The proportionality coefficients (Hocking parameter) are different for each plate. The frequencies and damping rates of the bubble eigenmodes are studied as a function of the problem parameters. The frequency of the volume (breathing) mode of free oscillations can vanish in a certain interval of the values of the Hocking parameter. This frequency significantly depends on the gas pressure, giving rise to double response: when the external frequency is close to the eigenfrequencies of both the volume and shape modes and when the unlimited growth of the amplitude occurs irrespective of the Hocking parameter. The radial pulsations become small with increase in the gas pressure and the bubble behavior is consistent with the dynamics of an incompressible drop. Different Hocking parameters determine different damping rates, but dissipation in the whole system is determined by their total contribution.

Numerical simulation of acoustic droplet vaporization near a wall

Numerical simulations are performed for acoustic-driven vaporization of a volatile droplet near a wall by introducing two level-set functions to track the droplet and bubble surfaces. The level-set method is combined with the ghost-fluid and semi-implicit pressure correction methods to implement the effects of liquid-vapor phase change and bubble compressibility. The computations demonstrate the bubble growth in the whole acoustic vaporization process of a dodecafluoropentane droplet and its interaction with a nearby wall. The effects of acoustic pulsing amplitude and frequency as well as initial droplet location and size on the bubble growth and wall shear stress are quantified.

An approach to couple velocity/pressure/void fraction in two-phase flows with incompressible liquid and compressible bubbles

A numerical approach to incorporate the compressibility of bubbles to a two-phase solver with incompressible liquid is presented. The scheme introduces a bubble mass density equation and the ideal gas law (though other thermodynamic relations can also be used) to compute the void fraction for use in the continuous phase equations. Pressure and velocity are strongly coupled on a collocated grid scheme by obtaining face velocities through nonlinear interpolation from nodal values using an algebraic equation. Tight coupling is achieved for pressure and void fraction by careful treatment of the bubble transport and compressibility terms in the resulting pressure Poisson equation. The novel proposed implicit strategy prevents numerical instabilities even at high void fractions and highly compressible bubbles. In addition, the proposed method can capture acoustic waves for void fractions between 0.1% and 90% with errors in speed of sound of less than 2% respect to the speed of sound of isothermal compressible bubbles and water mixtures. 1D, 2D and 3D numerical tests, including the bubbly flow around a surface ship, are performed to demonstrate robustness and range of applications of the proposed scheme. The approach is shown to be stable at high void fractions when other schemes fail.

A sharp-interface level-set method for compressible bubble growth with phase change

A sharp-interface level-set method is presented for simulating the growth and collapse of a compressible vapor bubble. The interface tracking method is extended to include the effects of bubble compressibility and liquid-vapor phase change by incorporating the ghost fluid method to efficiently implement the matching conditions of velocity, stress and temperature at the interface. The numerical results for one-dimensional compressible flows and spherical bubble growth show good agreement with the exact solutions. The level-set method is applied to investigate the effects of phase change, ambient temperature and wall on the compressible bubble growth and collapse.

Low-frequency measurement of encapsulated bubble compressibility

Interest in measuring underground water flow has motivated synthesis of encapsulated microbubbles for use as contrast agents. The large acoustic attenuation in earth prohibits use of the high frequencies required to exploit resonant scattering. Instead, contrast enhancement must rely on the reduction of acoustic impedance due to higher compressibility of the microbubbles. Bubble compressibility is measured at the kilohertz frequencies of interest using a resonance tube filled with water and observing the change in tube resonance frequency due to the presence of bubbles for different void fractions [Wilson and Dunton, J. Acoust. Soc. Am. 125, 1951 (2009)]. Buoyancy makes it difficult to maintain a uniform distribution of bubbles throughout the tube in order to relate sound speed to resonance frequency. Therefore, the bubbles were restrained with acoustically transparent barriers to form discrete layers within the water column. A model was developed to investigate the effect on the tube resonance frequency due to different spatial distributions of the bubble layers, and the predictions were compared with measurements. Good agreement with the known compressibility of air was obtained experimentally with only three or four layers. [Work supported by Advanced Energy Consortium.]

The effect of depth-dependent distribution of bubbles on internal waves

A new type of gravity waves associated with the subsurface layers of bubbles existing ubiquitously in the ocean is considered. Due to bubble compressibility, such a layer creates a vertical density gradient. Although the density changes due to bubbles are small, the corresponding gradient can be significant, at least comparable with or even exceeding the natural density gradient due to the temperature or salinity variations. As a result, the bubbles may affect propagation of short-period internal waves or even be exclusively responsible for the internal modes in otherwise homogeneous water. These modes can be strongly localized near the surface and thus contribute to ripple modulation, affect sound propagation, etc. The dispersion equation for the bubble-affected internal waves is derived, and the corresponding modal structures are plotted. Some estimates are made and limitations of the simple model considered under real conditions are discussed.

Deformation of a Spherical Bubble in Soft Solid Media under External Pressure

In this paper, a theoretical investigation on the deformation of a spherical bubble embedded in soft solid media under externally applied pressure is presented. The effects that surface tension and mechanical properties have on interactions between the bubble compressibility and the surrounding medium are quantified. Within the framework of classical plasticity theory and following the refined treatment for large plastic displacements set forth by Chadwick, solutions are found for the finite deformation of the bubble radius and the internal bubble pressure in terms of implicit functions. Solutions are applicable to a wide range of material properties and external forcing conditions when soft solid media undergo elastic and finite plastic deformations. The validity of the solutions is not restricted to small values of the ratio between yield stress and elastic modulus. It is hypothesized that the existence of a plastic region in the neighbourhood of the bubble might explain upward bubble migration in soft solids due to pressure fluctuations in the presence of a gravitational field. Examples of the main features of the solutions are discussed in terms of dimensionless parameters.

On the Stability of Parallel Bubbly Cavitating Flows

This paper illustrates the effects of the dynamics of bubbles with arbitrary vapor-gas contents on the inviscid and viscous stability of two-dimensional parallel bubbly flows of low void fraction. The linear perturbation equations derived for the stability analysis include the effects of bubble compressibility, inertia, and energy dissipation due to the viscosity of the liquid and the transfer of heat and mass as a consequence of compression/expansion of the noncondensable gas and evaporation/condensation of the vapor contained in the bubbles. Numerical solution of the spatial stability problem for two-dimensional inviscid shear layers and Blasius boundary layers confirms that the presence of the dispersed phase is generally in favor of stability. Significant deviations from the classical results for compressible and incompressible single phase fluids are observed, especially when the occurrence of large compliant and/or resonant oscillations of the bubbles greatly enhances their dynamic coupling with the perturbation field. More importantly, the present analysis points out some major differences in the stability of parallel flows with noncondensable gas bubbles with respect to cavitating flows containing bubbles with a dominant content of vapor. Unconditional stability is predicted in the travelling bubble cavitation limit for low pressures and high vapor mass fraction of the bubble contents. Results are shown to illustrate these effects for some representative flow configurations and conditions. [S0098-2202(00)00603-9]

Foam in porous media: thermodynamic and hydrodynamic peculiarities

Thermodynamic and hydrodynamic properties of foams in porous media are examined from a unified point of view. We show that interactions between foam films (lamellae) and wetting films covering the pore walls play an important role in treating experimental data and constructing a general theory of foam residence and motion through porous media. Mechanisms of in situ bubble generation, foam patterning, and rheological peculiarities of foams in pores are discussed in detail. In particular, we clarify the difference between foam lamellae and liquid lenses, focusing on intermolecular forces in thin foam and wetting films. A consistent description of conditions of mechanical equilibrium of curved lamellae, including dynamic effects, is presented for the first time. This microlevel approach enables us to describe the dependence of the capillary pressure in the Plateau border on the current state of the pair ‘wetting film–foam lamella’. We review a theory of foam patterning under a load. Two driving forces are invoked to explain specific interactions between the solid skeleton and foams. The binding forces caused by bubble compressibility and the pinning forces due to capillarity determine a specific ordering of lamellae in porous media. The microscopic bubble train model predicts asymptotic expressions for the start-up-yield pressure drop. We consider key problems that underlay the understanding of physical mechanisms of anomalous foam resistance. Different micromechanical models of foam friction are thoroughly discussed. Bretherton's (1961) theory of the forced, steady fluid–fluid displacement is reviewed in application to bubble transport through pore channels. The origins of disagreement of the theory and experiment are discussed. The Bretherton theory is augmented based on a new sailboat model, which accounts for thermodynamic coupling of foam lamellae and wetting films. Special attention is paid to studies of stick-slip motion of lamellae and bubbles in pores of varying diameter. Finally, we discuss macroscale models and analyze topical problems of foam behavior in porous media, including reservoirs, granular, and fibrous materials.

Assessment of pulmonary surfactant function using a captive-bubble surfactometer

A captive-bubble surfactometer was built to measure the surface properties of reconstituted pulmonary surfactants ( l-α-dipalmitoyl phosphatidylcholine (DPPC), Exosurf, Alveofact) and whole lung surfactants obtained from normal and injured rat lungs (silica induced Lipoproteinosis). Whole surfactants from normal or injured rats were further characterized by protein and phospholipid measurements. We used soluble test substances (ethanol, water) to ascertain the precision, reliability, and cleanliness of the captive-bubble surfactometer. We performed three types of experiments by controlling the system pressure on the air bubble: adsorption, dynamic, and quasi-static cycling. Lateral views of the bubble were continuously recorded. The bubble height and diameter were determined by image analysis and were used for the calculation of bubble tension and related parameters. Adsorption was slow with DPPC, faster with Exosurf and Alveofact, and fastest with whole lung surfactants. During the dynamic cycling experiments, DPPC immediately exhibited low bubble tension. The bubble tension for Exosurf, Alveofact, and whole lung surfactants showed both decreasing values at minimum area and increasing values at maximum area during dynamic cycling. In initial cycles of the quasi-static cycling experiments, isotherm hystereses were different for the various surfactants, and the bubble tension and compressibility were least with pure DPPC as compared to Exosurf and Alveofact. In contrast to all other surfactants, DPPC showed minimal refinement of film characteristics after repeated cycling. Whole lung surfactants exhibited surface properties comparable to those of reconstituted surfactants, albeit at only half the phospholipid concentration. Whole lung surfactant from injured rat lungs was characterized by increased lipid and protein content, whereas changes in the phospholipid composition and surface activity were only subtle compared to surfactant obtained from normal rat lungs. The characterization of the surface properties of biological substances using the captive-bubble surfactometer is feasible and discriminates between different reconstituted and whole surfactants. This method is useful for studying biological materials because it enables measurements of surface properties under dynamic non-equilibrium conditions without film leakage, which is in contrast to other methods.

Nonlinear response of an ideal gas bubble to ambient pressure change in a quiescent fluid

This paper is concerned with the small-amplitude oscillations of a bubble composed of an ideal gas in response to anabrupt change in the ambient pressure field. Specifically, we consider the bubble response to a pressure pulse and a pressure step in an otherwise quiescent fluid. The method of analysis employed in the present study is a standard two-timing expansion to eliminate a secular behavior encountered in the asymptotic expansion. In the impulse response the secularity is self-induced due solely to the nonlinearity of the problem whereas the secularity in the step response arises from the change in the equilibrium bubble volume caused by the ambient pressure change. The two-timing solution for each response shows that the secularity modifies the natural frequency of the radial oscillation. Further, the critical intensity of either the pressure pulse or the pressure step for existence of the steady-state bubble radius is determined from the frequency modulated solution and the stability of the bubble response is also discussed in terms of the bubble compressibility and heat transfer across the interface.

Thermodynamic corrections to the sound velocity in a bubbly medium

For sufficiently low frequencies so that the adiabatic assumption holds, the sound velocity in a bubbly medium consisting of an air—water froth has been described by Wood's equation [A. L. Anderson and L. D. Hampton, J. Acoust. Soc. Am. 67, 1865–1889 (1980)] where the adiabatic compressibilities and densities of the bubble (heretofore air) and water are weighted by their respective fractional volumes. For adiabatic volume changes, bubble compressibility is inversely proportional to the ratio of specific heats. Heretofore, the specific heats considered were those for air. But bubbles innately have two additional degrees of freedom due to the energies partitioned into surface tension and buoyancy. These two additional degrees of freedom are investigated and a corrected ratio of specific heats is developed for incorporation into Wood's equation. In all cases, this correction lowers the sound velocity in a bubbly medium. [Work supported by the Independent Research Program of the Naval Ocean Systems Center.]

The collapse of a non-hemispherical bubble attached to a solid wall

The problem of the collapse of a vapour/gas bubble attached to a solid wall and initially perturbed from a hemispherical shape is solved numerically by the variational method, in which the bubble's viscosity and compressibility in liquid are neglected. The effects of surface tension on the collapsing bubble are taken into account. The rebounding processes of a non-hemispherical gas bubble are simulated: the gas inside the bubble undergoes an adiabatic process. The results of numerical calculations are given for two initial shapes: one is close to a prolate spheroid, the other is close to an oblate spheroid. The governing equations for the motion of a bubble can be written in matrix form, which is simpler than that derived from perturbation theory. This analysis using the variational method may be applied to more complicated problems.