Bubble Compression Research Articles

Deformation behaviour of geotechnical materials with gas bubbles and time dependent compressible organic matter

Geotechnical materials may contain organic matters and gas bubbles during the process of their formation. The existence of compressible gas bubbles and organic matters may affect the excess pore water pressure distribution during compression and the deformation behaviour of the materials. Immediate settlement and creep have been observed in the early stage of consolidation curves of brown coal and peat samples, which can not be explained with Terzaghi's consolidation theory where soils are considered as fully saturated and soil particles are incompressible. A numerical model has been developed to model the consolidation behaviour of brown coal and peat considering the inclusion of gas bubbles and the time dependent compressible organic matters. In the model, the materials are assumed to contain incompressible minerals, compressible organic matters, gas bubbles and water. Consolidation of the materials is considered as a coupling process of water extrusion and volume variation of gas bubbles and organic matters. The model has been validated using the experimental results from one dimensional consolidation curves of brown coal and historical test results of peat. The gas content and the compressibility of organic matters can be obtained using the proposed model. The model can be used to analyze compression behaviour of geotechnical materials containing compressible particles and gas bubbles.

Fast collapse of a vapor bubble

The dynamics of collapse of a vapor bubble under the action of an instantaneously applied external pressure has been calculated. In the initial state the bubble is in thermal and mechanical equilibrium with the surrounding liquid. The bubble compression causes vapor condensation and establishment of the pressure of saturated vapor in the bubble at the interface temperature. An adiabatic increase in the temperature is presumably observed in the body of the bubble. The temperature field and the heat fluxes close to the interface have been calculated. The mass flux from the bubble has been found from the heat balance. The pressure field in the liquid was calculated for a nonviscous and incompressible liquid. As a result, a system of equations has been obtained for calculating the vapor pressure in the bubble, the bubble radius and the compression rate. The role of the condensation process in the bubble dynamics has been elucidated. The pressure and the temperature in the final stage of collapse of a bubble have been found.

Motions of deformable inclusions in a horizontally oscillating vessel with a compressible fluid

The paper is concerned with the analysis of rigid particle and compressible gas bubble motion in a horizontally oscillating vessel with a compressible fluid. A nonlinear differential equation describing motion of inclusions with respect to the vessel is derived and solved by the method of direct separation of motions. It is shown that rigid particles and gas bubbles can move both in nodes and antinodes of the pressure, depending on their size, density, and vibration parameters. The conditions under which different kinds of motion can incur have been determined. An expression for the critical radius of the bubbles which are affected by the negligible vibrational force is found. Also an approximate expression has been obtained for the average velocity of bubble׳s motion in the fluid; relationship between this velocity and bubble radius and vibration parameters has been revealed. A simple physical explanation of the noticed effects is proposed. Series of numerical experiments has been conducted, their results confirming those obtained theoretically. These results may be of interest for development of the flotation theory and other technological processes.

Extending Water Retention Curves to a Quasi‐Saturated Zone Subjected to a High Water Pressure up to 1.5 Megapascals

Core Ideas A quasi‐saturated zone with trapped air was subjected to high water pressure. Saturation was measured using a dielectric soil moisture sensor. Saturation increase due to compression of air was well described by Boyle's law. The water retention curve was extended to the positive water pressure domain. We propose a mathematical model for the water retention curve in the extended domain. On closure of an underground facility, recovery of the geoenvironmental conditions is one of the essential issues for ensuring proper implementation of closure. At the Mizunami Underground Research Laboratory, Gifu, Japan, a tunnel flooding test is underway in which a section of a deep underground tunnel is filled with groundwater and the existing desaturated zone with trapped air is subjected to high water pressure. Water saturation in the unsaturated zone as a function of capillary pressure is well understood. However, the process of a saturation increase due to a further increase in water pressure is less well studied. In this study, a simplified laboratory setup using test sands with trapped air was established in a pressure chamber. The relationship between the positive water pressure up to 1.5 MPa and saturation was measured and the effect of the compression of trapped air bubbles on the change in saturation was investigated. The experimental results showed that the saturation increased further from the initial saturation of about 0.85 at zero suction. Most of the saturation increase occurred up to a water pressure of 0.5 MPa, at which the saturation reached 0.98. At 1.5 MPa, the air bubbles were compressed to a non‐detectable level so that the sands were fully saturated. A mathematical model was established based solely on Boyle's law to define the water retention curve in a broad sense for the domain where the water pressure is positive. The measured water pressure–saturation data closely followed the relationship estimated with the established model.

Understanding soft glassy materials using an energy landscape approach.

Many seemingly different soft materials-such as soap foams, mayonnaise, toothpaste and living cells-display strikingly similar viscoelastic behaviour. A fundamental physical understanding of such soft glassy rheology and how it can manifest in such diverse materials, however, remains unknown. Here, by using a model soap foam consisting of compressible spherical bubbles, whose sizes slowly evolve and whose collective motion is simply dictated by energy minimization, we study the foam's dynamics as it corresponds to downhill motion on an energy landscape function spanning a high-dimensional configuration space. We find that these downhill paths, when viewed in this configuration space, are, surprisingly, fractal. The complex behaviour of our model, including power-law rheology and non-diffusive bubble motion and avalanches, stems directly from the fractal dimension and energy function of these paths. Our results suggest that ubiquitous soft glassy rheology may be a consequence of emergent fractal geometry in the energy landscapes of many complex fluids.

Post Dural Puncture Headache—Review and Suggested New Treatment

Objectives: After reading this article, readers should be able to recognize Post Dural Puncture Headache, understand its mechanism and diagnostic criteria, evaluate the different treatment options available, and be familiar with a novel treatment option. Background: Post-dural puncture headache is the most common serious complication resulting from lumbar puncture and epidural or spinal anesthetics. The syndrome is characterized by severe headache that occurs within 48 hours following the puncture, located in the frontal and/or occipital region, worsened in the upright position and refractory to routine analgesia. The syndrome incidence was reported to be approximately 1% with typical obstetric anesthesiology practice which reflects more than 20,000 cases per 2014 in the US. Two possible mechanisms are hypothesized as responsible for this syndrome; cerebrospinal fluid leakage and pneumocephalus. Multiple methods of treatment have been applied with wide-ranging results. Design or Methods: Review article with introduction of a novel treatment option. Results: We postulate that Hyperbaric Oxygen Therapy can be used to treat post-dural puncture headache. The rationale for treatment is dual: enhancement of fibroblast proliferation at the site of dural puncture to facilitate faster closure of the tear and compression of air bubbles in case of pneumocephalus according to Boyle’s law. We also claim that hyperbaric oxygen therapy should be considered a prophylactic treatment, if a dural tear is suspected.

Deformation of a shock wave under strong compression of nonspherical bubbles

The deformation of a radial convergent shock wave appearing inside a spheroidal cavitation bubble under strong compression is studied. It is shown that the shock wave in the course of its convergence can be deformed strongly. In particular, initially the most convex parts of the contour of the surface of the shock wave in its axial cross section can first become rectilinear and then be transformed into concave regions. Along with the formation of concave regions in the contour, sharpenings appear in it. Further small rectilinear regions can be formed instead of sharpenings. In the considered cases of initially elongated and flattened bubbles, the closure of the shock wave begins in the center of the bubble, just as under the closure of a spherical shock wave in an ideal spherical bubble.

Evaluation of friction heating in cavitating high pressure Diesel injector nozzles

Variation of fuel properties occurring during extreme fuel pressurisation in Diesel fuel injectors relative to those under atmospheric pressure and room temperature conditions may affect significantly fuel delivery, fuel injection temperature, injector durability and thus engine performance. Indicative results of flow simulations during the full injection event of a Diesel injector are presented. In addition to the Navier-Stokes equations, the enthalpy conservation equation is considered for predicting the fuel temperature. Cavitation is simulated using an Eulerian-Lagrangian cavitation model fully coupled with the flow equations. Compressible bubble dynamics based on the R-P equation also consider thermal effects. Variable fuel properties function of the local pressure and temperature are taken from literature and correspond to a reference so-called summer Diesel fuel. Fuel pressurisation up to 3000bar pressure is considered while various wall temperature boundary conditions are tested in order to compare their effect relative to those of the fuel heating caused during the depressurisation of the fuel as it passes through the injection orifices. The results indicate formation of strong temperature gradients inside the fuel injector while heating resulting from the extreme friction may result to local temperatures above the fuel's boiling point. Predictions indicate bulk fuel temperature increase of more than 100°C during the opening phase of the needle valve. Overall, it is concluded that such effects are significant for the injector performance and should be considered in relevant simulation tools.

Determination of Undissolved Air Content in Oil by Means of a Compression Method

This article describes a combination of experimental and mathematical methods for determination of undissolved air content in hydraulic oil. The experimental part consists in determination of oil bulk modulus considering an influence of undissolved air by means of a volume compression method in steel pipe. A multiphase model of an oil/undissolved air mixture is subsequently defined using Matlab SimHydraulics software. The multiphase model allows to include volume compression of oil and air bubbles independently of each other. Furthermore, time dependencies of pressures are mathematically simulated during compression of the multiphase mixture of oil and undissolved air for different concentrations of undissolved air. The undissolved air content is determined by comparing of mathematically simulated and experimentally measured time dependencies of pressure increases.

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

Steady-state size distribution of air bubbles in polar ice

Between the close-off depth and the bubble-to-hydrate transition zone in polar ice sheets, the geometrical properties of air bubbles, such as number concentration and size of bubbles, are mainly controlled by firn temperature and ice accumulation rate prevailing during the snow to ice transformation [3], and by the bubble compression in the course of bubbly ice densification [13]. This implies that the data on the bubble properties can be used for reconstruction of the past climate change. On the basis of our earlier studies of bubbly ice densification and the new measurements of air bubbles in the Antarctic ice cores, we have developed a theory of bubble evolution in polar ice and propose an inverse procedure for bubble size conversion to specified conditions at the close-off depth. Both outcomes of the research contribute to elaboration of the new paleoclimatological tool based on the bubble properties.

Investigation of the crater-like microdefects induced by laser shock processing with aluminum foil as absorbent layer

This paper reports that 3D crater-like microdefects form on the metal surface when laser shock processing (LSP) is applied. LSP was conducted on pure copper block using the aluminum foil as the absorbent material and water as the confining layer. There existed the bonding material to attach the aluminum foil on the metal target closely. The surface morphologies and metallographs of copper surfaces were characterized with 3D profiler, the optical microscopy (OM) or the scanning electron microscopy (SEM). Temperature increases of metal surface due to LSP were evaluated theoretically. It was found that, when aluminum foil was used as the absorbent material, and if there existed air bubbles in the bonding material, the air temperatures within the bubbles rose rapidly because of the adiabatic compression. So at the locations of the air bubbles, the metal materials melted and micromelting pool formed. Then under the subsequent expanding of the air bubbles, a secondary shock wave was launched against the micromelting pool and produced the crater-like microdefects on the metal surface. The temperature increases due to shock heat and high-speed deformation were not enough to melt the metal target. The temperature increase induced by the adiabatic compression of the air bubbles may also cause the gasification of the metal target. This will also help form the crater-like microdefects. The results of this paper can help to improve the surface quality of a metal target during the application of LSP. In addition, the results provide another method to fabricate 3D crater-like dents on metal surface. This has a potential application in mechanical engineering.

BEM-based numerical study of three-dimensional compressible bubble dynamics in stokes flow

The dynamics of compressible gas bubbles in a viscous shear flow and an acoustic field at low Reynolds numbers is studied. The numerical approach is based on the boundary element method (BEM), which is effective as applied to the three-dimensional simulation of bubble deformation. However, the application of the conventional BEM to compressible bubble dynamics faces difficulties caused by the degeneration of the resulting algebraic system. Additional relations based on the Lorentz reciprocity principle are used to cope with this problem. Test computations of the dynamics of a single bubble and bubble clusters in acoustic fields and shear flows are presented.

A modified model for simplified description of evolution of a single bubble upon increase in the pressure of the surrounding fluid

The problem of evolution of a single vapor bubble after an increase in the pressure of the surrounding fluid is considered. In contrast to the classical formulation of this problem, the fluid pressure is set at a finite distance from the bubble. For the case when this distance is large, an analytical solution is found, which relates the bubble compression rate with its current radius. On the basis of the solution obtained, the regimes of bubble compression and fluid pressure upon bubble compression in the collapse regime are investigated.

Direct numerical simulation of three-dimensional dynamics of compressible bubbles in acoustic field using boundary element method

In the present work the dynamics of bubbles containing compressible gas is studied in the presence of an acoustic field at low Reynolds numbers. The numerical approach is based on the boundary element method (BEM), which is effective for three-dimensional simulation. The application of the standard BEM to the compressible bubble dynamics faces the problem of the degeneracy of the algebraic system. To solve this problem, additional relationships based on the Lorentz reciprocity principle are used. Test calculations of the dynamics of one and several bubbles in an acoustic field are presented.

Macro-mechanical modeling of blast-wave mitigation in foams. Part III: verification of the models

Three different approaches to macro-mechanical modeling of blast-wave mitigation in foam namely: the single-phase effective gas flow model, the two-phase mixture model and the single bubble/shock wave interaction model are critically reviewed. The nature and extent of the approximations inherent in the formulation of the first two models were examined in Part I of this study. In this part, the applicability of the aforementioned approaches is verified based on a comparison of experimental pressure records obtained in shock tube tests with the results of numerical predictions that used the models under consideration. Deficiencies and inconsistencies that are found during this comparison are clarified and possible improvements are suggested. It is emphasized that both the single-phase and the two-phase approaches predict well the refraction of the incident shock at the air/foam interface while they do not uniquely determine the relaxation process and the shape of the transmitted shock wave front. Various flexibilities that are exploited to better describe the inter-phase interactions do not improve the results significantly. The single bubble model is examined with particular attention paid to the manner in which it predicts the shape of the shock wave front. Connections between the flow viscosity and the transient dynamics of the bubble compression that occur at scales of the shock wave front thickness are explored.

Generation of cavitation luminescence by laser-induced exothermic chemical reaction

Absorption of high power laser radiation by aqueous carbon suspensions is known to result in the formation of highly compressed bubbles of hydrogen and carbon monoxide through the endothermic carbon-steam reaction. The bubbles expand rapidly, overreaching their equilibrium diameter, and then collapse tens to hundreds of microseconds after formation to give a flash of radiation. Here we report on the effects of laser-initiated exothermic chemical reaction on cavitation luminescence. Experiments with hydrogen peroxide added to colloidal carbon suspensions show that both the time of the light flash following the laser pulse and the intensity of luminescence increase with hydrogen peroxide concentration, indicating that large, highly energetic gas bubbles are produced. Additional experiments with colloidal carbon suspensions show the effects of high pressure on the luminescent intensity and its time of appearance following firing of the laser.

Modified Bubble Core Fields and Bubble Shape in Laser Driven Plasma

Bubble core fields as well bubble shape modification due to the nondepleted electrons inside the bubble is investigated theoretically. It is found that the slope of transverse fields are reduced significantly, however, the slope of longitudinal electric field, which plays a key role on electrons acceleration in bubble, changes little. Moreover a modified longitudinal compressed bubble shape leads to a shorter dephasing distance which makes the electrons acceleration energy reduced to some extent. As a comparison we perform particle-in-cell simulations whose results are consistent with that of our theoretical consideration.

Temperature-Dependent Biphasic Shrinkage of Lipid-Coated Bubbles in Ultrasound

Lipid-coated microbubbles and emulsions are of interest as possible ultrasound-mediated drug delivery vehicles and for their interesting behaviors and fundamental properties. We and others have noted that bubbles coated with the long chain saturated phospholipid distearoylphosphatidylcholine (DSPC) rapidly shrink to a quasistable size when repeatedly insonated with short ultrasound pulses; such stability may adversely affect the bubble's subsequent ability to deliver its pharmacological cargo. Bubbles coated with the unsaturated lipid dioleoylphosphatidylcholine (DOPC) did not show stability but did undergo an abrupt change from rapid initial shrinkage to a slow persistent shrinkage, leading ultimately to dissolution or dispersion. As DOPC and DSPC differ not only in chain saturation but also phase behavior, we performed additional studies using dimyristoyl PC (DMPC) as a coat lipid and controlled the solution temperature to study bubble behavior on exposure to repeated ultrasound pulses for the same coat, in both fluid and gel phases. We find, first, that essentially all bubbles show an initially rapid shrinkage, in which gas loss exceeds the limit imposed by gas diffusion into the surrounding medium; this rapid shrinkage may be evidence of nanoscopic bubble fragmentation. Second, upon reaching a fraction of their initial size, bubbles begin a slower shrinkage with a shrinkage rate that depends on the resting phase state of the coat lipid: fluid DMPC monolayers give a more rapid shrinkage than gel phase. DOPC-coated bubbles showed no temperature-dependent responses in the same temperature range. The results are especially interesting in that bubble compression during the pulse is likely to adiabatically heat the bubble and fluidize the coat, regardless of its initial phase state; thus, some structural feature of the resting coat, such as defect lines in the gel phase, may be important in the subsequent response to the ~3 μs ultrasound pulse.

Compressible multi-scale magnetic constructs: decorating the outer surface of self-assembled microbubbles with iron oxide nanoparticles

This paper reports the elaboration of size-controlled resilient echogenic micron-size bubbles that have a soft shell made from self-assembled perfluoroalkylated phosphates and iron oxide nanoparticles grafted on their external surface. The high echogenicity, characteristic of compressible gas bubbles, is retained. These hybrid constructs have potential as bimodal contrast agents for ultrasound and magnetic resonance imaging.