The Evolution of a Gas Bubble Near an Inclined Wall

The nonlinear dynamics of a gas bubble close to an inclined wall is investigated numerically. The fluid is assumed to be inviscid and incompressible and the flow irrotational. A time-integration boundary integral method is used to solve the Laplace equation for the velocity potential to calculate the shape and position of the bubble. Improvements to the previous research on this subject have been made in the surface triangulation of the initial spherical bubble, the integration of the influence coefficients, the calculations of the normal vector and tangential velocity vector at a node, the time integration scheme, etc. Comparisons have been carried out between the results of the present three-dimensional model and the results of a validated axis-symmetrical bubble code (Wang et al., 1996a,b, 1998) for axis-symmetrical cases. The comparisons demonstrate the robustness and accuracy of the present method. Simulations have been carried out for a gas bubble initiated at 3.0R _m, 2.0R _m, and 1.0R _m (R _m being defined as the maximum radius of the bubble) from an inclined wall with various buoyancy parameters and wall angles. All the simulations are performed at high resolution and without numerical instabilities occurring nearly up until the re-entrant jet impacts on the opposite bubble surface. The following qualitative features have been observed. When a bubble is initiated at $3.0R_{\rm m}$ or more away from an inclined wall, the jet is roughly symmetric; the jet direction is roughly the same as that of the motion of the bubble centroid, which can be approximately predicted by the Kelvin impulse theory. When a bubble is initiated around 2.0R _m from a wall, the jet is obviously asymmetric and inclined upwards; the Kelvin impulse theory can only be used to predict the location where the jetting occurs, but it can no longer be used to predict the jet direction. When a bubble is initiated at 1.0R _m or less near an inclined wall and the buoyancy and Bjerknes attraction are comparable, the jet is roughly in the upward direction. Received 6 August 1997 and accepted 9 April 1998     

Numerical study of bubble rise and interaction in a viscous liquid

In this article, the flow instabilities during the rise of a single bubble in a narrow vertical tube are studied using a transient two-dimensional/axisymmetric model. To predict the shape of the bubble deformation, the Navier-Stokes equations in addition to an advection equation for liquid volume fraction are solved. A modified volume-of-fluid technique based on Youngs' algorithm is used to track the bubble deformation. To validate the model, the results of simulations for terminal rise velocity and bubble shape are compared with those of the experiments. The effect of different parameters such as initial bubble radius, channel height, liquid viscosity and surface tension on the shape and rise velocity of the bubble is investigated.     

Single cavitation bubble generation and observation of the bubble collapse flow induced by a pressure wave

This study utilizes a U-shape platform device to generate a single cavitation bubble for a detailed analysis of the flow field characteristics and the cause of the counter jet during the process of bubble collapse caused by sending a pressure wave. A high speed camera is used to record the flow field of the bubble collapse at different distances from a solid boundary. It is found that a Kelvin–Helmholtz vortex is formed when a liquid jet penetrates the bubble surface after the bubble is compressed and deformed. If the bubble center to the solid boundary is within one to three times the bubble’s radius, a stagnation ring will form on the boundary when impinged by the liquid jet. The fluid inside the stagnation ring will be squeezed toward the center of the ring to form a counter jet after the bubble collapses. At the critical position, where the bubble center from the solid boundary is about three times the bubble’s radius, the bubble collapse flow will vary. Depending on the strengths of the pressure waves applied, the collapse can produce a Kelvin–Helmholtz vortex, the Richtmyer–Meshkov instability, or the generation of a counter jet flow. If the bubble surface is in contact with the solid boundary, the liquid jet can only move inside-out without producing the stagnation ring and the counter jet; thus, the bubble collapses along the radial direction. The complex phenomenon of cavitation bubble collapse flows is clearly manifested in this study.     

Bubble generation and transport in a microfluidic device with high aspect ratio

Bubble generation and transport in a micro-device composed of a micro-T-junction and a following serpentine micro-channel was experimentally investigated. It has a rectangular cross-sectional with an aspect ratio of 7.425. Air and water were used as gas and liquid, respectively. Mixtures of water–glycerol and water–Tween-20 were used to study the effects of liquid viscosity and surface tension. Compared with previous T-junction bubble generation, the liquid and gas inlets orientation was switched in this work. The continuous flow was driven from the perpendicular channel and the dispersion flow was from the main channel. It shows that the break-up process has three periodic steps under certain operating conditions. The dimensionless bubble length L/w in the micro-channel with high aspect ratio is much larger than that in square microchannels. A correlation is proposed to correlate L/w with liquid flow rate J_L, gas flow rate J_G, and liquid viscosity μ_L. Surface tension σ can change the bubble shape but almost does not affect the bubble length in this fast break-up process. Additionally, a long bubble may be broken up at the corners at the same time because the locations of gas and liquid are exchanged relative to the concave and convex portions of an elbow after a turn which may result in the change of fluid velocities and gas–liquid pressure drop.     

Ellipsoidal Oscillations of a Gas Bubble with Periodic Variation of the Surrounding Fluid Pressure

Ellipsoidal linear and nonlinear oscillations of a gas bubble under harmonic variation of the surrounding fluid pressure are studied. The system is considered under conditions in which periodic sonoluminescence of the individual bubble in a standing acoustic wave is observable. A mathematical model of the bubble dynamics is suggested; in this model, the variation of the gas/fluid interface shape is described correct to the square of the amplitude of the deformation of the spherical shape of the bubble. The character of the air bubble oscillations in water is investigated in relation to the initial bubble radius and the fluid pressure variation amplitude. It is shown that nonspherical oscillations of limited amplitude can occur outside the range of linearly stable spherical oscillations. In this case, both oscillations with a period equal to one or two periods of the fluid pressure variation and aperiodic oscillations can be observed.     

NUMERICAL STUDY OF THE BEHAVIOR OF A BUBBLE ATTACHED TO A TIP IN A NONUNIFORM ELECTRIC FIELD

In order to investigate the effects of a nonuniform electric field on the behavior of a bubble, a numerical study on the shape of a bubble attached to a conducting tip on a supporting wall is performed. The equilibrium bubble shape is determined by solving the free boundary problem that consists of the governing equation for electric field and the normal stress condition at the bubble surface. A numerically generated composite orthogonal coordinate system is employed to solve the free boundary problem. A bubble on a tip is found to be extended in the direction parallel to the applied electric field. The elongation increases steeply with an increase of the electric field strength and the height of the tip. It is also observed that a highly elongated bubble has a shape with slender waist. The bubble shape obtained from numerical studies are qualitatively similar to the shapes observed in experiments. If the contact radius is maintained during bubble deformation, the contact angle and the aspect ratio increase with the increase of the electric field strength and the tip height. On the other hand, if the contact angle is fixed during bubble deformation, the contact radius decreases as the electric field strength increases. In order to estimate the effect of electric field on the bubble departure volume, the surface tension force and the downward electric force exerted on a bubble are also computed for a bubble of fixed volume under the fixed contact angle condition. The sum of the two forces is found to decrease with increasing strength of nonuniform electric field. This fact suggests that the bubble departure volume decreases in a nonuniform electric field.     

Biaxial deformation of dough using the bubble inflation technique. I. Experimental

The bubble inflation test has been used to determine the equi-biaxial stress-strain curve of flour/water dough. This was achieved by undertaking experimental measurements of strain, wall thickness and radius of curvature at the top of the bubble as well as applied pressure. It was observed that the bubble was spherical initially but changed to an elliptical shape at large strains. The analysis derived by Bloksma (1957) was also used to calculate stress and strain at the top of the inflated bubble from gauge pressure and bubble volume data. It was found that the analysis led to accurate bubble heights at moderate strains only, a consequence of the non-spherical bubble shape. In addition, at the top of the bubble, the analytical strain was larger and the thickness was much smaller than the experimental values. The bubble wall thickness distribution was more uniform than the analytical predictions. The discrepancies in bubble height, radius of curvature, strain and thickness had a major effect in the analytical stress-strain curve, as both stress and strain were overestimated, the stress being in error by a factor of four at large strains. Therefore, it is concluded that when the bubble inflation test is used, it is necessary that experimental readings of strain, thickness and radius of curvature as well as pressure should be made to ensure accurate stress-strain curves.     

The dynamics and dissolution of gas bubbles in a viscoelastic fluid

This paper reports an experimental study of the motion of dissolving and non-dissolving gas bubbles in a quiescent viscoelastic fluid. The objective of the investigation was to determine the influence of the abrupt transition in bubble velocity, which had been observed at a critical radius of approx. on the rate of mass transfer. Thus, a range of bubble sizes from an equivalent (spherical) radius of 0.2–0.4 cm was employed using CO₂ gas, and five different fluids, including one Newtonion glycerine/water solution and four viscoelastic solutions of Separan AP30 in water (0.1, 0.5, 1% by weight) and in a water/glycerine mixture.The experimental data on bubble velocity shows that the discontinuous increase with bubble volume observed previously for air bubbles in viscoelastic fluids, does not occur for dissolving CO₂ bubbles—presumably due to the continuous decrease in bubble volume. Instead, a very steep but definitely continuous transition is found. Mass transfer rates are found to be significantly enhanced by viscoelasticity, and comparison with available theoretical results shows that the increase is greater than expected for purely viscous, power-law fluids. We conclude that a fully viscoelastic constitutive model would be necessary for a successful analysis of the dissolution of a gas bubble which is translating through a (high molecular weight) polymer solution.     

Dynamic detachment of a gas bubble from a solid flat substrate performing normal harmonic vibrations

This paper presents an investigation of the detachment of a bubble from a solid flat substrate according to a dynamic scenario, i. e., due to strong vibrations of the surface shape of the bubble caused by normal nonacoustic harmonic vibrations of the substrate. The Layzer’s model based on an analysis of single-mode solutions near the bubble top was used to study its detachment in microgravity, where the dynamics of the bubble surface is due to competition between liquid inertia forces and surface tension forces. Detachment of the bubble from the substrate was determined from the condition of its elongation during vibrations by a magnitude comparable to the radius of the bubble in equilibrium. The dependence of the vibration intensity required for the detachment of the bubble on the problem parameters was determined using a number of empirical assumptions. The volume of the detached bubbles was estimated.     

Strong interaction between a buoyancy bubble and a free surface

The growth and collapse of buoyant vapor bubbles close to a free surface in an inviscid incompressible fluid is investigated in this paper. The strong interaction between the deforming bubble and the free surface is simulated numerically by a boundary-integral method (Taib 1985; Blake et al., 1987). Improvements are made in the calculation of the singular integrals, the use of nonuniform boundary elements, and the choice of time-step size. The present numerical results agree better with the experimental observations of Blake and Gibson (1981) than previous numerical predictions for bubbles initiated at one maximum radius from the free surface. There is also concurrence of flow features with the experiments for a bubble initiated as close as half maximum radius from the free surface, where other numerical efforts have failed. The effects of buoyancy on bubbles initiated close to a free surface are also investigated. Vastly different features, depending on the distance of the bubble to the free surface and the buoyancy-force parameter, have been observed.     

Parametric Analysis for a Single Collapsing Bubble

This work presents a sensitivity analysis for cavitation processes, studying in detail the effect of various model parameters on the bubble collapse. A complete model (Hauke et al. Phys Rev E 75:1–14, 2007) is used to obtain how different parameters influence the collapse in SBSL experiments, providing some clues on how to enhance the bubble implosion in real systems. The initial bubble radius, the frequency and the amplitude of the pressure wave are the most important parameters determining under which conditions cavitation occurs. The range of bubble sizes inducing strong implosions for different frequencies is computed; the initial radius is the most important parameter characterized the intensity of the cavitation processes. However, other parameters like the gas and liquid conductivity or the liquid viscosity can have an important effect under certain conditions. It is shown that mass transfer processes play an important role in order to correctly predict the trends related with the effect of the liquid temperature, which translates into the bubble dynamics. Moreover, under some particular circumstances, evaporation can be encountered during the bubble collapse; this can be profitably exploited in order to feed reactants when the most extreme conditions inside the bubbles are reached. Thus, this paper aims at providing a global assessment of the effect of the different parameters on the entire cycle of a single cavitating spherical bubble immersed in an ultrasonic field. This work has been partially supported by Ministerio de Ciencia y Tecnologia, under grant number CTM2004-06184-C02-02.     

Measurement of liquid film thickness in micro square channel

In micro channels, slug flow becomes one of the main flow regimes due to strong surface tension. In micro channel slug flow, elongated bubble flows with the thin liquid film confined between the bubble and the channel wall. Liquid film thickness is an important parameter in many applications, e.g., micro heat exchanger, micro reactor, coating process etc. In the present study, liquid film thickness in micro square channels is measured locally and instantaneously with the confocal method. Square channels with hydraulic diameter of D_h = 0.3, 0.5 and 1.0 mm are used. In order to investigate the effect of inertial force on the liquid film thickness, three working fluids, ethanol, water and FC-40 are used. At small capillary numbers, liquid film at the channel center becomes very thin and the bubble interface is not axisymmetric. However, as capillary number increases, bubble interface becomes axisymmetric. Transition from non-axisymmetric to axisymmetric flow pattern starts from lower capillary number as Reynolds number increases. An empirical correlation for predicting axisymmetric bubble radius based on capillary number and Weber number is proposed from the present experimental data.     

nfluence of exciting parameters on the vibration of single cavitation bubble driven by intensive sound

根据考虑了液体可压缩性的改进的微气泡动力学方程,采用改进的初始半径对单泡超声空化现象进行了数值计算研究. 结果表明,微气泡振动对一些参量很敏感：微气泡振动半径与初始半径的比值随振动频率的增大而减小;提高声场声压会加剧气泡崩塌程度,但过高的声压又不能使微气泡崩塌;微气泡崩塌速率随气泡初始半径的增加而增大,在一定范围内能保证空化泡稳定振动,在初始半径为1.6\,$\mu$m 处空化程度最强,如果继续增大初始半径则空化程度减弱、甚至消失;微气泡崩塌程度随黏滞系数和表面张力的增大而减弱,过大的黏滞系数和表面张力会使微气泡崩塌难以发生. 计算结果与他人的实验数据相比,发现液体的可压缩性使单泡空化强度增强, 对最佳空化区域范围的确定有较大的影响.     

Numerical simulation of a bubble rising in shear-thinning fluids

The motion of a single bubble rising freely in quiescent non-Newtonian viscous fluids was investigated experimentally and computationally. The non-Newtonian effects in the flow of viscous inelastic fluids are modeled by the Carreau rheological model. An improved level set approach for computing the incompressible two-phase flow with deformable free interface is used. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The simulation results demonstrate that the algorithm is robust for shear-thinning liquids with large density (ρ₁/ρ_g up to 10³) and high viscosity (η₁/η_g up to 10⁴). The comparison of the experimental measurements of terminal bubble shape and velocity with the computational results is satisfactory. It is shown that the local change in viscosity around a bubble greatly depends on the bubble shape and the zero-shear viscosity of non-Newtonian shear-thinning liquids. The shear-rate distribution and velocity fields are used to elucidate the formation of a region of large viscosity at the rear of a bubble as a result of the rather stagnant flow behind the bubble. The numerical results provide the basis for further investigations, such as the numerical simulation of viscoelastic fluids.     

Photoelastic determination of stress-intensity factors

The increasing number of analytical and numerical solutions for the crack-tip stress-intensity factor has greatly widened the scope of application of linear elastic fracture-mechanics technology. Experimental verification of a particular solution by elastic stress analysis is often a necessary supplement to provide the criteria for proper application to actual design problems. In this paper, it is shown that the photoelastic technique can be used to obtain rather good estimates of the stress-intensity factor for various specimen geometries and loading conditions. Treated are the following cases: wedge-opening load specimen, several notched rotating-disk configurations, and a notched pressure vessel. A sharp crack is simulated by a relatively narrow notch terminating in a root radius of 0.010 in or less. Stress distributions along the section of symmetry ahead of the notch tip are obtained using three-dimensional frozen-stress photoelasticity. The results are used to determine the stress-intensity factor, cK _I , by three methods. Two of these are based on Irwin's expressions for the elastic stress field at the tip cf a crack, and the other is a result of Neuber's hyperbolic-notch analysis. Agreement, with available analytical solutions is good.     

Evolution of deviations from the spherical shape of a vapor bubble in supercompression

This paper considers the evolution of small deviations of a cavitation bubble from a spherical shape during its single compression under conditions of experiments on acoustic cavitation of deuterated acetone. Vapor motion in the bubble and the surrounding liquid is defined as a superposition of the spherical component and its non-spherical perturbation. The spherical component is described taking into account the nonstationary heat conductivity of the liquid and vapor and the nonequilibrium nature of the vaporization and condensation on the interface. At the beginning of the compression process, the vapor in the bubble is considered an ideal gas with a nearly uniform pressure. In the simulation of the high-rate compression stage, realistic equations of state are used. The non-spherical component of motion is described taking into account the effect of liquid viscosity, surface tension, vapor density in the bubble, and nonuniformity of its pressure. Estimates are obtained for the amplitude of small perturbations (in the form of harmonics of degree n = 2, 3, ... with the wavelength λ = 2πR/n, where R is the bubble radius) of the spherical shape of the bubble during its compression until reaching extreme values of pressure, density, and temperature. These results are of interest in the study of bubble fusion since the non-sphericity of the bubble prevents its strong compression.     

RVE-based studies on the coupled effects of void size and void shape on yield behavior and void growth at micron scales

The present paper extends the Gurson and GLD models [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth, Part I—yield criteria and flow rules for porous ductile media. J. Mech. Phys. Solids 99, 2–15; Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Technol. 116, 290–297] to involve the coupled effects of void size and void shape on the macroscopic yield behavior of non-linear porous materials and on the void growth. A spheroidal representative volume element (RVE) under a remote axisymmetric homogenous strain boundary condition is carefully analyzed. A wide range of void aspect ratios covering the oblate spheroidal, spherical and prolate spheroidal void are taken into account to reflect the shape effect. The size effect is captured by the Fleck–Hutchinson phenomenological strain gradient plasticity theory [Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advance in Applied Mechanics, vol. 33, Academic Press, New York, pp. 295–361]. A new size-dependent damage model like the Gurson and GLD models is developed based on the traditional minimum plasticity potential principle. Consequently, the coupled effects of void size and void shape on yield behavior of porous materials and void growth are discussed in detail. The results indicate that the void shape effect on the yield behavior of porous materials and on the void growth can be modified dramatically by the void size effect and vice versa. The applied stress triaxiality plays an important role in these coupled effects. Moreover, there exists a cut-off void radius r_c, which depends only on the intrinsic length l₁ associated with the stretch strain gradient. Voids of effective radius smaller than the critical radius r_c are less susceptible to grow. These findings are helpful to our further understanding to some impenetrable micrographs of the ductile fracture surfaces.     

Characteristic lengths and maximum entropy estimation from probe signals in the ellipsoidal bubble regime

The bubble size, surface and volume distributions in two and three phase flows are essential to determine energy and mass transfer processes. The traditional approaches commonly use a conditional probability density function of chord-lengths to calculate the bubble size distribution, when the bubble size, shape and velocity are known. However, the approach used in this paper obtains the above distributions from statistical relations, requiring only the moments inferred from the measurements given by a sampling probe. Using image analysis of bubbles injected in a water tank, and placing an ideal probe on the image, a sample of bubble diameter, shape factor and velocity angle are obtained. The samples of the bubble chord-length are synthetically generated from these variables. Thus, we propose a semi-parametric approach based on the maximum entropy (MaxEnt) distribution estimation subjected to a number of moment constraints avoiding the use of the complex backward transformation. Therefore, the method allows us to obtain the distributions in close form. The probability density functions of the most important length scales (D, D₂₀, D₃₀, D₃₂), obtained applying the semi-parametric approach proposed here in the ellipsoidal bubble regime, are compared with experimental measurements.     

Dependence of the stability criterion of nucleate boiling on the compressibility of the vapor

The article gives the results of a study of the motion of bubbles and their deformation near the heating surface at different pressures. It was observed that, during the time of their growth, the gaseous medium in the bubbles is in a compressed state.Nomenclature R) radius of bubble - R_h) maximul radius of a deformed bubble in the horizontal plane - R_v) maximal radius of a deformed bubble in the vertical plane - ) specific weight - B) universal gas constant - ) surface-tension coefficient - p) pressure - ) edge wetting angle - g) acceleration due to gravity - V) volume - ) molecular weight - C_T) isothermal velocity of sound Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 77–81, July–August, 1971.