Stability of gas-bubble equilibrium shape in uniform flow of an ideal fluid

Steady-state motion of a bubble in the shape of an ellipsoid of revolution has been studied [1, 2]. Steady-state motion and small oscillations of an ellipsoid of revolution around the equilibrium state were studied with the help of Lagrangian equations [3]. In this paper, possible equilibrium shapes of a bubble in the form of a triaxial ellipsoid are studied. The dependence of the pressure difference at the stagnation point and within the gas bubble on deformation is determined for steady-state motion. The stability of the equilibrium shape with respect to small perturbations of the axes of the ellipsoid is investigated through analysis of potential energy in the neighborhood of the extremum.     

Single bubble growth in saturated pool boiling on a constant wall temperature surface

Nucleate pool boiling experiments with constant wall temperatures were performed using R11 and R113 for saturated pool boiling conditions. A microscale heater array and Wheatstone bridge circuits were used to maintain a constant wall temperature condition and to obtain measurements with high temporal and spatial resolution. Accurate heat flow rate data were obtained from microscale heater array by controlling the surface conditions at a high temporal resolution. Images of the bubble growth were captured using a high-speed CCD camera synchronized with the heat flow rate measurements. The geometry of the bubble was obtained from the images. In the asymptotic growth region, the bubble showed a growth rate that was proportional to t^1/5, which was slower than the growth rate proposed in previous analytical analyses. The bubble growth behavior was analyzed using a new dimensionless parameter to permit comparisons with previous results at the same scale. The comparisons showed good agreement in the asymptotic growth region. A non-dimensional correlation for the bubble radius that can predict the bubble growth and the heat flow rate simultaneously, was suggested. The required heat flow rate for the volume change of the observed bubble was estimated to be larger than the instantaneous heat flow rate measured from the wall. Heat, other than the instantaneous heat supplied from the wall, is estimated to be transferred through the interface between bubble and liquid, even with saturated pool conditions. This phenomenon under a saturated pool condition needs to be analyzed and the data from this study can supply the good experimental data with the precise boundary condition (constant wall temperature).     

Chaotic behavior of gas bubble in non-Newtonian fluid: a numerical study

In the present paper, the nonlinear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. Due to the importance of the bubble in the medical applications such as drug, protein or gene delivery, blood is assumed to be the reference fluid. Effects of viscoelasticity term, Deborah number, amplitude and frequency of the acoustic pulse are studied. We have studied the dynamic behavior of the radial response of bubble using Lyapunov exponent spectra, bifurcation diagrams, time series and phase diagram. A period-doubling bifurcation structure is predicted to occur for certain values of the effects of parameters. The results show that by increasing the elasticity of the fluid, the growth phenomenon will be unstable. On the other hand, when the frequency of the external pulse increases the bubble growth experiences more stable condition. It is shown that the results are in good agreement with the previous studies.     

Direct simulation of liquid–gas–solid flow with a free surface lattice Boltzmann method

Direct numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly.     

Heat exchange between a gas bubble and a liquid

The nonlinear problem of thermal and dynamic interaction between a single gas bubble and surrounding liquid is considered. This problem is met in studies of gas-liquid mixture flows, in particular, in Shockwave propagation in such media. A numerical solution is presented for various modes of bubble surface radial motion. The modes correspond to bubble behavior directly beyond a shock-wave front, where the latter enters the bubble screen, and to the behavior of a bubble located in the depths of the bubble curtain, where the wave becomes diffuse. Analytic solutions of the linearized problem of thermal conductivity for free and constrained small harmonic oscillations of a gas bubble in a liquid were obtained in [1, 2]. Cooling of a hot gas bubble was considered in [3], that study, however, contains inaccuracies. In particular, it was assumed in the solution that the gas density in the bubble was homogeneous. The equation for heat flux in dimensionless variables was written inaccurately. However, in the examples considered in [3] these inaccuracies do not lead to significant errors in the numerical results.     

On the modeling and simulation of a laser‐induced cavitation bubble

Single cavitation bubbles exhibit severe modeling and simulation difficulties. This is due to the small scales of time and space as well as due to the involvement of different phenomena in the dynamics of the bubble. For example, the compressibility, phase transition, and the existence of a noncondensable gas inside the bubble have strong effects on the dynamics of the bubble. Moreover, the collapse of the bubble involves the occurrence of critical conditions for the pressure and temperature. This adds extra difficulties to the choice of equations of state. Even though several models and simulations have been used to study the dynamics of the cavitation bubbles, many details are still not clearly accounted for. Here, we present a numerical investigation for the collapse and rebound of a laser‐induced cavitation bubble in liquid water. The compressibility of the liquid and vapor are involved. In addition, great focus is devoted to study the effects of phase transition and the existence of a noncondensable gas on the dynamics of the collapsing bubble. If the bubble contains vapor only, we use the six‐equation model for two‐phase flows that was modified in our previous work [A. Zein, M. Hantke, and G. Warnecke, J. Comput. Phys., 229(8):2964‐2998, 2010]. This model is an extension to the six‐equation model with a single velocity of Kapila et al. (Phys. Fluid, 13:3002‐3024, 2001) taking into account the heat and mass transfer. To study the effect of a noncondensable gas inside the bubble, we add a third phase to the original model. In this case, the phase transition is considered only at interfaces that separate the liquid and its vapor. The stiffened gas equations of state are used as closure relations. We use our own method to determine the parameters to obtain reasonable equations of state for a wide range of temperatures and make them suitable for the phase transition effects. We compare our results with experimental ones. Also our results confirm some expected physical phenomena. Copyright © 2013 John Wiley & Sons, Ltd.     

Oscillatory Marangoni convection around the air bubble in a vertical surfactant stratificationConvection de Marangoni oscillante autour d'une bulle d'air dans une stratification verticale surfactante

The solutocapillary Marangoni convection around a gas bubble in the inhomogeneous binary mixture of miscible fluids with a vertical surfactant concentration gradient was studied experimentally. A new phenomenon, the oscillatory instability of the surfactant mass transfer, near the bubble boundary, was detected and investigated. The interpretation of this effect as an interaction between the surfactant adsorption at the bubble free surface and solutocapillary and buoyancy convective mechanisms is proposed. The experimental data on oscillation period in relation to bubble dimensions, time, liquid layer thickness, physico-chemical fluid parameters and concentration gradients are presented and discussed. To cite this article: K. Kostarev et al., C. R. Mecanique 332 (2004).     

Supernova remnant evolution in wind bubbles: A closer look at Kes 27

Massive Stars (>8M_⊙) lose mass in the form of strong winds. These winds accumulate around the star, forming wind-blown bubbles. When the star explodes as a supernova (SN), the resulting shock wave expands within this wind-blown bubble, rather than the interstellar medium. The properties of the resulting remnant, its dynamics and kinematics, the morphology, and the resulting evolution, are shaped by the structure and properties of the wind-blown bubble. In this article we focus on Kes 27, a supernova remnant (SNR) that has been proposed by [1] to be evolving in a wind-blown bubble, explore its properties, and investigate whether the X-Ray properties could be ascribed to evolution of a SNR in a wind-blown bubble. Our initial model does not support the scenario proposed by [1], due to the fact that the reflected shock is expanding into much lower densities.     

储层含水条件下致密砂岩/页岩无机质纳米孔隙气相渗透率模型

页岩及致密砂岩储层富含纳米级孔隙,且储层条件下页岩孔隙(尤其无机质孔隙)及致密砂岩孔隙普遍含水,因此含水条件下纳米孔隙气体的流动能力的评价对这两类气藏的产能分析及生产预测具有重要意义.本文首先基于纳米孔隙内液态水及汽态水热力学平衡理论,量化了储层孔隙含水饱和度分布特征;进一步在纳米孔隙单相气体传质理论的基础上,考虑了孔隙含水饱和度对气体流动的影响;最终建立了含水饱和度与气相渗透率的关系曲线. 基于本文岩心孔隙分布特征,计算结果表明:储层含水饱和度对气体流动能力的影响不容忽视,在储层含水饱和度20%的情况下,气相流动能力与干燥情况相比将降低约10%;在含水饱和度40% 的情况下,气相流动能力将降低约20%.      

Dissipation of the energy of sound waves in small gas bubbles

One of the main factors affecting the dynamics of homogeneous solution type pulse reactors is the formation of gas bubbles on the fission-fragment tracks [1, 2]. The behavior of the reactor depends very considerably on the size (10^?5 cm) and growth rate of these bubbles [2], and it is, accordingly, a very important matter to study these properties. One convenient means of doing this lies in the acoustic method. The behavior of gas bubbles in the field of a sound wave has been studied in a large number of papers and reviews [3, 4]. In this paper we shall see the approximation of a sound wave of small amplitude to consider the dissipation of sound-wave energy in a gas bubble, at the same time allowing for inertia, surface tension, viscosity, heat transfer, and the diffusion of gas through the surface of the bubble.     

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.     

Mass transfer from a pulsating drop

The primary difficulty in solving the problem of mass transport through an isolated drop (or bubble) moving in a fluid medium at high Reynolds numbers lies in the extreme complexity of the hydrodynamic pattern of the phenomenon. For sufficiently high velocities a separation of the external flow will occur in the rear portion of the drops and bubbles, which leads to the appearance of a turbulent wake and a sharp increase of the hydrodynamic resistance. Beginning with those dimensions for which the resistance force acting per unit surface of the drop or bubble from the external medium becomes greater than the capillary pressure, the surface of the drops and bubbles begins to deform and pulsate. The local variations of the surface tension, resulting either from the process of convective diffusion or from adsorption of surface-active substances, have a large effect on the hydrodynamics of drops and bubbles (particularly on the deformation of their surface) [1, 2], The presence of vortical, and possibly even turbulent, motion within the drops and bubbles may, under certain conditions [1], lead to their fractionation.Naturally, at the present time such complex hydrodynamics cannot be described by exact quantitative relations. Several authors have attempted to solve this problem approximately within the framework of certain assumptions. In particular [3–6], a theory was developed for the boundary layer on the surface of spherical and ellipsoidal gaseous bubbles moving in a liquid, studies were made [7, 8] of the hydrodynamics of drops located in a gas flow and the conditions were found for which fractionation of such drops takes place. Of considerable practical interest is the development of the theory of mass transfer in pulsating drops and bubbles and finding in explicit form the dependence of the mass transfer coefficients on the hydrodynamic characteristics of these systems. Until this relationship is established, every theory which ignores the effect of hydrodynamics on the mass transfer rate from an individual drop or bubble cannot be considered in any way well-founded. This relates particularly to the theories [9, 10] which consider mass transfer in systems with concentrated streams of drops and bubbles. The present paper is devoted to the study of mass transport through the surface of an isolated drop in an irrotational gas or liquid stream for large Peclet numbers P.In conclusion the authors wish to thank V. G. Levich for his helpful discussions.     

The effect of an insoluble surfactant on the skin friction of a bubble

In this paper, we develop a novel moving mesh method suitable for solving axisymmetric free-boundary problems, including the Marangoni effect induced by surfactant or temperature variation. This method employs a body-fitted grid system where the gas–liquid interface is one line of the grid system. We model the surfactant equation of state with a non-linear Langmuir law, and, for simplicity, we limit ourselves to the situation of an insoluble surfactant. We solve complicated dynamic boundary conditions accurately on the gas–liquid interface in the framework of finite-volume methods. Our method is used to study the effect of a surfactant on the skin friction of a bubble in a uniaxial flow. For the limiting case where the surface diffusivity is zero, the effect of a tangential stress generated by the surface tension gradient, allows us to explain a new phenomenon in high concentration regimes: larger surface tension, but also larger deformation. Furthermore, this condition leads to the formation of boundary layers and flow separation at high Reynolds numbers. The influence of these complex flow patterns is examined.     

Simulated X-ray spectra from ionized wind-blown nebulae around massive stars

Using an ionization gas dynamics code, we simulate a model of the wind-blown bubble around a 40 M_⊙ star. We use this to compute the X-ray spectra from the bubble, which can be directly compared to observations. We outline our methods and techniques for these computations, and contrast them with previous calculations. Our simulated X-ray spectra compare reasonably well with observed spectra of Wolf–Rayet bubbles. They suggest that X-ray nebulae around massive stars may not be easily detectable, consistent with observations.     

Bubble velocities: further developments on the jump discontinuity

The motion of a gas bubble in a non-Newtonian fluid has been further examined in order to determine the conditions for the possible existence of a discontinuity in the bubble velocity-bubble volume log–log plot. It has been proposed in the past that this phenomenon was the result of a sudden change in the hydrodynamics of the moving bubble, resulting in a transition from a Stroke to a Hadamard regime. Furthermore, this abrupt transition was only qualitatively attributed to the elasticity of the fluid. Using our data as well as those of Leal et al., we demonstrate here that the discontinuity results as a balance between elastic and Marangoni instabilities, providing another major difference between Newtonian and non-Newtonian hydrodynamics.     

Validation of the Local Thermal Equilibrium Assumption in Forced Convection of Non-Newtonian Fluids through Porous Channels

In this paper, we assess the validity of the local thermal equilibrium assumption in the non-Newtonian forced convection flow through channels filled with porous media. For this purpose, the problem is solved numerically using local thermal non-equilibrium and non-Darcian models. Numerical solutions obtained over broad ranges of representative dimensionless parameters are utilized to map conditions at which the local thermal equilibrium assumption can or cannot be employed. The circumstances of a higher modified Peclet number, a lower modified Biot number, a lower fluid-to-solid thermal conductivity ratio, a lower power-law fluid index, and a lower microscopic and macroscopic frictional flow resistance coefficients, are identified as unfavorable circumstances for the local thermal equilibrium (LTE) condition to hold. Quantitative LTE validity maps that reflect the proportional effect of each parameter as related to others are presented.     

The question of the uniform-pressure condition in bubble dynamics

Spherical gas bubbles which oscillate radially under the action of an acoustic field in a fluid are considered. It is shown that the results of [1] in which the problem was solved in the complete formulation (with the use of the momentum equation for the gas) are inconsistent. In [1], the pressure in the bubble was not assumed to be uniform but some inaccuracies were made.     

Turbulent boundary layer on a catalytic surface in a nonequilibrium dissociating gas

The majority of the studies which consider the flow of a dissociating gas in a turbulent boundary layer are devoted to the investigation of either frozen or equilibrium flows on a flat plate.The frozen turbulent boundary layer has been studied by Dorrance [1], Kutateladze and Leont'ev [2], and Lapin and Sergeev [3]. A study of the effect of catalytic recombination processes at the plate surface on the heat transfer in a frozen turbulent boundary layer was made by Lapin [4].Kosterin and Koshmarov [5], Ginzburg [6], Dorrance [7], and Lapin [8] have studied the turbulent boundary layer on a plate in equilibrium dissociating gas.The calculation of the heat transfer in a turbulent boundary layer on a catalytic plate surface with nonequilibrium dissociation was made by Kulgein [9]. In this study the nonequilibrium nature of the dissociation process was taken into account only in the laminar sublayer, while the flow in the turbulent core was considered frozen. The solution was found numerically using a computer by means of a laborious iteration process.The present paper reports a method for calculating the turbulent boundary layer on a flat catalytic plate with arbitrary dissociation rate. The method, constructed using the assumptions customary for turbulent boundary layer theory, is a successive approximation method. Good convergence of the method is assured by the fact that the effect of the nonequilibrium nature of the dissociation process on the parameter distribution in the boundary layer and, consequently, on the friction and heat transfer may be allowed for merely by finding corrections, usually relatively small, to the distribution of these parameters in the equilibrium or frozen flows. The basis of the study is the two-layer scheme of the turbulent boundary layer. The Prandtl and Schmidt numbers and also their turbulent analogs are taken equal to unity. As the model of the dissociating gas we use the Lighthill model of the ideal dissociating gas [10], extended by Freeman [11] to nonequilibrium flows.     

Evaporation condensation-induced bubble motion after temperature gradient set-up

Thermocapillary (Marangoni) motion of a gas bubble (or a liquid drop) under a temperature gradient can hardly be present in a one-component fluid. Indeed, in such a pure system, the vapor–liquid interface is always isothermal (at saturation temperature). However, evaporation on the hot side and condensation on the cold side can occur and displace the bubble. We have observed such a phenomenon in two different fluids submitted to a temperature gradient under reduced gravity: hydrogen under magnetic compensation of gravity in the HYLDE facility at CEA-Grenoble and water in the DECLIC facility onboard the ISS. The experiments and the subsequent analysis are performed in the vicinity of the vapor–liquid critical point to benefit from critical universality. In order to better understand the phenomena, a 1D numerical simulation has been performed. After the temperature gradient is imposed, two regimes can be evidenced. At early times, the temperatures in the bubble and the surrounding liquid become different thanks to their different compressibility and the “piston effect” mechanism, i.e. the fast adiabatic bulk thermalization induced by the expansion of the thermal boundary layers. The difference in local temperature gradients at the vapor–liquid interface results in an unbalanced evaporation/condensation phenomenon that makes the shape of the bubble vary and provoke its motion. At long times, a steady temperature gradient progressively forms in the liquid (but not in the bubble) and induces steady bubble motion towards the hot end. We evaluate the bubble velocity and compare with existing theories.