Oscillations of a gas bubble in a non-Newtonian liquid under the action of an acoustic field

The evolution of the radius of a spherical cavitation bubble in an incompressible non-Newtonian liquid under the action of an external acoustic field is investigated. Non-Newtonian liquids having relaxation properties and also pseudoplastic and dilatant liquids with powerlaw equation of state are studied. The equations for the oscillation of the gas bubble are derived, the stability of its radial oscillation and its spherical form are investigated, and formulas are given for the characteristic frequency of oscillations of the cavitation hollow in a relaxing liquid. The equations are integrated numerically. It is shown that in a relaxing non-Newtonian liquid the viscosity may lead to the instability of the radial oscillations and the spherical form of the bubble. The results obtained here are compared with the behavior of a gas bubble in a Newtonian liquid.     

自由场水中爆炸气泡的物理特性

将水中爆炸气泡运动阶段周围流场假设为无粘、无旋、不可压缩的理想流体,运用边界元法模拟自由场中气泡的运动,在气泡运动模拟过程中引入数值光顺技术及弹性网格技术,避免因网格扭曲而导致的数值发散,并开发计算程序。计算值与实验值吻合良好,误差小于10%。从自由场水中爆炸气泡的基本现象入手,基于本文中开发的程序系统地研究了自由场中气泡的动力学特性。对流场中不同方位的压力进行分析,得出气泡中心的迁移方向及射流的攻击方向压力载荷比其他方向均大,说明气泡射流的攻击方向压力载荷最大,对水中结构造成严重毁伤,表明了气泡载荷的不对称性。计算了流场中不同位置的速度变化曲线,结果表明随着距气泡中心距离的增大,气泡运动引起的滞后流的速度迅速减小,且随着气泡的膨胀和坍塌,滞后流的方向逆转,总结了滞后流的衰减及变化规律。     

Thermal convection in an acoustic field

The linear stability of flow in a horizontal fluid layer is investigated within the framework of thermoacoustic convection. The flow is initiated by a longitudinal temperature gradient and the propagation of an acoustic wave in the fluid. Instability modes corresponding to perturbations of both plane and longitudinal roller and oblique wave type are detected. Using weakly nonlinear analysis, it is shown that these regimes develop softly; the stability of various secondary flows is investigated for small supercriticalities. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 10–21, May–June, 2000. The work was carried out with partial support from the Program of State Support for Leading Science Schools (grant No. 96-015-96084).     

Thermal convection in an acoustic field

Thermal vibrational convection is considered for an acoustic wavelength at the vibration frequency comparable with the dimensions of the cavity. Equations of the pulsatory and average motions of a medium that generalize the well-known equations of thermovibrational convection are obtained. Effective boundary conditions for average fields on rigid boundaries are formulated. The quasi-equilibrium stability problem for a plane horizontal layer heated from below and executing high-frequency oscillations is solved. It is shown that the compressibility effects can be significant even when the acoustic wavelength substantially exceeds the length of the layer. A destabilizing compressibility effect which can lead to instability of the layer even under conditions of weightlessness is established. Perm’, e-mail: lyubimov@psu.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 28–36, March–April, 2000. The work was carried out with partial financial support from the Program of State Support for Leading Science Schools (project No. 96-015-96084).     

On mass transfer in an acoustic field

Chemical processes governed by the laws of diffusion kinetics can be intensified by elastic oscillations. It is also known that the rate of combustion of liquid and solid fuels changes markedly with the onset of acoustic vibrations in the combustion chamber. Despite the extensive application of vibrational processes in technology, the mechanisms of heat and mass transfer in the presence of vibrations are not well known. The aim of this research was to analyze the mass transfer from a sphere in an acoustic field.Notation angular frequency of oscillations - wavelength - R characteristic dimension of axisymmetric body - s amplitude of displacement of fluid particles in a plane acoustic wave - B amplitude of oscillation velocity - x, y longitudinal and transverse coordinates - u, v longitudinal and transverse velocity components - v kinematic viscosity - U — A(x) cos t velocity of potential flow - ⁺ thickness of momentum boundary layer - ^– thickness of diffusion boundary layer - m dimensionless concentration - m_* concentration of diffusing component at surface of vaporization - t time - D diffusion coefficient - average density of mixture - erf error function - r radius of axisymmetric body - R Reynolds number - P diffusion Prandtl number - time average - N, N_d Nusselt numbers based on radius and diameter respectively - pulsating component of velocity or concentration - o stationary component of velocity or concentration In conclusion, the authors wish to thank S. S. Kutateladze and I. A. Yavorskii, who supervised the present work.     

Ultrasonic jet in an external acoustic field

The interaction of supersonic jets with external acoustic waves is investigated in connection with the emission of sound of discrete frequency by the jets. A plausible physical scheme explaining the appearance and maintenance of the oscillations of supersonic jets with discrete frequency was proposed in [1]. A model problem of the effect of pressure perturbations of a given frequency, traveling along the surface of a two-dimensional jet is also investigated there. The results of the solution of this problem (in particular, the presence of critical frequencies at which the perturbations in the jet grow indefinitely in the direction of motion of the flow) substantiate the hypothesis that by virtue of its periodic (cellular) structure a supersonic jet has the properties of a resonator. In [1] the more general problem of interaction of a supersonic jet with an external acoustic field is also formulated, which is in complete correspondence with the physical scheme of the phenomena developed in that article. In the present work this problem is solved in its complete form for plane and cylindrical jets for symmetric and antisymmetric perturbations in an external acoustic field, and also in the presence of subsonic accompanying flow in the outer medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 105–113, March–April 1974.     

Passive acoustic bubble sizing in sparged systems

Passive acoustic bubble sizing was investigated in both controlled tests and in a stirred, sparged tank typical of the biotechnology or minerals processing industries. Acoustic techniques have promise for industrial systems where other bubble analysis methods are impractical. Acoustic signals were studied for bubbles precisely formed at higher airflow rates. Acoustic pulses varied with bubble production rate as well as with bubble size. A technique of windowing pulses is proposed. Two alternative versions of this windowing technique were applied to a stirred, sparged tank, giving good agreement. It was shown that, in some cases, it may also be possible to acoustically estimate the spatial distribution of void fraction. Received: 13 June 2000/Accepted: 19 October 2000     

Instability of a spherical gas bubble in a variable-pressure field

Only a few studies, of which we mention [1–5], have been addressed to the problem of the stability of the accelerated motion of a spherical interface of two fluids. In the present paper we consider the problem of the stability of radial motion of the spherical boundary of a gas bubble in an incompressible inviscid liquid under the action of variable external pressure. Surface tension is not taken into account. We study the possibility of the existence of stable motions for broad classes of time dependence of the external pressure, namely for monotonic and periodic dependences. It is shown that stability is possible only for infinitely large bubble radii or for very specific assumptions concerning the initial conditions and the pressure-time dependence law.     

Observations on the dynamics of bubble cluster in an ultrasonic field

The dynamics driven interaction between the bubbles in a cavitation cluster is known to be a complex phenomenon indicative of a highly active nonlinear as well as chaotic behavior in ultrasonic fields. By considering the cluster of encapsulated microbubble with a thin elastic shell in ultrasonic fields, in this paper, the dynamics of microbubbles has been studied via applying the methods of chaos physics. Bifurcation, Lyapunov exponent, and time series are plotted with respect to variables such as amplitude, initial bubble radius, frequency and viscosity. The findings of the study indicate that a bubble cluster undergoes a chaotic unstable region as the amplitude and frequency of ultrasonic pulse are increased mainly due to the period doubling phenomenon. The results of the present study are supported by findings of previous studies.     

The effect of an acoustic field on a secondary convective flow in a layer

The effect of a traveling sonic wave on a convective flow in a horizontal layer with a fixed linear temperature distribution on the boundaries is investigated. Convective rolls with axes parallel to the basic flow (lengthwise rolls) are considered. On the basis of a weakly nonlinear analysis, it is shown that the lengthwise rolls appear smoothly and the regular flows are stable near the stability threshold. A direct numerical simulation is performed. Secondary near-critical flow regimes and regimes corresponding to finite supercriticalities are investigated.     

The flow in and around a droplet or bubble submerged in an unbound arbitrary velocity field

Summary A solution is presented for the flow fields interior and exterior to a single spherical droplet submerged in an unbounded fluid, for the general case when the unperturbed velocity isStokesian but otherwise quite arbitrary.A general equation for the terminal settling velocity is derived which contains as special cases the solutions ofHadamard-Rybczynski, Taylor and others. The drag force on a spherical droplet is also formulated. This equation contains as a special case the law ofFaxen.The function describing the interface and its deviation from sphericity is derived. This may be used for determining more accurate flow fields in an iterative procedure.

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Zusammenfassung Das Problem der Strömungsfelder in einer unbegrenzten Flüssigkeit wird sowohl innerhalb wie außerhalb eines einzelnen kugelförmigen Tropfens für den allgemeinen Fall gelöst, wenn die ungestörte Geschwindigkeit durch dieStokessche Gleichung angegeben werden kann, aber sonst willkürlich ist.Es wird eine allgemeine Formel für die Geschwindigkeit, die nach langer Zeit erreicht wird, angegeben. Sie enthält als Spezialfall die Lösungen vonHadamard-Rybczynski, Taylor u. a. Die schleppende Kraft, die auf den Tropfen einwirkt, wird formuliert. Diese Formel enthält das Gesetz vonFaxen als Spezialfall.Die Funktion der Grenzfläche und ihre Abweichung von der Kugelform wird bestimmt. Sie kann zur Bestimmung genauerer Strömungsfelder in einem Iterationsverfahren angewendet werden.

     

Viscous effects on the linear stability of a pulsanting bubble in acoustic fields

Summary A linear stability theory of the harmonic motion of cavitation bubbles subject to an acoustic field with respect to viscous perturbations is developed. The effects of viscosity are found to be significant only within a layer, adjacent to the gas-liquid interface, the thickness of which is proportional to , where ν is the kinematic viscosity of the liquid and ω the frequency of the acoustic field. We determine a maximum amplitude of the pressure oscillation below which radial oscillations are found to be stable for any frequency ω both in the subharmonic and in the synchronous case.

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Sommario Nel presente lavoro si studiano gli effetti della viscosità sulla stabilità lineare delle oscillazioni armoniche dell'interfaccia di una bolla gassosa immersa in un liquido indefinito e sollecitata da un campo acustico. In particolare si determina l'ampiezza limite delle oscillazioni di pressione al di sotto della quale le oscillazioni dell'interfaccia risultano stabili per qualunque frequenza del campo acustico. Si considerano sia il caso in cui il moto dell'interfaccia è sincrono rispetto all'eccitazione sia quello in cui è subarmonico.

     

Behavior of a small single bubble rising in a rotating flow field

A small single bubble was generated with a single-hole nozzle facing upward in a water bath contained in a rotating cylindrical vessel. The bubble size falls in the surface tension force dominant regime. The vertical, radial, and tangential migration velocities of the bubble were measured with two CCD cameras and a high-speed video camera. The tangential velocity component of water flow was measured with particle image velocimetry. A helical motion of the bubble was observed under every experimental condition. The direction of the helical motion was the same as that of the tangential velocity component. This helical motion is associated with the large initial shape deformation of the bubble near the nozzle exit and the subsequent regular shedding of vortices behind it. The period and amplitude of the helical motion were obtained by analyzing the trajectory of the bubble. These quantities were non-dimensionalized by the volume equivalent bubble diameter and the terminal bubble velocity in the vertical direction and correlated as functions of the Eotvos number. Empirical equations were proposed for the period and amplitude. Originally published in the Journal of JSEM, Vol. 4, No. 2, pp. 38–45 (2004).