微尺度空泡溃灭驱使微球运动的机理研究

受限空泡的溃灭是气泡动力学的核心问题,研究表明毫米尺度的空泡溃灭可以拉动附近同尺度的悬浮颗粒运动.本文针对受限空泡溃灭在微尺度下的行为开展研究,通过气泡驱动的球形微马达实验,给出了微气泡溃灭形成射流从而显著推动马达前进的现象,但由于溃灭时间很短,Micro PIV系统不能给出足够的流动细节.进而采用基于流体体积的数值手段模拟了这一过程,获得了流场的时空分布,并通过积分估算了微球获得的冲量,给出了微球所能达到的速度.结果表明这一问题与尺度密切相关,微尺度下空泡溃灭足以推动微球显著运动,在气泡尺寸固定的情况下,微球半径越小,微球与气泡间距离越近,推动的效果越明显.冲量定理则定性地解释了宏观尺度与微尺度下存在差异的原因.这一特殊的微流动问题不但扩展了空化研究的尺度范围,揭示了微尺度下空泡与颗粒作用的特性,而且对提高微马达的驱动效率也具有重要意义.     

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.     

气泡碰壁受力模型和反弹规律

对Mo=10-8~10-12及Re=5~750范围内的上升气泡与壁面垂直碰撞问题进行了理论求解，研究了不同控制参数下气泡碰壁反弹的规律.气泡上升和碰撞过程的运动方程考虑了浮力、液体阻力、附加质量力和与壁面碰撞时引起的薄膜诱导力.气泡碰壁过程气泡界面与壁面形成的液膜厚度变化规律由Stokes-Reynolds方程计算得到.膜内气泡变形引起的流体压强采用Young-Laplace方程求解.结果表明，基于SRYL方程的薄膜诱导力模型可以很好地预测不同Reynolds数下气泡0到多次的反弹轨迹，计算结果与实验结果吻合良好.气泡在碰壁反弹过程中会形成丰富的薄膜形状，如酒窝状变形，丘疹状变形和涟漪状变形.气泡界面变形会引起膜内压强的变化，压强的分布规律与气泡界面形状有着重要的关系.气泡在与壁面碰撞的过程中，薄膜诱导力会起主导作用，且随着Reynolds数的增加薄膜诱导力最大量级增大.气泡碰撞壁面时，反弹次数与Reynolds数有着直接的联系，不同Morton数下的气泡均在相同Reynolds数附近发生气泡反弹次数的变化.      

Motion of micrometer sized spherical particles exposed to a transient radial flow: attraction, repulsion, and rotation

It is now accepted that the physical forces in ultrasonic cleaning are due to strongly pulsating bubbles driven by the sound field. Here we have a detailed look at bubble induced cleaning flow by analyzing the transport of an individual particle near an expanding and collapsing bubble. The induced particulate transport is compared with a force balance model. We find two important properties of the flow which explain why bubbles are effectively cleaning: During bubble expansion a strong shear layer loosens the particle from the surface through particle spinning and secondly an unsteady boundary layer generates an attractive force, thus collecting the contamination in the bubble's close proximity.     

II. Recirculation flow induced by a bubble stream rising in a viscous liquid

The recirculation flow induced by the rising motion of a bubble stream in a viscous fluid within an open-top rectangular enclosure is studied. The three-dimensional volume averaged conservation equations are solved by a control-volume method using a hybrid finite differencing scheme to describe the liquid phase hydrodynamics. The momentum exhange between the bubbles and the liquid phase is modeled with a source term equals to the volumetric buoyancy force acting on the gas in the bubble stream. The volumetric buoyancy force accounts for in line interactions between bubbles through the average gas volume fraction in the gas liquid column which depends on the size and the rising velocity of bubbles. The fluid flow within an open-top rectangular enclosure is further investigated by particle image velocimetry for a bubble stream rising in a water-glycerol solution. The measured fluid velocities in a vertical plane are compared with the predictions of the numerical model over a wide range of fluid viscosity (43 mPa s-800 mPa s) and gas flow rates. Finally, the recirculation flows resulting from the interaction of two neighbouring vertical bubble streams are studied. Received: 23 July 1997 / Revised: 19 December 1997 / Accepted: 11 May 1998     

The use of a linear Halbach array combined with a step-SPLITT channel for continuous sorting of magnetic species

The Quadrupole Magnetic Sorter (QMS), employing an annular flow channel concentric with the aperture of a quadrupole magnet, is well established for cell and particle separations. Here we propose a magnetic particle separator comprising a linear array of cylindrical magnets, analogous to the array proposed by Klaus Halbach, mated to a substantially improved form of a parallel plate SPLITT channel, known as the step-SPLITT channel. While the magnetic force and throughput are generally lower than for the QMS, the new separator has advantages in ease of fabrication and the ability to vary the magnetic force to suit the separands. Preliminary experiments yield results consistent with prediction and show promise regarding future separations of cells of biomedical interest.     

Physical forces exerted by microbubbles on a surface in a traveling wave field

The effect of a wave with a varying traveling component on the bubble activity as well as the physical force generated by microbubbles on a surface has been studied. The acoustic emission from a collection of bubbles is measured in a 928 kHz sound field. Particle removal tests on a surface, which actually measures the applied physical force by the bubbles on that surface, indicate a very strong dependence on the angle of incidence. In other words, when the traveling wave component is maximized, the average physical force applied by microbubbles reaches a maximum. Almost complete particle removal for 78 nm silica particles was obtained for a traveling wave, while particle removal efficiency was reduced to only a few percent when a standing wave was applied. This increase in particle removal for a traveling wave is probably caused by a decrease in bubble trapping at nodes and antinodes in a standing wave field.     

Force,momentum and topology of a moving magnetic domain

The following general relations involving force, momentum and topological winding number of a translating magnetic domain are derived from the Landau—Lifshifz equation in a context appropriate to bubbles: The gyrotropic force tending to deflect a steadily moving domain is proportional to a mean winding number linear in Bloch-point coordinates. The time derivative of the canonical momentum for a domain of integer winding number is equal to the total force, which must include gyrotropic and dissipative terms. A new contour integral expresses the momentum in the limit of vanishing wall thickness. Approximate equations of quasi-steady domain motion are cast into a form resembling Hamiltion's equations for a particle. Discussion centers on applications to gradientless propagation, bubble saturation velocity, and the Blochline model of inertial effects, and on general limitations of the theory.     

非球形效应对强声场中次Bjerknes力的影响

考虑了非球形气泡在声场中的形状振动,推导了非球形气泡和球形气泡之间的次Bjerknes力方程,数值模拟了声场中非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡之间的次Bjerknes力,并对非球形气泡和球形气泡之间的次Bjerknes力的影响因素进行了分析讨论.研究结果表明:当驱动声压振幅大于非球形气泡的Black阈值且又能使得非球形气泡稳定振动时,在第一个声驱动周期内,非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡的次Bjerknes力方向差异较大,在大小上是两个球形气泡次Bjerkens力的数倍,且有着更长的作用距离.非球形气泡和球形气泡之间的次Bjerknes力取决于非球形气泡的形状模态、两个气泡初始半径的比值、驱动声压振幅、气泡间距和两个气泡的相对位置.     

Interaction of a bubble and a bubble cluster in an ultrasonic field

Using an appropriate approximation, we have formulated the interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster. The behavior of the bubbles is observed in coupled and uncoupled states. The oscillation of bubbles inside the cluster is in a coupled state. The numerical simulation demonstrates that the secondary Bjerknes force can be influenced by the number density, initial radius, distance, driving frequency, and amplitude of ultrasound. However, if a bubble approaches a bubble cluster of the same initial radii, coupled oscillation would be induced and a repulsive force is evoked, which may be the reason why the bubble cluster can exist steadily. With the increment of the number density of the bubble cluster, a secondary Bjerknes force acting on the bubbles inside the cluster decreases due to the strong suppression of the coupled bubbles. It is shown that there may be an optimal number density for a bubble cluster which can generate an optimal cavitation effect in liquid for a stable driving ultrasound.     

Theoretical analysis of interaction between a particle and an oscillating bubble driven by ultrasound waves in liquid

A theoretical model is developed to describe the interaction of a particle and an oscillating bubble at arbitrary separation between them. The derivation of the model is based on the multipole expansion of the particle and bubble velocity potentials and the use of Lagrangian mechanics. The model consists of three coupled ordinary differential equations. One of them accounts for the pulsation of the bubble and the other two describe the translation of the bubble and particle in an infinite, incompressible liquid. The model here is accurate to order 1/d~(10), where d is the distance between the centers of the particle and bubble. The effects of the size and density of the particle are investigated, namely, the interaction between the particle and bubble changes from repulsion to attraction with the increment of the particle density, and the increment of the particle size makes the interaction between the particle and bubble stronger. It is demonstrated that the driving frequency and acoustic pressure amplitude can affect the interaction of the particle and bubble. It is shown that the correct modeling of the translational dynamics of the bubble and particle at small separation distances requires terms accurate up to the tenth order.     

Mixing-induced CP violating sources for electroweak baryogenesis from a semiclassical approach

The effects of flavor mixing in electroweak baryogenesis is investigated in a generalized semiclassical WKB approach. Through calculating the non-adiabatic corrections to the particle currents, it is shown that extra CP violation sources arise from the off-diagonal part of the equation of motion of particles moving inside the bubble wall. This type of mixing-induced source is of first order in a derivative expansion of the Higgs condensate, but it is oscillation suppressed. The numerical importance of the mixing-induced source is discussed in the minimal supersymmetric standard model and compared with the source term induced by a semiclassical force. It is found that in a large parameter space where oscillation suppression is not strong enough, the mixing-induced source can dominate over that from the semiclassical force.     

不同沙粒底面下气泡脉动特性实验研究

通过高速摄影系统对电火花气泡与不同沙粒底面间的相互作用进行了实验研究,并改变气泡与沙粒底面之间的距离.实验结果表明:气泡在与沙粒底面的相互作用中会产生两种明显不同的现象,即形成与近刚性壁面类似的气泡射流以及“蘑菇状”气泡,“蘑菇状”气泡撕裂形成两个气泡,随后产生两个反方向的沿轴线方向的射流.沙粒底面边界具有刚性与弹性两种特征.另外,随着气泡与沙粒底面之间的距离d的增大,气泡脉动周期先增大然后减小,存在气泡脉动周期峰值.对于不同的沙粒底面边界,出现气泡脉动周期峰值的距离d随着沙底粒径的增大而越小.     

Collective bubble dynamics near a surface in a weak acoustic standing wave field

The transport of bubbles to a neighboring surface is very important in surface chemistry, bioengineering, and ultrasonic cleaning, etc. This paper proposes a multi-bubble transport method by using an acoustic standing wave field and establishes a model that explains the multi-bubble translation by expressing the balance between Bjerknes forces and hydrodynamic forces on a bubble in a liquid medium. Results indicated that the influence of primary Bjerknes force, secondary Bjerknes force, and buoyancy force on the bubble translation depends on the position of the target bubble in the acoustic field. Moreover, it was found that increasing the size of a bubble or pressure amplitude can accelerate the bubble motion and enhance the bubble-bubble interaction. The secondary Bjerknes force between two bubbles can switch from an attractive one when they oscillate in phase to a repulsive one when the bubble oscillations are out of phase. These findings provide an insight into the multi-bubble translation near a surface and can be applied to future bubble motion control studies, especially in drug delivery, sonoporation, and ultrasonic cleaning.     

Casimir Interaction between a plate and a cylinder

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate sphere, where it is known at large separations. The force has an unexpectedly weak decay approximately L/[H3 ln(H/R)] at large plate-cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.     

Model for bubble pulsation in liquid between parallel viscoelastic layers

A model is presented for a pulsating spherical bubble positioned at a fixed location in a viscous, compressible liquid between parallel viscoelastic layers of finite thickness. The Green's function for particle displacement is found and utilized to derive an expression for the radiation load imposed on the bubble by the layers. Although the radiation load is derived for linear harmonic motion it may be incorporated into an equation for the nonlinear radial dynamics of the bubble. This expression is valid if the strain magnitudes in the viscoelastic layer remain small. Dependence of bubble pulsation on the viscoelastic and geometric parameters of the layers is demonstrated through numerical simulations.     

Irreversible electrokinetic repulsion at zero-Reynolds-number sedimentation

Stokes-flow reversibility is violated in electrolyte solutions by a streaming-potential mechanism, where nonuniform convective currents within Debye layers surrounding charged particles induce electric fields in the electroneutral Ohmic bulk. We demonstrate the irreversibility consequences of this phenomenon for the problem of particle-pair sedimentation, where the two particles experience a repulsive force driven by bulk Maxwell stresses. At small separations the force scales inversely with the third power of separation distance. This singular behavior is associated with the counterrotation of the two torque-free particles, which leads through a lubrication mechanism to an intense electric field in the narrow gap between them. At large separations the force follows an inverse dependence upon the fourth power of separation, now associated with rectilinear particle motion.     

Influences of different forces on the bubble entrainment into a stationary Gaussian vortex

Simulations of bubble entrainment into a stationary Gaussian vortex are performed by using the combined particle tracking method (PTM) and boundary element method (BEM). Before the bubble is captured by the vortex core, oscillation and migration of the quasi-spherical nucleus are solved by using improved RP equation and the momentum theorem in the Lagrangian reference frame simultaneously, and the trajectory of the nucleus presents a kind of reduced helix shape. After captured by the vortex core, the bubble grows immediately and moves and deforms along the vortex core axis. The non-spherical evolution and deformation of the bubble is simulated by adopting a mixed Eulerian-Lagrangian method. The output of quasi-spherical stage is taken as the input of non-spherical stage, and all the behaviors of the entrained bubble can be simulated such as inception, motion, deformation and split. Numerical results agree well with published experimental data. On this basis, the influences of various factors such as viscosity, surface tension, buoyancy are studied systemically. Hopefully the results from this paper would provide some insight into the control on vortex bubble entrainment.     

过冷沸腾丝上气泡运动的动态模拟

本文以核态池沸腾100μm铂丝上单个气泡的动力学行为为研究现象进行数值模拟,采用能量方程求解丝上以运动气泡为中心的局部区域内的温度分布,同时引入了在核态池沸腾丝上运动气泡粘性力经验公式,以此来考虑Marangoni驱动力和粘件力相等时的运动气泡稳态速度,最后分析了气泡在运动过程中吸收热量的特性.为理论求解丝上核态沸腾运动气泡的稳态速度和吸热特性积累一些理论根据.     

Study on the bubble transport mechanism in an acoustic standing wave field

The use of bubbles in applications such as surface chemistry, drug delivery, and ultrasonic cleaning etc. has been enormously popular in the past two decades. It has been recognized that acoustically-driven bubbles can be used to disturb the flow field near a boundary in order to accelerate physical or chemical reactions on the surface. The interactions between bubbles and a surface have been studied experimentally and analytically. However, most of the investigations focused on violently oscillating bubbles (also known as cavitation bubble), less attention has been given to understand the interactions between moderately oscillating bubbles and a boundary. Moreover, cavitation bubbles were normally generated in situ by a high intensity laser beam, little experimental work has been carried out to study the translational trajectory of a moderately oscillating bubble in an acoustic field and subsequent interactions with the surface. This paper describes the design of an ultrasonic test cell and explores the mechanism of bubble manipulation within the test cell. The test cell consists of a transducer, a liquid medium and a glass backing plate. The acoustic field within the multi-layered stack was designed in such a way that it was effectively one dimensional. This was then successfully simulated by a one dimensional network model. The model can accurately predict the impedance of the test cell as well as the mode shape (distribution of particle velocity and stress/pressure field) within the whole assembly. The mode shape of the stack was designed so that bubbles can be pushed from their injection point onto a backing glass plate. Bubble radial oscillation was simulated by a modified Keller–Miksis equation and bubble translational motion was derived from an equation obtained by applying Newton’s second law to a bubble in a liquid medium. Results indicated that the bubble trajectory depends on the acoustic pressure amplitude and initial bubble size: an increase of pressure amplitude or a decrease of bubble size forces bubbles larger than their resonant size to arrive at the target plate at lower heights, while the trajectories of smaller bubbles are less influenced by these factors. The test cell is also suitable for testing the effects of drag force on the bubble motion and for studying the bubble behavior near a surface.