On the oscillations of a charged drop of a finite-conductivity viscous liquid

A dispersion relation for the capillary oscillations of a charged spherical drop of a viscous incompressible finite-conductivity liquid is derived and analyzed. It is found that electric currents inside the charged drop equalize its potential and produce liquid flows interacting with both potential and eddy poloidal liquid flows inside the drop that are due to drop oscillations. Taking into account the finiteness of the rate of potential equalization over the drop surface leads to an additional damping of the capillary oscillations that arises because of the increased role of energy dissipation.     

Capillary oscillations of a drop in an electric field

The capillary oscillations of a conducting spheroidal drop with small eccentricity in an electric field are studied. The effect of the electric field is to lower the natural frequencies of oscillations and the damping coefficient.     

Critical conditions for instability of a highly charged oblate spheroidal drop

The spectrum of capillary oscillations of a charged oblate spheroidal drop is calculated in neglect of the interaction between modes by means of a perturbation expansion in the small deviation of the equilibrium shape of the drop from spherical. The critical conditions for instability of its nth mode with respect to the self-charge are calculated in the form of an analytical function describing how the dimensionless Rayleigh parameter characterizing the stability of the drop depends on the value of the spheroidal deformation. Zh. Tekh. Fiz. 69, 10–14 (July 1999)     

A possible mechanism of the acoustic action on partially fluid-saturated porous media

The motion of a liquid drop under the action of acoustic vibration is studied for two limiting cases: the high-frequency case, when the effect of viscous forces can be ignored, and the low-frequency case, when the viscosity is significant. Equations describing the motion of a drop in an axially symmetric capillary with a varying cross section are derived by taking into account the hysteresis of the wetting angle. Numerical calculations are performed for cylindrical, conic, and corrugated capillaries.     

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes, the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop.     

Dispersion properties of two-dimensional phonon crystals with a hexagonal structure

Acoustic and optical properties of two-dimensional phonon crystals with a hexagonal symmetry are described. Differential-difference equations describing plane oscillations of a two-dimensional lattice of material structures are derived in a harmonic approximation, and dispersion dependences of acoustic and optical phonons are calculated. Branches of optical oscillations and intervals of forbidden frequencies are shown to appear when a lattice consists of two types of atoms.     

On oscillatory wave processes on the surface of massive bodies nonuniform in composition

A set of interrelated nonlinear differential equations describing the simultaneous oscillations of material density (acoustic waves) and gravitational potential is derived in terms of Lagrangean formalism (taking into account the gravitational potential is necessary when massive bodies are considered). The natural frequencies of these oscillations are found. It is shown that, when interacting with the gravitational potential, the spectrum of the surface waves is greatly distorted and depends on the 2D surface wavevector not linearly (as a typical spectrum of phonons in a solid) but quadratically. The concept proposed in this work allows one to detect additional acoustic low-frequency signals due to internal disturbances. It is stated that a separate consideration of acoustic and gravitational waves is incorrect because of the strong correlation between them.     

On the influence of stochastic pulsations of a bubble on its translational motion

This communication is devoted to theoretical analysis of the dynamics of a solitary cavitation bubble pulsating in a compressible viscous liquid under the action of a nonuniform acoustic field. The system of two nonlinear ordinary second-order differential equations is integrated numerically. In the range of acoustic field parameters corresponding to the principal resonance region, the bubble performs large-scale spatial oscillations. It is shown that in a very small range of initial radii, the bubble stops its oscillatory motion due to stochastic pulsations and is expelled into the region of the acoustic-pressure block. Therefore, stochastic pulsations of the bubble radically change the form of the solution to the system of the above-mentioned equations.     

Dynamics of Acoustooptic Modulation in a Gyrotropic Medium

A system of equations describing the transformation of dynamic optical transfer functions in gyrotropic crystals with cubic syngony perturbed by a spatially-dependent dynamic field of a slowly varying acoustic signal is derived in the first approximation of the method of slowly varying amplitudes (SVA). The general solution of these equations is obtained in the form of a converging functional series. It can be used to calculate the dynamics of polarization parameters in the angular spectra of interacting light beams for arbitrary power and spatiotemporal structure of the acoustic signal field.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Nonlinear Waves in Carbon Nanotubes under Conditions of Electron-Phonon Bonding

Relative simplicity of the atomic structure of carbon nanotubes being hollow cylinders with walls formed by rings of six carbon atoms (generally, the walls can be multilayered) enables the researchers to use this class of substances as model one to reveal the basic mechanisms of the dynamics of quasi-one—dimensional systems. The present work studies the nonlinear properties of carbon nanotubes with strong electron interactions described by the Hubbard Hamiltonian. A microscopic Hamiltonian describing electrons in carbon nanotubes with allowance for the electron mobility, Coulomb repulsion of electrons in one site of carbon nanotubes, and changes in spacing of the neighboring sites caused by acoustic oscillations is suggested. An effective nonlinear system of equations describing the dynamics of electron wave functions within the framework of the suggested Hamiltonian is derived. The existence of nonlinear stable periodic oscillations of electron wave functions in the examined model, in particular, corresponding to acoustic oscillations with different polarization states is established. The influence of the problem parameters on the character of nonlinear wave stability is revealed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 76–81, June, 2005.     

Generation of the vorticity mode by sound in a Bingham plastic

This study investigates interaction between acoustic and non-acoustic modes, such as vorticity mode, in some class of a non-newtonian fluid called Bingham plastic. The instantaneous equations describing interaction between different modes are derived. The attention is paid to the nonlinear effects in the field of intense sound. The resulting equations which describe dynamics of both sound and the vorticity mode apply to both periodic and aperiodic sound of any waveform. They use only instantaneous quantities and do not imply averaging over the sound period. The theory is illustrated by an example of acoustic force of vorticity induced in the field of a Gaussian sound beam. Some unusual peculiarities in both sound and the vorticity induced in its field as compared to a newtonian fluid, are discovered.     

Acoustic phase conjugation in a three-phase medium

Acoustic phase conjugation is studied in a sandy marine sediment that contains air bubbles in its fluid fraction. The considered phase conjugation is a four-wave nonlinear parametric sound interaction caused by nonlinear bubble oscillations which are known to be dominant in acoustic nonlinear interactions in three-phase marine sediments. Two various mechanisms of phase conjugation are studied. One of them is based on the stimulated Raman-type sound scattering on resonance bubble oscillations. The other is associated with sound interactions with bubble oscillations whose frequencies are far from resonance bubble frequencies. Nonlinear equations to solve the phase conjugation problem are derived, expressions for acoustic wave amplitudes with a conjugate wave front are obtained and compared for various frequencies of the excited bubble oscillations.     

Instability of a charged spherical drop moving parallel to an external electrostatic field

It is shown that the pressure of electrostatic fields induced by the self-charge of a drop and by the polarization charge and aerodynamic pressure of a laminar gas flow around a moving charged drop acting simultaneously reduce the critical instability conditions for the surface of the drop. For these conditions, the spectrum of capillary oscillations of the drop is calculated. It is found that, at various values of the charge, field strength, and velocity of the drop, the vibrational instability of the drop surface develops through the interaction of different oscillation modes, namely, second and third, second and fourth, and third and fifth.     

Renormalized turbulence theory for the ion acoustic problem

Renormalized kinetic theory for the long range collective oscillations of turbulent plasmas is developed through infinite order summations of the interactions in the Vlasov-Poisson self-consistent field equations. Three levels of renormalized turbulence theory are derived, and the simply renormalized equations are solved for the problem of ion acoustic instability. The physical predictions of renormalized turbulence theory are discussed and used to interpret several experiments on ion acoustic turbulence.     

Stability analysis of ultrasound thick-shell contrast agents

The stability of thick shell encapsulated bubbles is studied analytically. 3-D small perturbations are introduced to the spherical oscillations of a contrast agent bubble in response to a sinusoidal acoustic field with different amplitudes of excitation. The equations of the perturbation amplitudes are derived using asymptotic expansions and linear stability analysis is then applied to the resulting differential equations. The stability of the encapsulated microbubbles to nonspherical small perturbations is examined by solving an eigenvalue problem. The approach then identifies the fastest growing perturbations which could lead to the breakup of the encapsulated microbubble or contrast agent.     

Aeroacoustic source analysis in a corrugated flow pipe using low-frequency mitigation

Our study is focused on a phenomenon often encountered in flow carrying pipes, since flow instabilities caused by geometric features may generate acoustic signals and, thereafter, interact with these signals in such a way that powerful pure tones are produced. A modern example is found in the so-called ‘singing risers’, or the gas pipes connecting gas production platforms to the transport network. But the flow generated resonance in a fully corrugated circular pipe may be silenced by the addition of relatively low frequency flow oscillations induced by an acoustic generator. Experiments reported here, aimed at investigating in more detail the coupling between the flow in the pipe, the acoustically generated flow oscillations and the emitted resulting noise, are performed in a specifically designed facility. A rectangular transparent channel using glass walls enables us to use optical techniques to describe in detail the flow field in the corrugation vicinity, in addition to more standard hot-wire anemometry and acoustic pressure measurements with microphones, with and without the acoustically generated low-frequency oscillations.     

Anharmonic interactions of elastic and orientational waves in one-dimensional crystals

Planar oscillations of a chain of dumbbell-shaped particles possessing three degrees of freedom are studied. This system models the dynamics of quasi-one-dimensional crystals consisting of elongated anisotropic molecules. A system of nonlinear differential equations describing the anharmonic interaction of the elastic and orientational waves in the lattice, corresponding to different degrees of freedom of the particles, is constructed assuming a cubic interparticle interaction potential. It is shown that in the low-frequency approximation the system obtained is equivalent to the equations of the moment theory of elasticity, widely employed for describing nonlinear and dispersion properties of layered crystals and phase transformations in alloys. Some types of three-wave collinear interactions are investigated, suggesting the possibility of exciting orientational waves in organic crystals because of their nonlinear interaction with acoustic waves. Fiz. Tverd. Tela (St. Petersburg) 39, 137–144 (January 1997)     

声悬浮液滴的表面毛细波及八阶扇谐振荡

采用声悬浮方法研究了自由液滴表面的毛细波形成机理,并利用主动调制声场技术激发了液滴的八阶扇谐振荡.实验结果表明,当声场调制频率接近液滴本征频率的两倍时,液滴将由轴对称受迫振荡向非轴对称扇谐振荡模态转变.实验与理论分析证实,参数共振是毛细波与扇谐振荡的形成原因.扇谐振荡的本征频率随液滴赤道半径的增大而减小,可通过修正的Rayleigh方程来描述. 关键词： 声悬浮 液滴 毛细波 扇谐振荡     

Instability of a charged spherical viscous drop moving relative to a medium

It is shown that, as the velocity of the flow around a charged drop of viscous liquid increases the drop charge value critical for the occurrence of drop instability rapidly decreases. It is found that, for some domains of values of the charge, the ratio of densities of the media, and the ambient velocity, the even and odd modes of the drop capillary oscillations pairwise couple with each other, which represents drop vibrational instability against the tangential discontinuity of the velocity field at the drop surface. At medium velocities larger than those associated with such domains, the instability growth rates for odd modes exceed the increments of even modes with smaller orders, which corresponds to the parachute-like deformation of the drop in the flow.