Stability of a viscous liquid jet in a high-frequency alternating electric field

The stability of a liquid electrolyte placed in a tangential electric field oscillating harmonically at high frequency is considered assuming that the liquid is viscous and Newtonian. It is shown that, if the Peclet number calculated from the thickness of the Debye layer is small, the problem can be solved separately for the electrodynamic part of the problem in the Debye layer and for the hydrodynamic part of the problem in the jet. The linear stability of the trivial solution of the problem is investigated. A dispersion relation is derived and used to study the effect of the amplitude and frequency of electric field oscillations on the stability of the jet. It is shown that the presence of the external oscillating field has a stabilizing effect on the jet. The basic stability regimes as functions of the control parameters of the problem and bifurcation changes in the regimes are investigated.     

Instability of a liquid jet in a high-frequency alternating electric field

Stability of a liquid (electrolyte) jet in a tangential electric field harmonically oscillating with a high frequency is considered under an assumption of an ideal liquid. It is demonstrated that it is possible to solve the electrodynamic and hydrodynamic parts of the problem inside the jet separately if the Peclet number based on the Debye layer thickness is small. Linear stability of the trivial solution of the problem is studied. A dispersion relation is derived, which is used to study the effect of the amplitude and frequency of electric field oscillations on jet stability. An increase in the amplitude of oscillations is demonstrated to exert a stabilizing effect, whereas an increase in frequency leads to insignificant destabilization of the jet.     

ANALYSIS OF JANUS PARTICLES IN ELECTRIC FIELD

对外加电场作用下无穷大电解质溶液中二维Janus 导电颗粒的受力特性进行研究。在量级分析的基础上,对电解质溶液电渗流动的基本方程组进行解耦,通过引入有限域确保解的存在性,进而得到圆形颗粒周围电场和流场的解析解与半解析解。基于半解析解给出颗粒所受力矩与外加电场方向角之间的变化曲线,从而得到二维Janus 圆形颗粒的平衡姿态及其稳定性特性。在此基础上,通过数值方法给出了电解质溶液中二维Janus 胶囊的受力特性,平衡姿态及其稳定性特性。     

Annular surface-charged jet in an external electric field

The problem of the shape of an annular charged jet in an external electric field is considered. In the strong-field approximation, the formulation of the problem is reduced to a system of ordinary differential equations. The asymptotics of the solutions at large distances from the point of outflow are investigated. The condition of formation of the jet profile non-increasing along the streamwise coordinate is found.     

Structure and stability of the interface in a magnetizable fluid

The problems of interface stability in magnetizable and polarizable fluids are considered in the case of the surface tension tensor dependent on the electromagnetic field strength. For describing this dependence the model proposed by A.N. Golubyatnikov (1986) is used. The investigation of the internal interface structure showed that for single-component systems, as a rule, the dependence of the surface tension on the field strength corresponds to surface phase properties paramagnetic in the normal and diamagnetic in the tangential direction. It is shown that within the framework of the model adopted the thermodynamic stability of the surface depends on the thickness of the interphase layer. Necessary stability conditions are obtained for plane interfaces in media with a constant magnetic permeability outside the interphase layer. The problem of stability of the horizontal free surface of an ideal magnetic field in an external magnetic field (similar to the problem of stability of the horizontal interface of two polarizable fluids in an external electric field) is solved for an arbitrary orientation of the external field relative to the interface. The stability loss is now accompanied by qualitative effects absent in the case of the surface tension tensor independent of the electromagnetic field strength.     

Heat transfer in the assimilation of a pre-heated jet into non-uniform streams

 The flow assimilation of a pre-heated jet into non-uniform external streams has been examined. Two possible families of downstream velocity and temperature profiles are identified. The formulation of the problem allows for a comprehensive numerical solution over the entire flow and temperature field downstream of the jet source. The role of the respective families of downstream asymptotes is elucidated, and consistency is demonstrated between a spatial stability analysis of the profiles and the numerical results. Received on 12 May 2000     

横向交流电场下液膜参数不稳定性分析

当将运动的平面液膜置于横向的交流电场之间时会产生参数振荡现象.为了得到交流电场下平面液膜的色散关系并为液膜的破碎行为分析提供理论基础,本文基于漏电介质模型对液体的电学特性进行假设,对平面液膜在直流和交流电场下的参数不稳定性进行了分析.由于主流是基于时间的流动,在稳定性分析中引入了Floquet理论.在文中,将电场定义为...     

Some problems in the theory of plane jets of conducting fluid

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation).The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field.The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12].This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.     

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.     

Plasma in a high-frequency electric field with a reflective condition on the boundary

An analytical solution is obtained for the linearized problem of the behavior of a collisional gas plasma in a half-space in an external alternating electric field. It is assumed that the electrons are mirror-reflected from the plasma boundary. The solution is used for finding the screened field. The case of an external field frequency close to the plasma frequency is investigated separately.     

Model of Nonlinear Evolution of Long-Wave Perturbations on an Ideally Conducting Jet with Current in a Longitudinal Magnetic Field. Collision of Magnetized Jets

Within the framework of the magnetohydrodynamic approach, a system of equations is derived for nonlinear evolution of long-wave axisymmetric perturbations on a conducting fluid jet with surface electric current, located along the axis of a conducting solid cylinder in a longitudinal magnetic field. The fluid is assumed to be inviscid, incompressible, and ideally conducting, like the cylinder walls. It is shown that, if the longitudinal field is uniform and the axial flow is shear-free, this system can be either hyperbolic or elliptic-hyperbolic, depending on problem parameters. The boundaries of hyperbolicity and ellipticity regions in the space of solutions are determined. In the hyperbolicity region, equations of characteristics and conditions on them are obtained. The problem of the decay of velocity discontinuity on the jet is considered. Conditions are found for the existence of a continuous self-similar solution in the hyperbolicity region, corresponding to collision of jets.     

电场作用下无黏聚焦射流的时间不稳定性研究

基于电场作用下的流动聚焦实验建立了简化的理论模型,开展了带电同轴液气射流的时间不稳定性分析.在无黏假设下,得到了扰动在时间域内发展演化的解析形式的色散关系,分析了主要控制参数对不稳定模态的影响.结果表明,只有轴对称扰动和第一类非轴对称扰动在时间域内是增长的;液气界面的表面张力对轴对称扰动有着双重影响而对非轴对称扰动起抑制作用;外层气体的流速以及密度的增加均能促进射流的失稳.这些结论与实验结果是定性一致的.结果也表明,在不考虑初始界面电荷密度时,单一的轴向电场能抑制射流的失稳.      

Stability of a volumetrically charged dielectric fluid jet accelerated in an electric field collinear to the jet

In the approximation linear in the amplitude of capillary waves (generally nonaxisymmetric) on the surface of a volumetrically charged dielectric fluid jet accelerated in an external electrostatic field collinear to the jet axis, a dispersion equation is derived and analyzed. It is shown that for certain values of physical parameters the effect of the external electric field stabilizing the capillary waves and the destabilizing effect of the capillary forces and the electrostatic forces exerted by the jet charge may compensate one another for both axisymmetric and nonaxisymmetric, with a high degree of asymmetry, waves. The instability of flexural waves cannot be suppressed completely and can be realized for sufficiently small wave numbers.     

Stability of Transonic Shock Solutions for One-Dimensional Euler–Poisson Equations

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler–Poisson systems are investigated. First, a steady transonic shock solution with a supersonic background charge is shown to be structurally stable with respect to small perturbations of the background charge, provided that the electric field is positive at the shock location. Second, any steady transonic shock solution with a supersonic background charge is proved to be dynamically and exponentially stable with respect to small perturbations of the initial data, provided the electric field is not too negative at the shock location. The proof of the first stability result relies on a monotonicity argument for the shock position and the downstream density, and on a stability analysis for subsonic and supersonic solutions. The dynamical stability of the steady transonic shock for the Euler–Poisson equations can be transformed to the global well-posedness of a free boundary problem for a quasilinear second order equation with nonlinear boundary conditions. The analysis for the associated linearized problem plays an essential role.     

Similarity autooscillations in a plane jet

Experimental investigations into the stability of a plane jet [1, 2] show that after the stationary flow has lost its stability a stable autooscillatory regime arises. In the present paper, an autooscillatory flow in a jet is studied theoretically on the basis of a plane-parallel flow in a fairly wide channel in the presence of a field of external forces. The external forces are such that at zero amplitude of the autooscillations they produce a Bickley—Schlichting velocity profile. The excitation of the secondary regimes is studied by the methods of bifurcation theory [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 26–32, May–June, 1979.We thank M. A. Gol'dshtik and V. N. Shtern for discussing the formulation of the problem and the results.     

Stability of a surface-charged viscous jet in an electric field

The stability of a surface-charged cylindrical jet in a longitudinal uniform electric field with respect to capillary pertubations is investigated in the linear approximation. The evolution of both axisymmetric and azimuthal-periodic perturbations is analyzed. In the latter case the first two modes among the azimuthal wavenumbers — bending and Bohr — are considered. Axisymmetric and bending instabilities lead to the transverse disintegration of the jet into individual drops and the Bohr mode to the longitudinal separation of the input jet into two parts. It is found that the axisymmetric and bending instabilities, respectively, can be completely suppressed and significantly attenuated by means of an external longitudinal field. In this case the role of the Bohr mode becomes more important leading under certain conditions to longitudinal longwave jet splitting. Events which can be interpreted as manifestations of longitudinal partition of the jet (dumbbell-like cross-section, branching nodes) are observed in experiments with evaporating polymer-solution microjets. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 29–40, March–April, 1998. The work was carried out with support from the Russian Foundation for Fundamental Research (project No. 97-01-00153).     

Solution of the problem of flow of a non-axisymmetric swirling submerged jets

This paper considers the problem of a non-axisymmetric swirling jet of an incompressible viscous fluid flowing in a space flooded with the same fluid. The far field of the jet is studied under the assumption that the angular momentum vector corresponding to the swirling of the jet is not collinear to the momentum vector of the jet. It is shown that the main terms of the asymptotic expansion of the full solution for the velocity field are determined by the exact integrals of conservation of momentum, mass, and angular momentum. An analytical solution of the problem describing the axisymmetric swirling jet is obtained.     

The role of external influences in the formation of waves on the surface of a flowing-down film of a viscous fluid

The example of two non-stationary forces is used to study the impact of external influences leading to the occurrence of additional ponderomotive forces on the wave regimes of the film freely flowing down a vertical surface. The first case describes a ferromagnetic fluid film affected by the magnetic field, and the second case touches upon a dielectric fluid film affected by the electric field. For the given forces, in the case of small flow rates, the problem is reduced to the solution of a model equation for the perturbation of the film thickness. The numerical solutions of the problem are obtained, and several characteristic scenarios of evolution of periodical perturbations are considered. It is shown that changes in the boundaries of the region of linear stability of the unperturbed flow with a flat free surface under the influence of ponderomotive forces have a great impact on the flow.     

Charged jet of an incompressible liquid in an electric field

The problem of the jet flow of an incompressible liquid with free boundaries in an electric field is solved in the approximation of a laminar boundary layer. An exact solution for a round jet is found in the class of self-similar solutions. In the case of a flat slit jet, a solution is constructed in the form of a series in powers of the coordinate transverse to the plane of symmetry. The dependence of the radius (half-width) on the longitudinal coordinate is given. Branch of the Karpov Physicochemistry Institute, State Science Center, Obninsk 249020. Karpov Physicochemistry Institute, State Science Center, Moscow 115523. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 12–16, July–August, 1998.     

电场作用下流动聚焦的实验研究

通过在流动聚焦的同轴液-气射流区域施加电场, 开展了电场力和气动力共同作用下锥形以及带电射流的不稳定性特性实验研究. 实验在精密设计的流动聚焦装置上完成, 分析了外部电压、气体压力降和液体流量等主要控制参数对流动聚焦过程的影响, 获得了锥形的振动模式和稳定模式及其之间的转换, 得到了射流的滴模式、轴对称模式、共存模式和非轴对称模式及其转换并定量分析了电场对射流尺寸参数的影响. 结果表明, 相比于单一的流动聚焦, 该方法能够增强锥形的稳定性, 促进液体射流雾化, 减小颗粒的直径, 因此在科技领域和工程实际中具有重要的应用价值.