Instability and flow of a weakly conducting fluid in the presence of oxidation-reduction reactions at electrodes and recombination

Experiments show that a weakly conducting fluid in a plane-parallel system of electrodes is set into motion if the field intensity is sufficiently great [1–5]. The loss of stability is due to the formation of charges near the electrodes and the influence of the Coulomb forces on these charges. The formation of the space charges is usually attributed to oxidation-reduction electrode reactions and bulk recombination of the ions formed at the electrodes [1–4]. In the present paper, the stability of a weakly conducting fluid in a plane-parallel system of electrodes with symmetric distribution of the space charge is studied. The methods of the theory of solution bifurcation are used to construct the stationary flow which arises after the loss of stability and to investigate the stability of this flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 20–26, July–August, 1981.     

Stability of Thermocapillary Flow in a Flat Layer with Allowance for the Soret Effect

The stability of thermocapillary two-component liquid flow is studied taking into account thermal diffusion. An explicit expression is obtained to construct neutral Marangoni numbers under the assumption of monotonicity of perturbations. The thermocapillary and hydrodynamic instability mechanisms are considered. It is shown that plane perturbations are the greatest hazard to the stability of return flow.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 86–92, September–October, 2005.     

Stability of the boundary layer of a non-Newtonian liquid obeying a power-type rheological law

The stability of the stationary (steady-state) laminar boundary layer of a non-Newtonian liquid obeying a power-type rheological law at a semiinfinite plate situated in a longitudinal flow is analyzed. An approximate formula is derived for estimating the minimum Reynolds number at which the flow loses stability with respect to slight two-dimensional perturbations. Calculations of the point of stability loss for aqueous solutions of carboxyl methyl cellulose are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–124, March–April, 1971.     

Rayleigh stability of shear flow in relaxing media

The stability of steady-state flow is considered in a medium with a nonlocal coupling between pressure and density. The equations for perturbations in such a medium are derived in the linear approximation. The results of numerical integration are given for shear motion. The stability of parallel layered flow in an inviscid homogeneous fluid has been studied for a hundred years. The mathematics for investigating an inviscid instability has been developed, and it has been given a physical interpretation. The first important results in flow stability of an incompressible fluid were obtained in the papers of Helmholtz, Rayleigh, and Kelvin [1] in the last century. Heisenberg [2] worked on this problem in the 1920's, and a series of interesting papers by Tollmien [3] appeared subsequently. Apparently one of the first problems in the stability of a compressible fluid was solved by Landau [4]. The first investigations on the boundary-layer stability of an ideal gas were carried out by Lees and Lin [5], and Dunn and Lin [6]. Mention should be made of a series of papers which have appeared quite recently [7–9]. In all the papers mentioned flow stability is investigated in the framework of classical single-phase hydrodynamics. Meanwhile, in recent years, the processes by which perturbations propagate in media with relaxation have been intensively studied [10–12].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 87–93, May–June, 1976.     

Self-oscillatory flow in asymptotic boundary layers

The loss of stability of a suction-controlled boundary-layer flow with respect to small but finite perturbations is analyzed. Hard excitation of self-oscillations is a special characteristic of this kind of flow. An unstable state of self-oscillation exists within a certain distance of the neutral curve (in the range of stability of the original flow) for all Reynolds numbers Re.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 64–68, March–April, 1976.The author wishes to thank M. A. Gol'dshtik and V. N. Shtern for interest in this work.     

Hydrodynamic stability of Poiseuille flow of a viscoplastic non-Newtonian fluid

The hydrodynamic stability of Poiseuille flow of a viscoplastic fluid is investigated. The flow is shown to be stable for infinitesimal disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 152–154, November–December, 1974.In conclusion the authors thank S. A. Regirer for critical remarks.     

On nonisothermal electroconvection

The flow from the tip of a needle electrode is caused by the Coulomb force acting on the space charge [1–3]. This charge is formed because of the dependence of the conductivity on the temperature, nonuniformity of which is due to Joule heating [1] and the electric field intensity [2] or processes near the electrode [3–5]. The present paper considers the stability of a dielectric liquid between spherical electrodes in order to elucidate the possibility of a thermoelectrohydrodynainic flow due to Joule heating. In the presence of external heating, the possibility of such a flow has been demonstrated both experimentally and theoretically [6–8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 133–137, March–April, 1980.     

Oscillatory rotationally symmetric loss of stability of nonisothermal couette flow

A study is made of the stability of nonisothermal Couette flow — steady flow of a viscous heat conducting fluid between two rotating concentric cylinders heated to different temperatures. The methods of perturbation theory are used to establish conditions sufficient for bifurcation of a neutral curve of oscillatory instability from the neutral curve of monotonic instability. Computer calculations show that for certain values of the parameters of the problem these conditions are realized and there is an oscillatory loss of stability of the nonisothermal Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–80, January–February, 1984.I thank V. I. Yudovich for constant interest in the work.     

Stability of viscous flow between rotating and stationary disks

The linear problem of the stability of viscous flow between rotating and stationary parallel disks is solved in the locally homogeneous formulation using the method of normal modes. The main flow is assumed to be selfsimilar with respect to the radial coordinate. The system of sixth-order equations, derived for the amplitude functions of the disturbances, is integrated by a finite difference method. The stability characteristics with respect to disturbances of four types are calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–87, November–December, 1991.     

Stability of colliding flows

The stability of the flow in the interaction region of colliding streams is investigated in the framework of linear theory. To simplify the analysis, the treatment is restricted to the case of an ideal fluid and an irrotational main flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti Gaza, No. 5, pp. 143–147, September–October, 1981.     

Limit of main flow stability in spherical layers

This paper presents the results of an experimental study of the stability limit for the main flow of an incompressible viscous liquid between two concentric spheres rotating coaxially. In the space of the governing parameters, a three-dimensional surface of the main flow stability is obtained.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–70, July–August, 1996. In memory of Yurii Nikolaevich Belyaev     

Effect of nonisothermality of the surface of a thin profile on the stability of a laminar boundary layer

Investigations of the stability of a subsonic laminar boundary layer have shown that, other things being equal, the stability of the laminar flow is considerably improved by cooling the entire surface of the body to a constant temperature T_w=const lower than the temperature of the free stream [1–3]. This is attributable to an increase in the critical Reynolds number of loss of stability and a decrease in the range of unstable perturbations of the Tollmien-Schlichting wave type when the surface is cooled. Recently, in the course of investigating the stability of laminar flow over a flat plate it was found [4, 5] that a similar improvement in flow stability can be achieved by raising the temperature of a small part of the surface near the leading edge of the plate. In this study we examine the possibility of delaying the transition to turbulent flow by creating a nonuniform temperature distribution along the surface of thin profiles, where the development of an adverse pressure gradient in the outer flow has a destabilizing effect on the boundary layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 36–42, September–October, 1986.In conclusion, the authors wish to thank M. N. Kogan for useful discussions of their results.     

Stability of two-phase gas-solid particle flow in a boundary layer

The stability of a boundary layer above a flat plate with a pressure gradient in the case when a gas flow carries suspended particles of an admixture is considered on the basis of the equations for the aeromechanics of heterogeneous media [1, 2]. The investigation is carried out in the framework of the same assumptions as in [3], where the stability of Poiseuille flow in a channel was studied. The velocity profile of the unperturbed flow is selected from the Falkner-Skan family. The Chebyshev spectral element method is used for the calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 60–64, March–April, 1987.     

Linear stability in the flow of a liquid film concurrent with a gas flow

The two-phase flow of liquid films are often encountered in practice, but the number of theoretical papers devoted to this problem is limited. The problem of the linear stability of a viscous liquid film subjected to a gas flow has been formulated in [1] and, in somewhat different form, in [2]. The linear stability of plane-parallel motion in films has been studied analytically in [1–8] for some limiting cases. The range of validity of the analytic approaches remains an open question. Therefore, an exact numerical analysis of flow stability over a fairly broad range is required. In the present paper a separate solution of the problem for the gas and the liquid is shown to be possible. The Orr-Sommerfeld equation has been integrated numerically, and the results are compared to the results of analytic calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–146, January–February, 1976.The author is grateful to É. É. Markovich for directing the work and to V. Ya. Shkadov for his interest in the work and many useful comments.     

Locality properties of the problem of hydrodynamic stability

Locality properties are formulated for short-wave length disturbances in the problem of hydrodynamic stability, which together with global flow stability enable us to study the stability of particular sections of the stream, e.g., the flow core or the zone next to the wall. The locality properties are illustrated in the spectrum of small perturbations of plane Poiseuille flow and flows which are obtained by deforming a small section of the Poiseuille parabola. Such a deformation produces points of inflection which lead to the appearance of growing perturbations with wavelength of the order of the deformation zone. It is shown that discontinuities in the velocity profile leads to the loss of stability for high enough Reynolds' numbers.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 2, pp. 56–61, March–April, 1970.     

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.     

DYNAMICS AND STABILITY OF PINNED–CLAMPED AND CLAMPED–PINNED CYLINDRICAL SHELLS CONVEYING FLUID

The paper examines the dynamics and stability of fluid-conveying cylindrical shells having pinned–clamped or clamped–pinned boundary conditions, where “pinned” is an abbreviation for “simply supported”. Flügge's equations are used to describe the shell motion, while the fluid-dynamic perturbation pressure is obtained utilizing the linearized potential flow theory. The solution is obtained using two methods — the travelling wave method and the Fourier-transform approach. The results obtained by both methods suggest that the negative damping of the clamped–pinned systems and positive damping of the pinned–clamped systems, observed by previous investigators for any arbitrarily small flow velocity, are simply numerical artefacts; this is reinforced by energy considerations, in which the work done by the fluid on the shell is shown to be zero. Hence, it is concluded that both systems are conservative.     

Convective and absolute instabilities in counter-rotating spiral Poiseuille flow

We present results of an experimental study on the stability of Taylor–Couette flow in case of counter-rotating cylinders and an imposed axial through flow. We are able to confirm results form recent numerical investigations done by Pinter et al. [24] by measuring the absolute and convective stability boundaries of both propagating Taylor vortices (PTV) and spiral vortices (SPI). Thus our work shows that these theoretical concepts from hydrodynamic stability in open flows apply to experimental counter-rotating Taylor–Couette systems with an imposed axial through flow. PACS 47.20.-k, 05.45.-a, 47.15.fe     

Nonlinear Electrohydrodynamic Stability of a Poiseuille Two–Layer Flow

The long–wave stability of the Poiseuille two–layer flow of homogeneous viscous dielectrics between plate electrodes under a constant potential difference is studied in an electrohydrodynamic approximation. A linear asymptotic stability analysis shows that surface polarization forces are a destabilizing factor, in addition to viscous stratification. The method of many scales is used to obtain the Kuramoto—Sivashinsky equation governing the weakly nonlinear evolution of the interface between the dielectrics. Within the framework of the approaches used, it is shown that nonlinear interactions limit perturbation growth and the interface does not fail even for a rather large potential difference.     

Laminar boundary layer with uniform suction on flat plate in oscillating flow

We examine unsteady incompressible fluid flow in a laminar boundary layer with uniform suction for longitudinal flow over a flat plate when the external stream is a flow with constant velocity, on which there is superposed a sinusoidal disturbance convected by the stream, analogous to [1]. We study the stability of such flow in the boundary layer.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 3, pp. 66–70, May–June, 1970.