Interaction of a magnetic liquid with a conductor containing current and a permanent magnet

The present study investigates the force exerted by a magnetic liquid on a conductor with a current or a permanent magnet located near its infinite free surface. It is shown that this force is equal to the weight of the liquid raised by the magnetic field above the original horizontal level. The force is found for the cases when the liquid is weakly magnetic and when the shape of its surface differs little from plane. Consideration is given to the equilibrium of a magnet suspended on a small spring near the surface of the magnetic liquid. The critical height is found at which the magnet ceases to be held by the spring and is torn off into the liquid. The experimentally obtained values of the magnitude of of the force acting on the magnet and the height of collapse of the magnet into the liquid are in good agreement with the theoretical results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 176–181, March–April, 1988.The authors are grateful to V. V. Gogosov for valuable discussion of the study.     

Forces acting on a weakly conductive dielectric in an electric field

The nature of the forces acting on a weakly conductive liquid dielectric in an electric field will be considered. In the general case there act upon the liquid dielectric a Coulomb force related to space charge and a polarization force [1]. In many studies the motion of a conductive liquid dielectric has been explained by the presence of the polarization force, with the Coulomb force being ignored. In the present study it will be demonstrated that the force related to space charge may be larger than or of the same order as the forces connected with polarization of the medium and, generally speaking, must be considered in describing the equations of motion in concrete cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 155–157, January–February, 1977.     

Electroconvective stability of a weakly conducting liquid

In inhomogeneous electric fields, at sufficiently high field strengths, a weakly conducting liquid becomes unstable and is set in motion [1–4]. The cause of the loss of stability and the motion is the Coulomb force acting on the space charge formed by virtue of the inhomogeneity of the electrical conductivity of the liquid [4–13]. This inhomogeneity may be due to external heating [4–6], a local raising of the temperature by Joule heating [2, 7, 8], and nonlinearity of Ohm's law [9–13]. In the present paper, in the absence of a temperature gradient produced by an external source, a condition is found whose fulfillment ensures that the influence of Joule heating on the stability can be ignored. Under the assumption that this condition is satisfied, a criterion for stability of a weakly conducting liquid between spherical electrodes is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–142, July–August, 1979.     

Diffraction of plane waves by an infinitely long elastic rod floating on the surface of a liquid

The interaction of plane waves coming from infinity with an infinitely long elastic rod floating on the surface of a liquid is considered. The liquid is assumed to be ideal and have infinite depth. It is assumed that the rod cannot become separated from the liquid. The parameters of the waves that pass through the rod and are reflected from it are determined, and the force factors in the transverse sections of the rod are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 62–67, September–October, 1980.     

Inductive acceleration of an electrically conductive particle in a viscous liquid

The characteristics of the motion of a particle in an electrically conducting liquid with constant crossed electric and magnetic fields present have been investigated in connection with the problem of MHD-separation in many papers (for example, see the bibliography in [1]). The separation of electrically conducting particles contained in a dielectric liquid, which can be accomplished with the help of a variable magnetic field [2], is also of practical interest. The ponderomotive force acting on a spherical conducting particle near a straight conductor through which the discharge current of a capacitor bank is flowing is found in this paper, and the motion of a particle in a viscous liquid under the action of this force is investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 31–34, November–December, 1984.     

Forces exerted by a liquid on a vapor bubble growing within IT

Using the basic equations of hydromechanics and also the Lagrange equations of the second kind, expressions are derived for the force acting between a liquid and a vapor bubble growing within it. Cases studied include those of the growth of a bubble on a thin filament or plane surface in an ideal liquid and a liquid of low viscosity. The sign of the hydrodynamic forces depends on the particular law of growth of the vapor bubble.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 165–170, May–June, 1973.     

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.     

Stability of heterogeneous equilibrium in a system with liquid phases

Gibbs's method is used to study the equilibrium and stability in a heterogeneous system consisting of single-component liquid phases. The coefficient of surface tension is assumed to be a constant independent of the state of the phases. An expression is obtained for the second variation of the corresponding functional, and this expression can be used to analyze the stability of nucleating centers. It is shown that in the absence of external force fields and surface tension forces the equilibrium state of a closed thermodynamic system consisting of single-component liquid phases satisfying the classical Gibbs inequalities is always stable.Translated from Izvestlya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 88–94, March–April, 1982.     

Development of quasiharmonic motions of a gas-streamlined liquid film

Quasiharmonic wave motions of a thin liquid film flowing in a vertical plane due to gravitational force, capillary forces, and a tangential stress acting on the film-gas boundary are considered. The region of existence and spectral characteristics of the quasiharmonic wave solutions in different film-motion regimes (cocurrent and countercurrent) are found.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 66–73, January–February, 1976.     

A numerical study of the occurrence of convection in a liquid layer under the influence of periodic external forces

The development of convection in a horizontal liquid layer located in a periodically modulated gravitational field (or with periodically varying temperature gradient) is examined. The effect of modulation frequency on stability is studied. Modulation stabilizes equilibrium if the direction of the gravitational force remains constant at all times. In the opposite case, stabilization occurs only at sufficiently high frequencies. In [1] the dependence of the critical Rayleigh number on modulation amplitude of the external force for several fixed frequencies was examined. In all cases examined in [1], the modulation proves to have a stabilizing influence.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 81–86, May–June, 1972.     

Method for calculating the dynamics of vapor bubbles when a liquid boils in a centrifugal force field

The specific feature of the study of the dynamics of vapor bubbles during boiling of a liquid in a centrifugal force field is the fact that the velocity of a bubble is much greater than the rate of change of its radius, and its movement occurs in fields of variable pressure and underheating that have to be determined in the solution of the problem. In addition, when investigating processes occurring when liquid helium boils in a centrifugal force field, its thermodynamic parameters may be close to the critical values, and the dependences of the thermophysical properties of the liquid and vapor on the temperature and pressure must be taken into consideration. The equation of state of a substance close to its critical thermodynamic point cannot be an approximation to the equation of state of an ideal gas, as has been suggested in a series of articles. The nonequilibrium nature of the phase transition must be taken into consideration in the case of substances existing at near-critical parameters and substances with a low coefficient of accommodation. A marked deformation of the bubbles, which also has to be taken into account, will be observed in strong centrifugal force fields. Such studies have not appeared in the specialist journals. Equations of the two-temperature and two-velocity hydrodynamics of two-phase media in a one-dimensional form for substances obeying the equation of state for an ideal gas were discussed in [1, 2] with allowance for the dependence of the thermophysical properties on the temperature and pressure. In strong centrifugal force fields the one-dimensional approach is unacceptable and the flow of liquid around a buoyant bubble must be taken into account. A joint examination of the change in the temperature field with time in the vicinity of a vapor bubble with changes in its dimensions and position was made for the first time in [3–8]. The present article is an extension of the latter work and takes the aforementioned factors into account.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–71, July–August, 1984.     

Motion of a nonisothermal jet in a field of centrifugal forces

Considerable interest attaches to the study of a jet of viscous liquid in a field of body forces that depend on an axial coordinate. Such flows are realized when slag cotton is obtained by the action on a molten mineral of the centrifugal force of drums rotating in the vertical plane [1]. The behavior of a film of liquid on a rotating cylinder was considered in [2, 3]. The instability of a molten layer and jet separation are explained on the basis of the Taylor mechanism in [4]. In the present paper, a particular solution is given for accelerating nonisothermal jets of a viscous incompressible liquid. This solution is used to explain the dynamics of jet separation from a uniformly rotating drum. The flow stability is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 27–36, September–October, 1980.We thank A. A. Zaitsev for discussing the results of the work.     

Branching of rotationally symmetric solutions describing flows of a viscous liquid with a free surface

Equilibrium shapes of a liquid, situated on the outer or inner surface of a rigid cylinder and rotating together with it as a solid body, are studied. We determine the principal part of the solution of the equilibrium equation for small deviations of the determining parameter from the critical value. The bifurcation of rotationally symmetric motions with a free boundary in a body force field is also investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 127–134, March–April, 1973.The authors thank V. Kh. Izakson for his discussion of the work.     

Influence of liquid layers on energy absorption during particle impact

The influence of the thickness of a covering liquid layer and its viscosity as well as the impact velocity on energy loss during the normal impact on a flat steel wall of spherical granules with a liquid layer was studied. Free-fall experiments were performed to obtain the restitution coefficient of elastic-plastic γ- Al2O3 granules by impact on the liquid layer, using aqueous solutions of hydroxypropyl methylcellulose with different concentrations for variation of viscosity （1-300 mPa s）, In the presence of a liquid layer, increase of liquid viscosity decreases the restitution coefficient and the minimum thickness of the liquid layer at which the granule sticks to the wall. The measured restitution coefficients were compared with experiments performed without liquid layer. In contrast to the dry restitution coefficient, due to viscous losses at lower impact velocity, higher energy dissipation was obtained, A rational explanation for the effects obtained was given by results of numerically solved force and energy balances for a granule impact on a liquid layer on the wall. The model takes into account forces acting on the granule including viscous, surface tension, capillary, contact, drag, buoyancy and gravitational forces. Good agreement between simulations and experiments has been achieved.     

Pressure Waves in a Gas–Liquid Medium with a Stratified Liquid–Bubbly Mixture Structure

Evolution and decay of pressure waves of moderate amplitude in a vertical shock tube filled by a gas–liquid medium with a nonuniform (stepwise) distribution of bubbles over the tube cross section are studied experimentally. The gas–liquid layer has the form of a ring located near the tube wall or the form of a gas–liquid column located in the center of the tube. It is shown that the nonuniformity of bubble distribution over the tube cross section increases the attenuation rate of pressure waves.     

Chemoconcentration capillary effect associated with the motion of a drop in a liquid

The effect of a surface chemical reaction involving a weak soluble surface active substance on the motion of a drop in a liquid is investigated. It is shown that as a result of the Marangoni effect the non-uniformity in the distribution of the substance along the surface associated with the proper motion of the drop and the chemical reaction has an important influence on the nature of the motion of the drop and on the force exerted by the surrounding Liquid. Under certain conditions this Leads to the development of a thrust proportional to the velocity of the drop (chemoconcentration capillary effect). The condition of occurrence of the thrust is obtained, together with its dependence on various physical parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 147–154, January–February, 1988.     

Motion of deforming solid of revolution in a viscous incompressible liquid

In [1] a model of a wave generator, together with an experimental apparatus to determine the traditional forces generated by the model in water, is described. At the surface of the model six axisymmetric traveling waves are generated, giving rise to motion of the body and the surrounding liquid. The steady flow of liquid caused by oscillations of a cylindrical surface of infinite length was investigated in [2, 3]. The present work investigates the tractional forces of an elongated solid of revolution in a liquid produced by waves traveling over the flexible cylindrical part of the body. The hydrodynamic surface forces are determined by numerical integration of the Navier-Stokes equation. Graphs of the tractional force against the velocity and amplitude of the waves are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 145–149, May–June, 1977.In conclusion, thanks are due to M. A. Il'gamovfor his interest in the work and for useful advice.     

Comparison of the drag coefficients of bodies moving in liquids with various stratification profiles

For bodies moving in liquids with various stratification profiles, the relation between the drag coefficients considered as functions of the Froude number is investigated. The problems of stratified liquid dynamics have not previously been studied from this viewpoint, either experimentally or theoretically. On the range of the Froude numbers F₁-1, the drag force coefficients obtained from bench measurements of the towing resistance to the uniform horizontal motion of models in two-layer and continuously stratified liquids are compared. The experimental data obtained in a thermocline are then compared with the results of [1,2] for linearly stratified and two-layer liquids.Nizhnii Novgorod. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 4–11, July–August, 1996.     

Prediction of amount of entrained droplets in vertical annular two-phase flow

Prediction of amount of entrained droplets or entrainment fraction in annular two-phase flow is essential for the estimation of dryout condition and analysis of post dryout heat transfer in light water nuclear reactors and steam boilers. In this study, air–water and organic fluid (Freon-113) annular flow entrainment experiments have been carried out in 9.4 and 10.2 mm diameter test sections, respectively. Both the experiments covered three distinct pressure conditions and wide range of liquid and gas flow conditions. The organic fluid experiments simulated high pressure steam–water annular flow conditions. In each experiment, measurements of entrainment fraction, droplet entrainment rate and droplet deposition rate have been performed by using the liquid film extraction method. A simple, explicit and non-dimensional correlation developed by Sawant [Sawant, P.H., Ishii, M., Mori, M., 2008. Droplet entrainment correlation in vertical upward co-current annular two-phase flow. Nucl. Eng. Des. 238 (6), 1342–1352] for the prediction of entrainment fraction is further improved in this study in order to account for the existence of critical gas and liquid flow rates below which no entrainment is possible.Additionally, a new correlation is proposed for the estimation of minimum liquid film flow rate at the maximum entrainment fraction condition. The improved correlation successfully predicted the newly collected air–water and Freon-113 entrainment fraction data. Furthermore, the correlations satisfactorily compared with the air–water, helium–water and air–genklene experimental data measured by Willetts [Willetts, I.P., 1987. Non-aqueous annular two-phase flow. D.Phil. Thesis, University of Oxford]. However, comparison of the correlations with the steam–water data available in literature showed significant discrepancies. It is proposed that these discrepancies might have been caused due to the inadequacy of the liquid film extraction method used to measure the entrainment fraction or due to the change in mechanism of entrainment under high liquid flow conditions.     

Dispersed phase motion in laminar boundary layer flow over a wedge

The motion of a dispersed phase in the laminar boundary layer on a wedge is considered with allowance for the effect of not only the Stokes force, which coincides in direction with the flow velocity, but also the transverse force (Saffman force) resulting from the transverse nonuniforrnity of the flow over the individual particle [1–3].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 34–42, November–December, 1993.In conclusion, the authors wishes to thank S. V. Manuilovich for assisting with the numerical calculations.