Motion of a deformable droplet of magnetic fluid in a rotating magnetic field

The problem of the magnetic field-driven rotation of a magnetic fluid droplet in a viscous nonmagnetic fluid is solved analytically and experimentally. The shape of the droplet and the magnetic fields and velocities of both fluids are calculated in the weak-field approximation. The droplet is flattened for any relations between the parameters of the system. The instability of the axisymmetric shape of the droplet is established experimentally. A result of the instability is a sudden change in the droplet shape from a flattened ellipsoid of revolution to a triaxial ellipsoid elongated in the equatorial plane. The critical magnetic Bond number is determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 22–30, January–February, 2000. The work was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00182).     

On the First Critical Field in Ginzburg–Landau Theory for Thin Shells and Manifolds

In this article, we investigate the response of a thin superconducting shell to an arbitrary external magnetic field. We identify the intensity of the applied field that forces the emergence of vortices in minimizers, the so-called first critical field H _c1 in Ginzburg–Landau theory, for closed simply connected manifolds and arbitrary fields. In the case of a simply connected surface of revolution and vertical and constant field, we further determine the exact number of vortices in the sample as the intensity of the applied field is raised just above H _c1. Finally, we derive via Γ-convergence similar statements for three-dimensional domains of small thickness, where in this setting point vortices are replaced by vortex lines.     

On solving the problem of an ideal incompressible fluid flow around large-aspect-ratio axisymmetric bodies

Based on Babenko’s fundamental mathematical ideas, principally new (unsaturated) algorithms are developed for the numerical solution of problems of a potential axisymmetric ideal fluid flow around bodies of revolution, in particular, an ellipsoid of revolution with an aspect ratio equal to 1000. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 56–67, September–October, 2006.     

Analytic Description of Layer Undulations in Smectic A Liquid Crystals

We investigate the layer undulations that appear in smectic A liquid crystals when a magnetic field is applied in the direction parallel to the smectic layers. In an earlier work (García-Cervera and Joo in J Comput Theor Nanosci 7:795–801, 2010) the authors characterized the critical field using the Landau–de Gennes model for smectic A liquid crystals. In this paper, we obtain an asymptotic expression of the unstable modes using Γ-convergence theory, and a sharp estimate of the critical field. Under the assumption that the layers are fixed at the boundaries, the maximum layer undulation occurs in the middle of the cell and the displacement amplitude decreases near the boundaries. Our estimate of the critical field is consistent with the Helfrich–Hurault theory. When natural boundary conditions are considered, the displacement amplitude does not diminish near the boundary, in sharp contrast with the Dirichlet case, and the critical field is reduced compared to the one calculated in the classical theory. This is consistent with the experiments carried out by Ishikawa and Lavrentovich (Phys Rev E 63:030501(R), 2001). Furthermore, we prove the existence and stability of the solution to the nonlinear system of the Landau–de Gennes model using bifurcation theory. Numerical simulations are used to illustrate the predictions of the analysis.     

Convection of a ferrofluid in an alternating magnetic field

Parametric convective instability of a horizontal layer of a homogeneous ferrofluid under the action of an alternating magnetic field is studied. A case with rigid boundaries is considered. Convection thresholds are found. In an alternating magnetic field with a zero mean value, perturbations are found to have a synchronous character. These perturbations, however, can belong to different classes, because they depend on the temperature difference on the layer boundaries, the layer thickness, the frequency and amplitude of the alternating external field, and the physical properties of the ferrofluid. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 18–27, July–August, 2009.     

Numerical simulation of plasma motion in a magnetic field. Two-dimensional case

A model of dynamics and heating of a plasma cloud in a magnetic field is considered in a two-temperature approximation. Based on a predictor-corrector-type implicit difference scheme, spreading of a plasma cloud in an external magnetic field is numerically simulated, and the influence of this field on spread dynamics is evaluated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 121–132, May–June, 2007.     

Optimization of the Parameters of the Magnetic Filtration Process Using Response Surface Methodology

In this study, we aimed at optimizing the parameters which govern the separation efficiency in the magnetic filtration of magnetizable dispersed particles from a water medium. Response surface methodology (RSM) was used to determine the influence of the process parameters. Also, the optimal processing conditions were determined in order to reduce the external magnetic field strength, diameter of the filter matrix elements, and filter length to a safe level. A three-level central composite design (CCRD) involving the variables, such as external magnetic field strength (148–282 kA/m), diameter of the filter elements (0.005–0.011 m), and the filter length (0.01–0.10 m) was developed for this purpose. Data obtained from the RSM was subjected to the analysis of variance (ANOVA) using a second-order polynomial equation, which provided the optimized process conditions as 298 kA/m for external magnetic field strength, 0.0015 m for diameter of the filter elements, and 0.095 m for the filter length. The separation efficiency was optimized for magnetic filtration of micron sized particles that can be magnetized in an external magnetic field and the value was found to be 97%.     

Magnetosonic analysis and the method for diagnostics of expansion of a plasma cloud in a magnetized background

The problem of sub-Alfvén expansion of a superconducting plasma sphere in a homogeneous magnetized background is considered. The specifics of a self-consistent model of a low-frequency linear MHD approximation that we used in the present paper is the simultaneous allowance for the energy necessary for maintaining the field and plasma equilibrium at a moving boundary and the additional perturbation of a decelerating field generated by the currents induced in a background plasma. This has allowed us to clarify significantly the dependence of the radiated magnetohydrodynamic energy on the Mach-Alfvén number. We found and calibrated universal dynamic characteristics on the basis of which we developed new techniques for determining the initial energy and the velocities of expansion of an explosive plasma cloud with the use of the peak values of magnetic signals in the near (quasistatic), transient, and wave zones. The possibility of effective application of these techniques in experiments on laser-plasma cloud generation in a vacuum homogeneous magnetic field is shown. Institute of Laser Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 3–13, May–June, 1998.     

Stability of gas-bubble equilibrium shape in uniform flow of an ideal fluid

Steady-state motion of a bubble in the shape of an ellipsoid of revolution has been studied [1, 2]. Steady-state motion and small oscillations of an ellipsoid of revolution around the equilibrium state were studied with the help of Lagrangian equations [3]. In this paper, possible equilibrium shapes of a bubble in the form of a triaxial ellipsoid are studied. The dependence of the pressure difference at the stagnation point and within the gas bubble on deformation is determined for steady-state motion. The stability of the equilibrium shape with respect to small perturbations of the axes of the ellipsoid is investigated through analysis of potential energy in the neighborhood of the extremum.     

On the problem of controlling the efficiency of action of shaped-charge jets

It is suggested that noncontact action of a magnetic field on shaped-charge jet elements be used to decrease the penetration depth. A decrease in the depth is attained. A physicomathematical model for the process is constructed that allows one to optimize performance of devices used to realize the action of an external magnetic field. Lykov Academic Scientific Complex “Institute of Heat and Mass Exchange,” Minsk 220072. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 36–43, May–June, 1998.     

高气液比垂直管流连续携液实验

在可视化管流实验架上, 采用压缩空气和雾化液体作为实验介质, 模拟连续携液过程并测试 实验参数; 采用高速摄像仪捕捉到气流中液滴实际形状------椭球体. 实验发现: 圆球体模型、 椭球体模型计算结果与实验值分别偏差10{\%}, 58.3{\%}. 分析椭球体受力状态并结合实验数据导出了新的椭球体数学模型, 按照新模型计算的结 果与7口产水气井生产情况一致.     

On Perturbation and Marginal Stability Analysis of Magneto-Convection in Active Mushy Layer

This present study considers the problem of steady magneto-convection in a horizontal mushy layer with variable permeability and an impermeable mush–liquid interface during directional solidification of binary alloys. We model the flow by introducing a uniform magnetic field in the mushy layer which is considered as a porous medium where Darcy’s law holds and the permeability is a function of the local solid volume fraction. Basic-state solutions are obtained analytically using the no-flow condition. With the help of multiple shooting techniques, we obtain numerical solutions to the linear perturbation system for non-magnetic and magnetic cases. Numerical results are presented showing the effects of the magnetic field and the permeability of the layer. These results demonstrate that the application of an external magnetic field has stabilizing effects on the convection and can reduce the tendency for chimney formation in the mushy layer. In addition, variable permeability, which corresponds to an active mushy layer, indicates more stable and realizable flow system as compared to the case of constant permeability.     

Two alternatives of magnetic cumulation

This paper deals with phenomena leading to a considerable increase in magnetic field and energy density during compression of a magnetic flux trapped by a conducting shell and joint deformation of a magnetic field and material. The main features and merits of these two alternative schemes of magnetic cumulation are discussed. A comparison is made between the classical and schock-wave schemes of magnetic compression in a material with a phase transition from a nonconducting to a conducting state. The possibility of magnetic-energy cumulation during stretching of magnetic field line by a transverse flow of a conducting material is considered. Lavrent’ev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 32–47, September–October, 2000.     

Axisymmetric cavitation flow around a body in a tube

The problem of the axisymmetric flow around a body in a circular tube with arbitrary shape of the meridian section is reduced to the numerical solution of a system of two integral equations to determine the shape of the cavern and the intensity of the vortex rings arranged on the solid boundaries and the cavern boundary. Results of computations of the cavitation flow around a sphere, ellipsoid of revolution, and cone in a cylindrical tube, and also for a cone in converging and expanding tubes and in a hydrodynamic tunnel with the actual shape of the converging and working sections, are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 50–55, July–August, 1976.     

Unsteady laminar mixed convection about a spinning sphere with a magnetic field

The unsteady laminar boundary-layer flow over an impulsively started translating and spinning isothermal body of revolution in the presence of buoyancy force and magnetic field applied normal to the surface are investigated. Velocity components and temperature are obtained as series of functions in powers of time. Leading and first order functions are obtained analytically and second order functions are determined numerically. The general results are applied to a sphere to investigate the effects of magnetic field and buoyancy force on the velocity and temperature fields and the onset of separation. The magnetic field and buoyancy force are more effective for small rotational speeds and the presence of magnetic field retards the onset of separation. The effect of magnetic field on the temperature field and surface heat flux is weak, indirect and through the velocity field. The magnetic field is observed to initially increase the surface heat flux on the upstream face of the sphere and decrease it on the downstream face.     

Magnetovibrational flows in a magnetic fluid

A new type of flow in a magnetic fluid has been experimentally detected and investigated. The interaction between an alternating nonuniform magnetic field and a magnetic fluid leads to the parametric excitation of traveling capillary-gravitational waves which are the direct cause of the average flow. A necessary condition of formation of hydrodynamic flows in an alternating field is also the presence of time-dependent harmonics with multiple frequencies synchronized with the first harmonic, so that the time dependence of the ponderomotive force is generally pulsed. It is shown that for plane vibrational flows the classical theory cannot explain the high intensity of the average flows observed. It is suggested that the high intensity of magnetovibrational flows is related to the violation of the cylindrical symmetry of the traveling capillary-gravitational waves and the transition to a three-dimensional motion. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 124–133, January–February, 1998.     

Description of creep within the framework of the field theory of defects

The creep laws are described within the framework of the field theory with the use of evolution equations for the density flux of uniformly distributed defects. For the case of uniaxial deformation under constant stress, it is shown that a certain critical stress that has the sense of creep stability limit exists and two deformation regimes can occur, depending on the magnitude of the external load. The unstable-creep rupture time is determined for the system in the case where the stresses are greater than the critical stress and the initial rate exceeds the unstable stationary rate. Institute of the Physics of Strength and Materials Science, Siberian Division, Russian Academy of Sciences, Tomsk 634821. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 177–183, May–June, 2000.     

Scattering of nonspherical particles rebounding from a smooth and a rough surface in a high-speed gas-particle flow

Scattering indicatrices of nonspherical particles rebounding from a smooth and a rough surface are obtained by direct Monte Carlo simulations. Particles shaped as ellipsoids of revolution, rectangular prisms, and prisms with truncated vertices are considered. Surface roughness is defined as a two-dimensional profile whose scattering characteristics are close to those of real roughness induced by abrasive erosion of the surface in a high-speed gas-particle flow. Impact interaction of an individual particle with the surface is considered in a three-dimensional formulation. The scattering indicatrices of reflected particles are found to depend substantially on the particle shape in the case of rebound from a smooth surface and to be almost independent of the particle shape if the particles rebound from a rough surface. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 79–88, March–April, 2008.     

Instability of the quiescent state of an ideal conducting medium in a magnetic field

The linear stability of the quiescent states of an ideal compressible medium with infinite conductivity in a magnetic field is studied. It is shown by Lyapunov’s direct method that these quiescent states are unstable relative to small spatial perturbations, which decrease the potential energy (the sum of the internal energy of the medium and the energy of the magnetic field in this case). Two-sided exponential estimates of perturbation growth are obtained; the exponents in these estimates are calculated using the parameters of the quiescent states and the initial data for perturbations. A class of the most rapidly growing perturbations is separated and an exact formula to determine the rate of their increase is derived. An example is constructed of the quiescent states and the initial perturbations whose linear stage of evolution in time occurs in correspondence with the estimates. From the mathematical viewpoint, our results are preliminary, because the existence theorems for the solutions of the problems considered are not proved. Deceased. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Novosibirsk State University, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 148–155, March–April, 1999.     

On two linear invariant relationships in the problem of the motion of a body in a magnetic field

Existence conditions are considered for two linear invariant correlations in differential equations relative to gyroscope motion in a magnetic field with regard to the Barnett-London effect. It is proven that only a classical analogue of this case can exist. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 2, pp. 98–104, February, 1999.