Convective stability of a binary mixture in a fractured porous medium

The effect of the gravity field and the concentration and thermal gradients on the convective stability of a mixture in a nonhomogeneous porous medium containing a system of thin highly permeable fractures separating relatively impermeable blocks is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 88–97, January–February, 1994.     

Convective instability in a medium with spiral turbulence

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 61–66, January–February, 1990.     

Convective stability of a liquid in a spherical cavity

Three problems of convertive stability in a spherical liquid layer are considered. They differ with respect to the degree of freedom of the surface: a free, but nondeformable surface (a small droplet on a spider's web will serve as a model), a nonfree deformable surface (a droplet contaminated with an insoluble surface active agent), and a rigid unrestrained shell (dust-covered droplet). The Marangoni effects in the first two problems were investigated by Bratukhin [2] and are disregarded.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 24–28, May–June, 1992.     

Convective stability of a vertical layer of a non-newtonian liquid

We consider the convective stability of a non-Newtonian (nonlinearly viscous) liquid in a two-dimensional vertical channel. We solve a nonlinear boundary value problem concerning plane-parallel stationary convection for the case of piecewise-linear and power-law type rheological characteristics. We discuss the problem concerning the stability of equilibrium and of stationary motions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 88–95, September–October, 1973.The authors thank D. V. Lyubimov for his help in carrying out the calculations.     

Convective motions in a porous medium heated from below

Convective motions in a porous medium filling a horizontal cylinder with a cross section of arbitrary shape and heated from below are studied. The small-parameter method is used to obtain infinitely many stationary motions forming a one-parameter family. For small values of the parameter, all of these motions are stable with respect to small perturbations. The article also discusses the case of heating which is not strictly vertical. It is found that in this case only one stationary motion is stable.     

Research on stability of interface of jet containing suspended solid particles

Ｎｏｍｅｎｃｌａｔｕｒｅ　αｓ:ｐａｒｔｉｃｌｅｖｏｌｕｍｅｆｒａｃｔｉｏｎ;　ｕｇ:ｇａｓｉｎｓｔａｎｔａｎｅｏｕｓｖｅｌｏｃｉｔｙｖｅｃｔｏｒ;　ｕｓ:ｐａｒｔｉｃｌｅｉｎｓｔａｎｔａｎｅｏｕｓｖｅｌｏｃｉｔｙｖｅｃｔｏｒ;　Ｕ :ｍｅａｎａｘｉａｌｖｅｌｏｃｉｔｙｏｆｔｗｏ＿ｐｈａｓｅｊｅｔ;　Ｕ0 :ｘ＿ａｘｉａｌｖｅｌｏｃｉｔｙｏｆｔｈｅｅｘｉｔ,ｃｈａｒａｃｔｅｒｉｓｔｉｃｖｅ ｌｏｃｉｔｙｏｆｆｌｏｗ＿ｆｉｅｌｄ;　ｐ:ｉｎｓｔａｎｔａｎｅｏｕｓｆｌｏｗ＿ｆｉｅｌｄｐｒｅｓｓｕｒｅ;　 ｐ:ｍｅａｎ…     

Convective stability of fluid in a rotating horizontal annulus

The convective stability of quasi-equilibriumof a fluid layer formed by two horizontal coaxial cylindrical surfaces which have different temperatures and rotate at the same angular velocity about the axis of symmetry is investigated theoretically and experimentally. Consideration is carried out from the standpoint of thermal vibrational convection caused by the average lifting force generated as a result of vibrations of a nonisothermal fluid with respect to the cavity. The vibrations are induced by an external field. The action of the centrifugal force field is also taken into account. Stability of mechanical quasi-equilibrium with respect to monotonic plane perturbations, which are, as shown experimentally, the most dangerous, is studied within the framework of the linear analysis. The stability boundaries are constructed for layers of various relative thickness in the plane of control parameters, the centrifugal and vibrational Rayleigh numbers. The thresholds of excitation of two-dimensional convective structures obtained experimentally are in good agreement with the theoretical ones.     

Research on stability of moving jet containing dense suspended solid particles

Ｎｏｍｅｎｃｌａｔｕｒｅαｊ:ｐｈａｓｅｊｖｏｌｕｍｅｆｒａｃｔｉｏｎ;ｕｊ:ｐｈａｓｅｊｖｅｌｏｃｉｔｙｖｅｃｔｏｒ;Ｕ :ｍｅａｎｖｅｌｏｃｉｔｙｖｅｃｔｏｒ;Ｕ :ｍｅａｎａｘｉａｌｖｅｌｏｃｉｔｙ;Ｕｏ:ｍｅａｎｘ＿ａｘｉａｌｖｅｌｏｃｉｔｙｏｆｔｈｅｅｘｉｔ;Ｕ∞ :ｖｅｌｏｃｉｔｙｏｆｊｅｔｔｉｎｇｄｅｖｉｃｅ;ΔＵ :ｊｕｍｐｉｎｇｖｅｌｏｃｉｔｙｏｆｍｏｖｉｎｇｊｅｔ,ｃｈａｒａｃｔｅｒｉｓｔｉｃｖｅｌｏｃｉｔｙｏｆｆｌｏｗ＿ｆｉｅｌｄ ,ΔＵ =Ｕｏ-Ｕ∞ ;ｐ:ｐｒｅｓｓｕｒｅ;Ｐ :ｅｉｇｅｎｐｒｅｓ…     

Convective stability of a nonisothermal fluid in a rotating horizontal coaxial gap

The thermal fluid convection in a coaxial horizontal gap uniformly rotating about its axis is investigated. The threshold above which convective flows are excited and the structure of these flows are studied. It is found that convection ensues irrespective of whether the inner or outer boundary temperature is higher. Convection manifests itself in the threshold development of rolls elongated in the direction of the rotation axis and is determined by two different mechanisms. If the layer is heated from outside, the centrifugal convection mechanism plays a leading part and the diameter of the convective rolls is comparable with the layer thickness. If the higher is the temperature of the inner boundary of the layer, the centrifugal inertia force has a stabilizing effect and convection development is related with the action of thermal vibrational mechanism. The latter is determined by gravity-generated oscillations of the nonisothermal fluid relative to the cavity. The wave number of the vibrational convective structures is several times smaller than under centrifugal convection. The results obtained broaden our understanding of thermal convection in systems rotating in external static force fields.     

Convective stability of a horizontal binary-mixture layer on temperature gradient modulation

The free convection of a binary mixture in a horizontal cavity is numerically investigated on modulation of the temperature gradient about a certain mean value. The binary mixture stability diagrams are plotted in the modulation amplitude/frequency plane. It is shown that the modulation of the equilibrium temperature gradient may be both a stabilizing and a destabilizing factor in relation to the case in which the modulation is absent. The influence of the skin layer effect on the convective stability of the mechanical equilibrium of the mixture is studied by comparing the solution of this problem in the approximation of a low modulation frequency with that in a more accurate formulation. The skin effect is shown to be a stabilizing factor at high modulation frequencies; with decrease in the frequency it starts to play a destabilizing role, while at fairly low frequencies its effect is negligible.     

Convective stability analysis of a micropolar fluid layer by variational method

This paper studies Rayleigh-Bénard convection of micropolar fluid layer heated from below with realistic boundary conditions. A specific approach for stability analysis of a convective problem based on variational principle is applied to characterize the Rayleigh number for quite general nature of bounding surfaces. The analysis consists of replacing the set of field equations by a variational principle and the expressions for Rayleigh number are then obtained by using trial function satisfying the essential boundary conditions. Further, the values of the Rayleigh number for particular cases of large and small values of the microrotation coefficient have been obtained. The effects of wave number and micropolar parameter on the Rayleigh numbers for onset of stationary instability for each possible combination of the bounding surfaces are discussed and illustrated graphically. The present analysis establishes that the nature of bounding surfaces combination and microrotation have significant effect on the onset of convection.     

Convective stability of a horizontal rotating fluid layer with helical turbulence

The problem of the corrective stability of a horizontal layer of turbulent fluid rotating about a vertical axis with a fixed heat flow at the boundaries is investigated in the case in which the intensity of the helical background does not depend on the rate of rotation and the degree of heating.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 33–39, January–February, 1992.The author is grateful to S. S. Moiseev for proposing the subject and to G. Z. Gershuni and D. V. Lyubimov for useful discussions.     

Convective stability of a weakly conducting liquid in an electric field

In an inhomogeneously heated weakly conductive liquid (electrical conductivity 10^–12–1 cm^–1) located in a constant electric field a volume charge is induced because of thermal inhomogeneity of electrical conductivity and dielectric permittivity. The ponderomotive forces which develop set the liquid into intense motion [1–6]. However, under certain conditions equilibrium proves possible, and in that case the question of its stability may be considered. A theoretical analysis of liquid equilibrium stability in a planar horizontal condenser was performed in [2, 4]. Critical problem parameters were found for the case where Archimedean forces are absent [2]. Charge perturbation relaxation was considered instantaneous. It was shown that instability is of an oscillatory character. In [4] only heating from above was considered. Basic results were obtained in the limiting case of disappearingly small thermal diffusivity in the liquid (infinitely high Prandtl numbers). In the present study a more general formulation will be used to examine convective stability of equilibrium of a vertical liquid layer heated from above or below and located in an electric field. For the case of a layer with free thermally insulated boundaries, an exact solution is obtained. Values of critical Rayleigh number and neutral oscillation frequency for heating from above and below are found Neutral curves are constructed. It is demonstrated that with heating from below instability of both the oscillatory and monotonic types is possible, while with heating from above the instability has an oscillatory character. Values are found for the dimensionless field parameter at which the form of instability changes for heating from below and at which instability becomes possible for heating from above.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–23, September–October, 1976.In conclusion, the author thanks E. M. Zhukhovitskii for this interest in the study and valuable advice.     

Waves in a solid medium with liquid-filled pores

The dynamic nonlinear theory of deformation of a two-phase medium, a solid with pores filled with a liquid, is developed. The variational principle is used to derive nonlinear equations that take into account the motions of the solid and liquid phases and the porosity variations. All types of nonlinearity, including nonlinear friction, are also taken into account. Formulas for the velocities of the linear and nonlinear waves and the absorption coefficient are derived. The one- and three-dimensional cases are considered. In the three-dimensional case, an equation describing the wave profile evolution is obtained as well as a nonlinear Schrödinger equation. Their solutions are analyzed; soliton-type solutions and solutions for narrow beams are obtained.     

Convective stability of a horizontal rotating fluid layer with distributed heat sources

The results of investigating the convective instability of a horizontal layer of rotating fluid, created by a temperature difference applied at the boundaries of the layer and by heat sources distributed according to various laws, are presented. It is shown that, when the other parameters of the problem are fixed, an increase in the internal heat release lowers the limits of both monotonic and oscillatory stability of the layer, increases the wave number and reduces the neutral oscillation frequency. An increase in source concentration towards the center of the layer intensifies the effect. As the strength of the internal heat sources and their concentration towards the center of the layer increase, the oscillating convection that develops at the stability limit when the Prandtl number is low and the rotation fairly fast is first replaced by monotonic convection and then ceases altogether.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 21–28, January–February, 1989.