Dynamical properties of heterogeneous surface layers. capillary wave scattering

The dynamics of a heterogeneous liquid surface constituting a two-dimensional disperse system is considered. One of the surface phases (the dispersed phase) forms circular regions of diameter comparable with the characteristic length of the mechanical disturbances within the continuous disperse medium. Inhomogeneous boundary conditions for the Navier-Stokes equations with a discontinuity on the surface phase contact line are formulated. Special attention is paid to the conditions on this line. An approximate method of solving the surface wave diffraction problem and the results for the case of transverse surface wave scattering are described. It is shown that if the wavelength is close to the dimensions of the two-dimensional dispersed particles and their concentration is sufficiently high, the energy of the scattered waves may exceed that dissipated in the vorticity layer. Thus, a new nonclassical mechanism of surfactant action on capillary wave damping is possible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 129–137, January–February, 1991.     

Stability of frontal displacement of fluids in a porous medium in the presence of interphase mass transfer and phase transitions

To preserve the stability of the front relative to small perturbations when one fluid is displaced by another the pressure gradient must decrease on crossing the front in the direction of displacement. Initially, this criterion was established for the piston displacement of fluids [1, 2], and later in the case of two-phase flow of immiscible fluids in porous media for the displacement front corresponding to the saturation jump in the Buckley—Leverett problem [3, 4]. Below it is shown that the same stability criterion remains valid for flows in porous media accompanied by interphase mass transfer and phase transitions [5, 6]. Processes of these kinds are encountered in displacing oil from beds using active physicochemical or thermal methods [7] and usually reduce to pumping into the bed a slug (finite quantity) of reagent after which a displacing agent (water or gas) is forced in. The slug volume may be fairly small, especially when expensive reagents are employed, and, accordingly, in these cases the question of the stability of displacement is one of primary importance. These active processes are characterized by the formation in the displacement zone of multiwave structures which, in the large-scale approximation (i.e., with capillary, diffusion and nonequilibrium effects neglected), correspond to discontinuous distributions of the phase saturations and component concentrations [5–10]. It is shown that the stability condition for a plane front, corresponding to a certain jump, does not depend on the type of jump [11, 12] and for a constant total flow is determined, as in simpler cases, by the relation between the total phase mobilities at the jump. An increase in total flow in the direction of displacement is destabilizing, while a decrease has a stabilizing influence on the stability of the front. Other trends in the investigation of the stability of flows in porous media are reviewed in [13].Translated fron Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 98–103, March–April, 1986.     

Numerical investigation of unsteady shock waves in vapor-gas-droplet mixtures

The results of mathematical modeling of the evolution of unsteady shock waves in two-phase mixtures of inert gas, vapor and suspended liquid droplets with allowance for dynamic, thermal and mass phase interaction processes are presented. The influence of interphase mass transfer effects (droplet breakdown and evaporation, vapor condensation) on the structure of unsteady shock waves in vapor-gas-droplet mixtures is analyzed. The important influence of phase mass transfer and, in particular, droplet breakdown as a result of surface layer stripping by the gas flow on the distribution of the parameters of the carrier and dispersed components of the mixture behind the shock front is demonstrated. The effect of the principal governing parameters of the two-phase mixture on the unsteady shock wave propagation process is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 67–75, July–August, 1992.     

Stability of subsonic laminar boundary layer on a flat plate with volume energy supply

Reducing frction drag and delaying the laminar-turbulent transition are topical problems of modern aerodynamics. A series of methods of delaying transition are known: creation of a favorable pressure gradient, boundary layer suction, surface cooling, etc., [1, 2]. Here, the possibility of delaying transition by means of volume heat supply to the boundary layer is considered. For this purpose, a subsonic compressible laminar boundary layer with volume energy supply is subjected to a stability analysis. The nonself-similar flow in the boundary layer is determined by means of a finite-difference marching method. The flow stability characteristics are calculated on the basis of the linear theory in the plane-parallel approximation. It is shown that even on a thermally insulated surface volume energy supply to the flow leads to significant flow stabilization and reduced perturbation growth rates.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 62–67, March–April, 1988.     

Response of Generalized Thermoelastic Half-space with Voids to Mechanical and Thermal sources

The dynamic response of a homogeneous, isotropic, generalized thermoelastic half-space with voids subjected to normal, tangential force and thermal source is investigated. The displacements, stresses, temperature distribution and change in volume fraction field so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the response of various sources in the Lord–Shulman (L–S) theory and Green–Lindsay (G–L) theory for an insulated boundary and temperature gradient boundary. Some particular cases have been deduced.     

Effect of periodic action on boundary layer stability

The effect of a wave traveling over the surface and suction-blowing in the form of a traveling wave on boundary layer stability and laminarturbulent transition is investigated. The perturbation parameters are assumed not to be related to the parameters of the Tollmien-Schlichting wave. The parameters corresponding to an increase in the critical Reynolds number by a factor of 2–2.5 are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 109–115, May–June, 1988.The author is grateful to V. A. Kuparev for supplying the program for calculating the stability of the boundary layer.     

Effect of Convection on Formation of Adsorbed Surfactant Film under Dynamic Change of Solution Surface Area

The dynamics of the formation of a surface phase in aqueous solutions of surfactants in a tray with the Langmuir barrier system during one compression–expansion cycle of the interface boundary is investigated both experimentally and theoretically. Organic salts of fatty acids such as potassium laurate, caprylate, and acetate, which are members of the same homologous series, were used as surfactants. It is experimentally determined that the dependence of the surface pressure increment measured under the maximum compression of the surface on the volume concentration has a maximum, the position of which is different for all the studied surfactant solutions. It is shown that the position of the maximum corresponds to the concentration value at which a saturated monolayer of surfactant molecules is formed at the interface boundary. A theoretical model that considers the effect of the forced convection arisen in the bulk of the solution upon changing the surface area is proposed for the interpretation of the experimental results. The model allows one to render the main kinetic characteristics of the adsorption/desorption processes involving the compounds under study. A good agreement between the theoretical and experimental results is observed, but there is a discrepancy between them when diffusion is considered to be the only way surfactant molecules are transferred into the bulk phase. Based on the data, a new method for determination of the Langmuir–Shishkovsky constant is proposed.     

Formation of recirculation zones in the boundary layer on a moving surface

A study is made of the region of free interaction of a supersonic boundary layer on a moving surface formed by a weak shock wave impinging on it from without. In the equations of motion, allowance is made for the contribution of the pressure induced by the growth in the displacement thickness of jets passing near the surface. The results are given of the numerical solution of the corresponding nonlinear problem, and the basic structure of the recirculation zones is discussed. It is noted that there are regimes in which the main recirculation zone is accompanied by an additional eddy formation with circulation in the opposite direction. In contrast to a boundary layer on a fixed body, the points at which the streamlines separate are not on the wall but within the flow.Translated from Izvestiya Akademii Nauk SSSR, Meklianika Zhidkosti i Gaza, No. 5, pp. 3–10, September–October, 1980.     

Longitudinal-transverse interaction in a three-dimensional boundary layer

Three-dimensional flow is considered for an incompressible fluid in a boundary layer developing along a curved solid surface during interaction between it and a small uneven area (projection or depression) on the surface. It is shown that an important part in the formation of the flow round the uneven area may be played by the drop in the pressure across the boundary layer. Conditions are formulated under which this effect, which is connected with the action of centrifugal forces, is realized. On the assumption that the longitudinal dimension of the uneven area is of the order of Re^–3/14, its width of the order of O(Re^–3/7), and its height O(Re^–4/7), where Re is the Reynolds number, asymptotic equations are derived which describe the motion of the fluid in the neighborhood of the uneven area.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–50, May–June, 1987.     

Internal rotation in the hydrodynamics of weakly conducting dielectric suspensions

Hydrodynamic phenomena in weakly conducting single-phase media due to interphase electric stresses are reviewed in [1]. In the present paper, a model is constructed of a dielectric suspension with body couples due to the field acting on free charges distributed on the surface of the particles of the suspension. Averaging of the microscopic fields yields macroscopic equations for the field and the polarization of the dielectric suspension with allowance for the finite relaxation time of the distribution of the free charge on the phase interface. The developed model is used to consider the occurrence of spontaneous rotation of a dielectric cylinder in a weakly conducting suspension in the presence of an electric field; compared with the case of single-phase media [2], this is characterized by a significant reduction in the threshold intensity of the electric field with increasing concentration of the particles [3]. In the present model of a dielectric suspension, the destabilization of the cylinder is due to the occurrence of rotations of the particles of the suspension due to the interaction between the polarization and the motion of the medium. The relaxation equation for the polarization for the given model is analogous to the corresponding equation for media which can be magnetized [4–6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 86–93, March–April, 1980.     

Boundary layer on a blunt body in a flow of dusty gas

The problem of interaction of gas-dust flows with solid surfaces arose in connection with the study of the motion of aircraft in a dusty atmosphere [1–2], the motion of a gas suspension in power generators, and in a number of other applications [3]. The presence of a disperse admixture may lead to a significant increase in the heat fluxes [4] and to erosion of the surface [5]. These phenomena are due to the joint influence of several factors — the change in the structure of the carrier-phase boundary layer due to the presence of the particles, collisions of the particles with the surface, roughness of the ablating surface, and so forth. This paper continues an investigation begun earlier [6–7] into the influence of particles on the structure of the dynamical and thermal two-phase boundary layer formed around a blunt body in a flow. The model of the dusty gas [8] has an incompressible carrier phase. The method of matched asymptotic expansions [9] is used to obtain the equations of the two-phase boundary layer. In the frame-work of the refined classification made by Stulov [6], it is shown that the form of the boundary layer equations is different in the presence and absence of inertial precipitation of the particles. The equations are solved numerically in the neighborhood of the stagnation point of the blunt body. The temperature and phase velocity distributions in the boundary layer, and also the friction coefficients and the heat transfer of the carrier phase are found for a wide range of the determining parameters. In the case of an admixture of low-inertia particles that are not precipitated on the body, it is shown that even when the mass concentration of the particles in the undisturbed flow is small their accumulation in the boundary layer can lead to a sharp increase in the thermal fluxes at the stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1985.I thank V. P. Strulov for a discussion.     

Two-phase three-component flow through a porous medium with variable total flow

In analyzing the processes of the displacement of oil, in which intensive interphase mass transfer takes place, it is normally assumed that the partial volumes of the components as they mix are additive (Amagat's Law) [1, 2]. Then the equations of motion have an integral, which is the total volume flow rate through the porous medium, and the basic problems of frontal displacement, if there are not too many components in the system, permit an exact analytical study to be made [3–5]. If this assumption is rejected, the total flow becomes variable [3, 6, 7]. It appears that the consequences of this as applied to the processes of the displacement of oil by high pressure gases have not previously been considered. The results of such a study, developing the approach outlined in [4], are given below. The initial multicomponent system is simulated by a three-component one which contains oil (the component being displaced), gas (the neutral or main displacing component), and intermediate hydrocarbon fractions or solvent (the active component). It is shown that instead of the triangular phase diagram (TPD) normally used where the partial volumes of the components are additive, in this case it is convenient to use a special spatial phase diagram (SPD) of the apparent volume concentrations of the components to construct the solutions and to interpret them graphically. The method of constructing the SPD and its main properties are explained. A corresponding graphoanalytical technique is developed for constructing the solutions of the basic problems of frontal displacement which correspond to motions with variable total flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–120, May–June, 1985.     

Effect of moving wall on the three-dimensional separation of an incompressible fluid in front of an obstacle

The problem of the laminar boundary layer formed on the surface of a semiinfinite plate with a perpendicular semi-infinite circular cylinder in a uniform steady incompressible flow normal to the leading edge is considered. Near its sharp edge the plate has a stationary part and, located at a finite distance further downstream, a part of the surface moving downstream at a constant velocity. The first-order boundary layer equations are solved numerically by an implicit finite-difference method. The effect of the moving wall on the variation of the dimensions of the separation zone ahead of the obstacle over a broad range of the governing parameters and flow characteristics is investigated. The flow in the laminar boundary layer on the surface of a plate ahead of such an obstacle was calculated in [1, 2] without motion of the wall. Data on the structure of the separated flow are given in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 49–53, November–December, 1990.     

Finite element analysis of multicomponent two-phase flows with interphase mass and momentum transport

The application of the finite element method to multiphase flow problems with interphase mass and heat transfer is described. A general forinulation is used that determines the position of the interfacial boundary and allows for multiple solvents, differential volatilities and concentration- and temperature-dependent thermophysical properties. Species phase change and the dramatic volume change that acompanies interphase mass transfer make implementation of the theory challening, since these events lead to discontinuous velocities and concentrations at phase boundaries. These discontinuities are especially large in processes involving rapid evaporation or condensation. As examples we examine the effects of rapid drying on film and fibre formation of sol--gel materials, which are often laden with volatile species.     

Influence of surface tension on the stability of heterogeneous equilibrium of barotropic liquid phases

On the basis of the results of earlier work of the author [1] a study is made of the equilibrium and stability of a two-phase single-component heterogeneous liquid system with respect to perturbations of arbitrary shape. Allowance is made for the influence of surface tension, which plays a critical part in the formation of nucleating centers of a new phase [2]. Conditions of equilibrium are derived, and also a criterion of radial stability of a nucleating center of a new phase bounded by a closed spherical boundary. It is shown that radial stability of spherical nucleating centers also guarantees stability with respect to perturbations of arbitrary shape. The part played by the finite size of the system and the boundary conditions is elucidated. For this, two different cases are studied: a) a system under a constant external pressure, b) a system with fixed volume. In the first case, all equilibrium states are unstable. In the second, there are both unstable and stable configurations (depending on the corresponding values of two dimensionless parameters). The equation of the hyperbola of neutral stability is derived. The limits of a very small coefficient of surface tension and a very large size of the container are considered. The first situation corresponds to stable configurations, the second to unstable. For simplicity, the considered systems are assumed to be isothermal, and the equilibrium and stability are analyzed on the basis of the mechanical analog of Gibbs's principle, namely, the principle of a minimum of the mechanical potential energy of the barotropic heterogeneous liquid system. The case of nonisothermal perturbations leads to similar results, but the expressions for the corresponding dimensionless parameters are more cumbersome and less physically perspicuous.     

Interaction between the boundary layer and a supersonic flow when part of the wall is rapidly heated

There have been many theoretical studies of aspects of the unsteady interaction of an exterior inviscid flow with a boundary layer [1–9]. The mathematical flow models obtained in these studies by the method of matched asymptotic expansions describe a wide range of phenomena observed experimentally. These include boundary layer separation near the hinge of a flap, the flow in the neighborhood of the trailing edge of an oscillating airfoil [1–2], and the development and propagation of perturbations in a boundary layer excited by an oscillating wall or some other way [3–5]. The present paper studies the interaction of an unsteady boundary layer with a supersonic flow when a small part of the surface of a body in the flow is rapidly heated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 66–70, January–February, 1984.     

Heat transfer at the surface of a triangular body in a hypersonic viscous gas flow

The boundary layer on a semi-infinite triangular body of power-law shape is calculated for viscous interaction with an external hypersonic flow. The results of calculating the characteristics of the three-dimensional boundary layer are presented. The formation of secondary return flows and zones of intensified heat transfer on the surface of the body in the neighborhood of lines of flow divergence is noted.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 77–82, January–February, 1988.     

Double-Particle Approximation Analysis of the Residual Thermostressed State of Granular Composites

The local thermostressed state near spherical inclusions in SiC–TiB₂ composite ceramics is analyzed. The boundary value problem that is rigorously solved corresponds to the double-particle approximation of the mechanics of composites. The calculated results are in qualitative agreement with the well-known experimental dependences of the microfracture zone near a microcrack on the volume concentration and average size of the particles of the dispersed phase     

Drift of a reacting droplet due to the chemoconcentration capillary effect

The motion of a droplet with a first-order chemical reaction taking place at its surface with the participation of a surfactant dissolved in the external medium is considered. Approximate expressions are obtained for the velocity and other characteristics of the autonomous motion of the droplet caused by the surface capillary forces due to the nonuniform distribution of the surfactant over the surface of the moving droplet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 51–61, May–June, 1990.