Miscible Thermo-Viscous Fingering Instability in Porous Media. Part 1: Linear Stability Analysis

The development of the thermo-viscous fingering instability of miscible displacements in homogeneous porous media is examined. In this first part of the study dealing with stability analysis, the basic equations and the parameters governing the problem in a rectilinear geometry are developed. An exponential dependence of viscosity on temperature and concentration is represented by two parameters, thermal mobility ratio β _T and a solutal mobility ratio β _C , respectively. Other parameters involved are the Lewis number Le and a thermal-lag coefficient λ. The governing equations are linearized and solved to obtain instability characteristics using either a quasi-steady-state approximation (QSSA) or initial value calculations (IVC). Exact analytical solutions are also obtained for very weakly diffusing systems. Using the QSSA approach, it was found that an increase in thermal mobility ratio β _T is seen to enhance the instability for fixed β _C , Le and λ. For fixed β _C and β _T , a decrease in the thermal-lag coefficient and/or an increase in the Lewis number always decrease the instability. Moreover, strong thermal diffusion at large Le as well as enhanced redistribution of heat between the solid and fluid phases at small λ is seen to alleviate the destabilizing effects of positive β _T . Consequently, the instability gets strictly dominated by the solutal front. The linear stability analysis using IVC approach leads to conclusions similar to the QSSA approach except for the case of large Le and unity λ flow where the instability is seen to get even less pronounced than in the case of a reference isothermal flow of the same β _C , but β _T  = 0. At practically, small value of λ, however, the instability ultimately approaches that due to β _C only.     

The influence of radiation on the temperature profile of an induced discharge in argon at atmospheric pressure

This study presents a quantitative evaluation of the influence of radiation upon the parameters of a long induced discharge in argon at atmospheric pressure. Radiation heat transfer in the optically transparent tin plasma layers with thickness of the order of several centimeters) and reabsorption spectral intervals is examined. Experimental error produced by inaccurate knowledge of the transfer and optical characteristics of the plasma is evaluated. The effect of convection on radial temperature profile is evaluated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiztki, No. 6, pp. 35–43, November–December, 1971.     

Numerical study of ejection of material from a solid surface by intense radiation

The ejection process is described gas-dynamically for the case of normal incidence ona surface by a flow of radiation. A complete equation system is written down which is solved numerically. In this situation, the symmetry of the ejection offers an opportunity to eliminate one of the variables and makes it possible to carry out the calculation over time in a two-dimensional physical space. Absorption of the radiation energy by the solid is taken into account by the introduction of a discontinuity; the gas-dynamic quantities on both sides of the discontinuity are related by conservation laws and, at zero time, by the Jouguet rule. The gas is assumed to be ideal. The results of the calculation are presented in the form of curves. Conditions at the discontinuity which replaces the region of heating adjacent to the solid are discussed.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fi/iki, No. 4, pp. 127–133, July–August 1971.The authors are grateful to O. S. Ryzhov for interest in the work and for fruitful discussions and to I. V. Nemchinov for valuable advice and observations during the course of the work.     

Special characteristics of the flow of a gas-liquid bubble-type mixture with small reynolds numbers

In [1, 2], as a result of measurements of the hydraulic resistance and the friction in vertical tubes, a region of the flow with anomalously high values of these quantities was disclosed. The measured values of the resistance exceed by an order of magnitude values obtained using appropriate calculating methods. This region of the flow corresponds to bubble-type flow conditions with small reduced velocities of the liquid phase. The above communications do not give a clear explanation of the observed effect. The calculating method proposed in [2], which pretends to take this effect into consideration, does not describe the experimental results of other authors, for example, the results of [1]. In the present work the limits of the existence of this set of conditions were established, and the mean and pulsational characteristics of the friction were measured. It is shown that this region of anomalously high stresses corresponds to laminar and transitional Reynolds numbers. The results of measurement of the pulsations of the friction argue the absence of flow conditions of a gas-liquid mixture without pulsations, even with very small Reynolds numbers. The article proposes the possibility of the development of the “pseudoturbulent” transverse transfer of momentum due to the oscillating motion of the bubbles in the channel. A detailed explanation of an analogous effect in the hydrodynamics of blood was given by Regirer [3].     

Linear scales of turbulence in the semiempirical theory

The article makes a comparison between some of the characteristics of a turbulent boundary layer, calculated in [1, 2], with experimental data. The comparison shows, specifically, that the mixing path entering into the definition of the coefficient of turbulent viscosity, for different flows is not proportional to the integral scale of the turbulence, defined with respect to the correlation function.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 53–57, May–June, 1974.     

Approximate method of determining liquid oscillation frequencies in cavities of revolution

Variational methods [1–4], which require the use of computers, are widely used at present for determining the oscillation frequencies of liquid partially filling an arbitrary cavity of revolution. A technique is given in [5] for the approximate solution of this problem for a cavity which differs little from a cavity for which the solution is known. In the present paper we obtain an approximate first-order differential equation for the frequency squared, using the filling level as the independent variable. Calculations were made using this method for several cavities (sphere, cylinder with spherical base, cone with varying apex angles, torus). Comparison of these results with the results obtained experimentally by other theoretical methods shows that the proposed method is sufficiently accurate for engineering applications.The author wishes to thank I. V. Kolin for carrying out the calculations.     

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 variational problem of one-dimensional nonequilibrium gasdynamics

In [1] the problem of optimal profiling of the supersonic portion of a plane or axisymmetric nozzle for nonequilibrium flow is reduced to a boundary-value problem for a hyperbolic system of equations which includes the flow equations and the equations for the Lagrange multipliers. In view of the complexity of the solution of that system, the present paper presents an analogous study based on the one-dimensional formulation. The solution is illustrated by examples. It is noted that a similar solution undertaken in [2] is in error.     

Direct-contact heat transfer to a spherical liquid/vapor two-phase bubble trailing a wake

The paper deals with the heat transfer causing evaporation of liquid drops in a medium of an immiscible, less volatile liquid. Each drop turns into a two-phase bubble, consisting of a growing vapor phase and a reducing liquid phase, which continues to buoy up in the medium. The bubble is modeled as a sphere in which the yet-to-be vaporized liquid spreads over the rear surface while the rest is occupied by the heat-insulating vapor phase. The rear surface to serve as the effective heat transfer area is assumed to be covered with an axisymmetric wake instead of a boundary layer flow. The quasi-steady, overall heat transfer through the wake in the medium and the layer of the yet-to-be vaporized liquid in the bubble is predicted and compared with relevant experimental results.Die Untersuchung befaßt sich mit der durch die Verdampfung von Flüssigkeitstropfen in einem aus unvermischbarer, flüchtiger Flüssigkeit bestehendem, Medium verursachten Wärmeübertragung. Aus jedem Tropfen entsteht eine Zweiphasenblase, bestehend aus einer wachsenden Dampfphase und einer abnehmenden Flüssigkeitsphase, die in das Medium aufsteigt. Die Blase wird anhand eines Kugelmodells betrachtet, an dem sich die noch nicht verdampfte Flüssigkeit über die Rückseite verteilt und die restliche Fläche mit der wärmeisolierenden Dampfphase behaftet ist. Es wird angenommen, daß sich an der Rückseite als wirksamer Wärmeübergangsbereich ein achsensymmetrischer Nachlauf bildet. Es werden die quasi-gleichförmige Wärmeübertragung durch den Nachlauf in das Medium und durch die Schicht Lage der nicht verdampften Flüssigkeit in der Blase mathematisch berechnet und mit relevanten Versuchsergebnissen verglichen.     

Interaction between gravitational sedimentation and shear diffusion in a suspension moving in a rotational viscometer gap

The start up behavior of a concentrated suspension of nonaggregating settling particles in a rotational viscometer is examined. The results of one of the experiments are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 44–51, September–October, 1990.