Nonlinear capillary waves in thin films of viscous liquid and breaking of the films

A study is made of the dynamics of a thin film of viscous liquid with allowance for the influence of capillary forces and long-range van der Waals forces. Asymptotic solutions are found to problems of the dynamics of films in communication with a region of reduced pressure. It is shown that at a certain instant such a film breaks at its edge. The critical parameters that determine the instant of breaking are found and the form of the solution in the stage of breaking is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 47–55, July–August, 1982.     

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.     

Oscillatory rotationally symmetric loss of stability of nonisothermal couette flow

A study is made of the stability of nonisothermal Couette flow — steady flow of a viscous heat conducting fluid between two rotating concentric cylinders heated to different temperatures. The methods of perturbation theory are used to establish conditions sufficient for bifurcation of a neutral curve of oscillatory instability from the neutral curve of monotonic instability. Computer calculations show that for certain values of the parameters of the problem these conditions are realized and there is an oscillatory loss of stability of the nonisothermal Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–80, January–February, 1984.I thank V. I. Yudovich for constant interest in the work.     

Instability of a film of viscous liquid under the influence of an adjacent gas flow

A study is made of the instability of a film of viscous liquid adjacent to a gas flow. Despite a number of investigations, there is no unified theory of this problem capable of explaining the experimental results of different authors. The present paper gives a solution of the problem that is valid for a large class of flows of liquid films in the case of laminar and turbulent flow of the gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 28–36, March–April, 1979.     

Influence of surface tension on damping of the oscillations of a viscous incompressible fluid in a cylindrical channel

A numerical calculation is made of small oscillations of a viscous incompressible fluid that fills half of a horizontal cylindrical channel. The calculation is made with and without allowance for surface tension. The results of the calculation show that allowance for surface tension increases the damping of the oscillations. The general properties of problems of the normal oscillations of a heavy and capillary viscous incompressible fluid were studied in [1–3], in which the possibility of applying the Bubnov-Galerkin method to these problems was pointed out. A method for calculating the oscillations of a viscous incompressible fluid that partly fills an arbitrary vessel at large Reynolds numbers was developed in [3–5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–132, May–June, 1980.     

Nonisothermal flow of non-Newtonian fluids in a channel

A study is made of the nonisothermal motion of a rheologically complex fluid in a plane-parallel channel in the case of boundary conditions of the third kind on the outer surfaces of the channel walls and with allowance for the dissipation of mechanical energy and temperature dependence of the coefficients. A qualitative investigation of the problem is made for arbitrary temperature dependence of the yield. Special cases are considered: flow of linear viscoplastic medium and a power-law medium with abrupt change with the temperature of the yield point and consistency. It is shown that under certain conditions several different flow regimes can be realized simultaneously in the channel and the change in the flow rate of the medium in a channel with varying temperature of the surrounding medium can exhibit hysteresis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 3–10, May–June, 1980.     

Wave flow of a liquid film together with a flow of gas

The wave flow of a thin layer of viscous liquid in conjunction with a flow of gas was considered in a linear formulation earlier [1, 2]. In this paper the problem of the wave flow of a liquid film together with a gas flow is solved in a nonlinear setting. On this basis relationships are derived for calculating the parameters of the film and the hydrodynamic quantities.Ivanovo. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–18, January–February, 1972.     

Solution of the three-dimensional turbomachinery blade row flow field problem with allowance for viscosity effects

The three-dimensional viscous compressible flow in the interblade channel of a turbomachine blade row is examined. A mathematical model of steadystate separated turbulent polytropic-gas flow with allowance for wall flow effects is proposed. It is assumed that the thickness of the boundary layers and the scales of the wall flow interaction zones are small as compared with the characteristic dimension of the system. Subsonic flow calculations are made for near-design flow regimes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 119–127, November–December, 1991.The authors are grateful to G. Yu. Stepanov for his interest in their work and valuable advice.     

Stability of quasistatic equilibrium state of an inhomogeneous viscous layer on an inclined plane

A study is made of the stability against small perturbations [1] of a slow flow of an incompressible inhomogeneous linearly viscous liquid under the influence of a force of gravity on an unbounded inclined plane. Problems of such kind arise in glaciology when one estimates the stability of snow on mountain slopes or determines the catastrophic movement of a glacier; the results can also be applied to solifluction phenomena [2, 3]. Equations for perturbations of parallel flows of linearly viscous fluids in the case of a continuous variation of the viscosity and density across the flow were derived in [4]. An attempt to solve the hydrodynamic problem with allowance for a perturbation of the viscosity was made in [5]; however, in the equations for the perturbations, simplifications resulted in the neglect of terms that take into account perturbations of the viscosity. In the quasistatic formulation considered here in the case when allowance is made for perturbation of the density and viscosity, the equation for the perturbation amplitudes is an ordinary differential equation with variable coefficients; analytic solution of the equation is very difficult, even for long-wave perturbations. In this connection a study is made of the stability of a laminar model; the viscosity and density are constant within each layer. A similar hydrodynamic problem in the long-wave approximation was considered in [6]. In the present paper an exact solution is constructed in the quasistatic formulation for a two-layer model; the solution shows that the viscosity of the lower layer has an important influence on the stability. Essentially, instability is observed when the lower layer acts as a lubricant.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 20–24, November–December, 1973.     

Stability of flow of a thin layer of viscous magnetic liquid

The laminar flow of a thin layer of heavy viscous magnetic liquid down an inclined wall is examined. The stability and control of the flow of an ordinary liquid are affected only by alteration of the angle of inclination of the solid wall and the velocity of the adjacent gas flow. When magnetic liquids are used [1, 2], an effective method of flow control may be control of the magnetic field. By using magnetic fields of various configurations it is possible to control the flow of a thin film of viscous liquid, modify the stability of laminar film flow, and change the shape of the free surface of the laminarly flowing thin film, a factor which plays a role in mass transfer, whose rate depends on the phase contact surface area. The magnetic field significantly affects the shape of the free surface of a magnetic liquid [3, 4]. In this paper the velocity profile of a layer of viscous magnetic liquid adjoining a gas flow and flowing down an inclined solid wall in a uniform magnetic field is found. It is shown that the flow can be controlled by the magnetic field. The problem of stability of the flow is solved in a linear formulation in which perturbations of the magnetic field are taken into account. The stability condition is found. The flow stability is affected by the nonuniform nature of the field and also by its direction.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 59–65, September–October, 1977.     

Controlling the Free‐Surface Profile of Film Flow over Complex Topography

A twodimensional model describing nonisothermal viscous thin film flow over complex topography is considered. The model is based on the Navier–Stokes equations in the Oberbeck–Boussinesq approximation. A numerical analysis of the effect of thermal loading on the location of the film free surface is performed. It is shown that changing the substrate temperature function, it is possible to control the freesurface profile on separate topographical features. The results of solution of model problems are presented).     

Analytic investigation of friction and heat transfer in the neighborhood of a three-dimensional stagnation point at low and moderate Reynolds numbers

A study is made of hypersonic three-dimensional flow of a viscous gas past blunt bodies at low and moderate Reynolds numbers with allowance for the effects of slip and a jump of the temperature across the surface. The equations of the three-dimensional viscous shock layer are solved by an integral method of successive approximation and a finite-difference method in the neighborhood of the stagnation point. In the first approximation of the method an analytic solution to the problem is found. Analysis of the obtained solution leads to the proposal of a simple formula by means of which the calculation of the heat flux to a three-dimensional stagnation point is reduced to the calculation of the heat flux to an axisymmetric stagnation point. A formula for the relative heat flux obtained by generalizing Cheng's well-known formula [1] is given. The accuracy and range of applicability of the obtained expressions are estimated by comparing the analytic and numerical solutions. Three-dimensional problems of the theory of a supersonic viscous shock layer at small Reynolds numbers were considered earlier in [2–5] in a similar formulation but without allowance for the effects of slip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 143–150, March–April, 1988.     

Two-phase multicomponent turbulent jet with phase transitions

A mathematical model of a gas-droplet nonisothermal multicomponent polydisperse turbulent jet is proposed. This model takes into account phase velocity and temperature nonequilibrium, gas and liquid phase inhomogeneity, the droplet coagulation and disintegration, and the possibility of the presence of vapor condensation or fluid evaporation, depending on the specific conditions in the jet. Certain results of calculating the parameters of both a nonisothermal two-component polydisperse gas-disperse jet with phase transitions and droplet coagulation and a three-component polydisperse gas-disperse jet without allowance for phase transitions are presented. The results obtained are analyzed.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 130–138, September–October, 1995.     

Wave flow of a liquid film in a horizontal separator

The calculation of the motion of separated moisture in a linear horizontal separator is made on the basis of the analysis of the development of the waves in a flow of a thin layer of liquid along a vertical surface without allowance for the transverse flow of mass [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 174–176, March–April, 1985.     

Investigation of the flow and heat transfer of viscous reacting fluids in long tubes

Heat transfer and resistance in the case of laminar flow of inert gases and liquids in a circular tube were considered in [1–4], the justification of the use of boundary-layer type equations for investigating two-dimensional flows in tubes being provided in [4]. The flow of strongly viscous, chemically reacting fluids in an infinite tube has been investigated analytically and numerically in the case of a constant pressure gradient or constant flow rate of the fluid [5–8]. An analytic analysis of the flow of viscous reacting fluids in tubes of finite length was made in [9, 10]. However, by virtue of the averaging of the unknown functions over the volume of the tube in these investigations, the allowance for the finite length of the tube reduced to an analysis of the influence of the time the fluid remains in the tube on the thermal regime of the flow, and the details of the flow and the heat transfer in the initial section of the tube were not taken into account. In [11], the development of chemical reactions in displacement reactors were studied under the condition that a Poiseuille velocity profile is realized and the viscosity does not depend on the temperature or the concentration of the reactant; in [12], a study was made of the regimes of an adiabatic reactor of finite length, and in [13] of the flow regimes of reacting fluids in long tubes in the case of a constant flow rate. The aim of the present paper is to analyze analytically and numerically in the two-dimensional formulation the approach to the regimes of thermal and hydrodynamic stabilization in the case of the flow of viscous inert fluids and details of the flow of strongly viscous reacting fluids.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 17–25, January–February, 1930.     

The Development of the Asymptotic Viscous Dissipation Profile in a Vertical Free Convective Boundary Layer Flow in a Porous Medium

The effect of viscous dissipation on the development of the boundary layer flow from a cold vertical surface embedded in a Darcian porous medium is investigated. It is found that the flow evolves gradually from the classical Cheng–Minkowycz form to the recently discovered asymptotic dissipation profile which is a parallel flow.     

Nonisothermal displacement of high-paraffin oils by water with allowance for solid-phase precipitation

A mathematical model of the nonisothermal displacement of oil by water with allowance for solid-phase precipitation is proposed. Self-similar solutions of the problem of nonisothermal displacement of oil from a homogeneous, thermally insulated formation are obtained. The inverse problems of determining the relative phase permeabilities and the temperature dependence of the paraffin saturation concentration from laboratory displacement data are solved. Exact solutions of the non-self-similar problems of the displacement of high-paraffin oil by a slug of hot water and of the thermal delay problem are obtained. The nonisothermal displacement of high-paraffin oils by water with allowance for heat transfer to the surrounding strata is subjected to qualitative analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 126–137, May–June, 1989.The authors are grateful to A. K. Kurbanov and Yu. V. Kapyrin for useful discussions and their interest in the work.     

A two-parameter model of wave regimes for viscous liquid film flows

Wave regimes of viscous liquid film flows are considered when the viscosity coefficients vary in a wide range. An approximate model system of differential equations with two external governing parameters for the film layer thickness and the local flow rate is derived. The viscous dissipation of a film layer is taken into account in this system more accurately than in the well-known one-parameter Shkadov model. New properties of linear and nonlinear waves caused by the hydrodynamic instability of high-viscous liquid flows under gravity and surface tension are found.     

Flow of a viscous liquid in a bent tube of finite length that undergoes deformation

A study is made of the closed flow of a viscous incompressible Newtonian liquid in a deformed tube with a section used as a peristaltic pump connected to a given hydraulic load. The time-average flow rate of the liquid (blood) in the external section is determined, together with the pressure difference across the load and the condition for the absence of hemolysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 177–179, March–April, 1981.     

Flow of a viscous liquid in the gap between a moving and a fixed sphere at low reynolds numbers

In recent years, the investigation of various physiological processes, and also the problem of developing an artificial heart have stimulated studies in which blood flow in the heart, and also in the large arteries is treated as the flow of a viscous incompressible Newtonian liquid. Different assumptions have been made concerning the geometry of the heart. For example, in [1, 2] a sphere was used as model of a ventricle, the influence of the entrance and exit valves was not taken into account, and, since the Reynolds number is normally fairly high, the blood flow was treated as the flow of an ideal incompressible liquid. In the experimental study of [3], the ventricle was modeled by an ellipsoid and allowance was made for the influence of the entry mitral valve; a simplified cylindrical geometry was used in [4]. In the present paper, the model of the ventricle is a sphere. Allowance is made for the influence of an artificial entry ball valve. Configurations of this kind are encountered in an artificial heart with hydraulic drive. To use the problem as an analytic test in further computer calculations at high Reynolds numbers, and also to obtain analytic estimates for the trajectories of Lagrangian particles, the treatment is restricted to flows for which the influence of the nonlinear terms in the Navier-Stokes equations can be ignored.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 180–183, November–December, 1980.