Self-similar thinning of a liquid film separating liquid phases or a liquid and a solid phase

The article discusses the thinning of a thin flat film of liquid between coalescing bubbles or coalescing drops due to motion of the liquid under the action of capillary forces, under drag conditions of the surfaces of the film. A study was also made of the outflow of a liquid from a film separating a bubble (drop) from a solid surface. The problem of the decrease in thickness and subsequent breakaway of thin liquid films is of interest in investigations of the kinetics of coalescence and coagulation and in the theory of the stability of foams and lyophobic colloids in the presence of surfactants or electrolytes, as well as in the theory of heterogeneous boiling. Information on some work and on special characteristics of the statement of the problem may be found in [1].Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp, 39–48, March–April, 1973.     

Slow motions of a liquid drop in a viscous liquid

The problem of the fully established slow translational motion of a round drop (bubble) in a viscous liquid was solved by Adamar and Rybchinskii [1, 2]. The results of experimental measurements are rarely in agreement with the Adamar-Rybchinskii formula. This is connected with braking of the flow due to surface-active impurities, which are usually rather numerous in liquids. Nevertheless, we shall consider the problem of the not fully established motion of a drop in the simplest case, assuming that there are no surface-active substances. The article discusses problems of the vibrations and motions of a spherical drop in a viscous liquid, with arbitrary accelerations. An analysis is made of a formula for the force of resistance of a drop of liquid with a high viscosity, an elastoviscous drop, and a particle with slipping-through.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 32–37, November–December, 1975.     

Steady rise of a liquid drop in a viscous liquid

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 78–88, January–February, 1992.     

Phenomena of a liquid drop falling to a liquid surface

Two kinds of phenomenon have been observed when a liquid drop falls to a surface of the same liquid. The first, which can nearly always be observed, involves splash and some degree of penetration and cleavage and the conditions for this occurrence are identified. The experimental observations are compared with previous computational results. The second kind of colliding phenomena can be observed only by chance in an ordinary falling drop experiment and appears to be random. It includes the two phenomena investigated in this paper: the floating drop and the rolling drop.     

Control of a liquid–liquid heat exchanger

 The analytical solutions of equations describing the dynamics of distributed parameter systems are usually complicated in form and derivations and inconvenient to use for simulation and control system design. The liquid–liquid counter flow heat exchanger is an example of these disturbed parameter systems. An analytical solution of the dynamics of a symmetrically operated counter flow heat exchanger in the form of transfer function matrix is investigated in open-loop and close-loop conditions. The resulting non-linear model was linearized using perturbation approach. A feed-forward path controller to counteract at any disturbances in the boundary temperature and a non-interactive controller to decouple the outputs were implemented. Received on 22 February 2001 / Published online: 29 November 2001     

Displacement of a liquid from a horizontal circular tube by another liquid

We consider the axisymmetric problem of expulsion of one liquid from a horizontal circular pipe by another for the laminar flow regime.Studies of Taylor [1], Cox [2, 3], and others have been devoted to the experimental investigation of the displacement of a liquid from a capillary. Experiments on the displacement of mutually immiscible liquids show that the length of the combined flow region and the amount of displaced liquid remaining in this region are determined primarily by the magnitude of the interphase tension forces at the leading edge of the interface. The equilibrium of these forces and the hydrodynamic differential, established some time after the beginning of displacement, give rise to the rigid bullet-shaped form of the interface leading edge. This portion of the interface, whose stiffness is achieved as a result of the force balance, is termed the head of the interface between the liquids. The radius of the head-the relatively small autonomous portion of the interface-defines the dimensions and deformations of the entire remaining interface.The existence of a rigid autonomous interface head is the basis of the physical displacement model used in this article.     

Vaporization of a liquid injected into an immiscible liquid through a single nozzle

The basic characteristics of vaporization and flowing behavior of n-pentane injected through a single nozzle into a column of hot water have been studied photographically. Subcools at the nozzle-outlet have a strong influence on the critical temperature driving forces at over which vaporization can be maintained. The length of a Rayleigh jet is remarkably shortened when vaporization occurs, whereas mean diameters of drops are little affected whether vaporization occurs or not. A specific condition that a bubble appears in each drop is satisfied not on a specific line but over a wide region on the ΔT_∞ - U_N plane.     

Filtration of a piecewise-homogeneous liquid

The nonsteady filtration of two immiscible liquids, in the absence of pressure, in a homogeneous and isotropic porous medium, is considered. A nonlinear hydrodynamic problem is formulated, and a number of its features are noted. The solution of the corresponding linearized problem is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 62–69, November–December, 1976.     

Lifetime of a superheated liquid

The mathematical relationship between the lifetime of a superheated liquid and temperature is investigated. The energy equation is solved in conjunction with a non-equilibrium vapor formation model in order to specify the temperature variation of the liquid during the nucleation process. It is shown that the expectation time of a uniformly superheated liquid decreases with increasing temperature. The limit of superheat in the liquid is then identified as the liquid temperature above saturation at which boiling takes place almost instantaneously. Results compare favorably with classical nucleation kinetic data.     

Filtration of a gasified liquid

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 97–106, September–October, 1993.     

Rivulet flow of a viscoelastic liquid

A theoretical investigation is made of the rivulet flow of a viscoelastic liquid down an inclined plane. It is shown that elasticity causes a significant change in the shape of the rivulet, with height rise at the center. There is also a change in the relationship between the flow rate and the geometry of the rivulet. Elasticity is found to cause a flow in the cross-sectional plane in the form of counter-rotating vortices. In the Newtonian case the flow is purely axial.     

Wave resistance of a viscous liquid

In this paper we examine the resistance encountered by a system of normal stresses during its rectilinear motion along the surface of a viscous liquid of infinite depth. The problem is solved in the linear formulation, i.e., it is assumed that amplitudes of the waves which arise are small and the waves are shallow. The solution for the two-and three-dimensional problems is obtained in the general case in closed form. In the two-dimensional case a detailed study is made of the case when a constant pressure p₀, moving with the constant velocity U, is given on a segment of length 2l. In the three-dimen-sional problem the case is studied when the normal stress is concentrated on a segment of a straight line of length 2l, which can replace a ship moving along a straight course with the constant velocity U. The integrals obtained in both cases are studied using the stationary phase method, the application of which for the three-dimensional integrals with respect to a volume with boundaries is justified in §1 of the paper. As a result we obtain equations for the wave resistance in the two- (§2) and three-dimensional (§3) cases.     

Wave dispersion of a gas in a liquid

A novel method of dispersing a gas in a liquid by pressure pulses generated by waves propagating from a hydrodynamic oscillation generator is proposed. Devices that realize this method, wave dispersers, are created and investigated experimentally. The amplitude-frequency characteristics of the wave processes in the dispersers and the size distribution density functions of the gas bubbles are obtained. It is shown that there are optimal pressure values at the disperser inlet at which a minimum bubble size is achieved. The average diameter of the gas bubbles produced by water wave dispersers in the optimal operation regimes varied on the range from 0.3 to 0.6 mm, depending on the gas flow-rate.     

Instability of a compound liquid jet

In the linear Rayleigh theory [1] the degree of stability of a jet is determined by the viscosity and inertia characteristics of the fluids and the interphase surface tension. The stability of a jet in an infinite medium increases with increase in the viscosity of both the jet and the medium [2, 3]. The presence of two interfaces is responsible for various features of the development of instability in a liquid layer on the surface of a cylinder, and in particular a layer on the inner surface of a cylinder is more unstable than one on the outer surface [4]. In [5, 6] the breakup of a hollow jet in an external medium was investigated. In this paper we examine, in the linear approximation, the stability of a compound jet of nonmiscible liquids with respect to small axisynmetric perturbations of the interfaces. The instability characteristics are given for jets with inviscid and very viscous outer shells. The conditions governing the suppression of rapidly growing instabilities of the inner part (core) of the jet by a viscous shell are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–8, July–August, 1985.     

Motion of a bubble in a viscous liquid

The discussion concerns steady-state flow of a viscous fluid around a spherical bubble at small Reynolds number R. Asymptotic matching [1] provides a way of calculating the resistance force, which agrees well with the measured force for R < 5. The rate of growth or dissolution of the bubble is calculated on the assumption that the Péclet number is large.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 107–111, January–February, 1971.We are indebted to V. G. Levich for a discussion.