Motion of a three-phase contact line along a wet surface

The motion of the contact line in gas-liquid-solid systems is theoretically investigated for small values of the capillary number and Reynolds number. The possible existence on the solid substrate of a residual microscopic film formed by adsorbed liquid molecules is taken into account and the spreading characteristics of the liquid on dry and wet substrates are compared. It is shown that, in accordance with the experimental data, in the model employed the motion of the liquid during wetting is rolling motion, and that the increase in the dynamic contact angle is slower for a wet than for a dry substrate. The maximum dynamic contact angle is much less than 180°. The flow structure in the neighborhood of the moving contact line is analyzed and it is shown that under certain conditions regions with closed streamlines may be formed. The reason for this is the self-induced Marangoni effect — the reaction of the surface tension gradient on the liquid-solid boundary caused by the liquid flow on the flow that caused it.Based on a paper read at the Seventh Congress on Theoretical and Applied Mechanics, Moscow, August 1991. Presented by R. I. Nigmatulin.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 81–89, November–December, 1992.     

Determination of the equilibrium state of a capillary liquid in a vessel

This article describes a method for determination of the form of the equilibrium surface of a liquid in a given vessel of arbitrary axiosymmetric form. Capillary, gravitational, and centrifugal forces act on the liquid. Liquid volume and wetting angle are given. Curves are constructed for the case of negative overloads by a homogeneous gravitational field, which are used to find the equilibrium states. An example which illustrates the application of the method is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–7, July–August, 1973.     

A Parametric Model for Predicting Relative Permeability-Saturation-Capillary Pressure Relationships of Oil–Water Systems in Porous Media with Mixed Wettability

A parametric two-phase, oil–water relative permeability/capillary pressure model for petroleum engineering and environmental applications is developed for porous media in which the smaller pores are strongly water-wet and the larger pores tend to be intermediate- or oil-wet. A saturation index, which can vary from 0 to 1, is used to distinguish those pores that are strongly water-wet from those that have intermediate- or oil-wet characteristics. The capillary pressure submodel is capable of describing main-drainage and hysteretic saturation-path saturations for positive and negative oil–water capillary pressures. At high oil–water capillary pressures, an asymptote is approached as the water saturation approaches the residual water saturation. At low oil–water capillary pressures (i.e. negative), another asymptote is approached as the oil saturation approaches the residual oil saturation. Hysteresis in capillary pressure relations, including water entrapment, is modeled. Relative permeabilities are predicted using parameters that describe main-drainage capillary pressure relations and accounting for how water and oil are distributed throughout the pore spaces of a porous medium with mixed wettability. The capillary pressure submodel is tested against published experimental data, and an example of how to use the relative permeability/capillary pressure model for a hypothetical saturation-path scenario involving several imbibition and drainage paths is given. Features of the model are also explained. Results suggest that the proposed model is capable of predicting relative permeability/capillary pressure characteristics of porous media mixed wettability.     

Stability of Filtration of a Gas—Liquid Mixture

The stability of steady regimes of filtration of a gas—liquid mixture at pressure lower than the saturation pressure is studied for the case of a nonmonotonic dependence of the relative phase permeability of the liquid on the gas saturation. It is shown that periodic self–oscillations can appear, and their evolution leads to deterministic chaos due to the appearance and destruction of quasiperiodic motions.     

Problem of Increasing the Survivability of Two–Stage Ballistic Guns

The paper proposes methods for increasing the survivability of light–gas guns, including new designs and nonconventional modes of shot. It is established theoretically and experimentally that a decrease in the cone angle of the conical adapter to 2.5 — 3° leads to a severalfold increase in the survivability of the high–pressure chamber. A compound piston with a liquid or gel–like filler is designed. The mode of shot from a light–gas gun with superlight pistons and without a diaphragm is justified and tested experimentally. Conical and measuring adapters with liners made of thermally– and wear–resistant alloys are designed to prevent ablation of the light–gas gun barrel.     

Analysis of Seepage for Power-Law Fluids in the Fractal-Like Tree Network

This work studies the flow characteristics of power-law fluids in the fractal-like tree network. A fractal model is developed for the permeability of power-law fluid flow in fractal-like tree network based on straight capillary model, generalized Darcy’s law and constitutive equation for power-law fluids. Analytical expression for permeability of power-law fluids in the network is presented and found to be a function of network microstructural parameters such as the branching diameter ratio, the branching length ratio, the total number of branching levels, the bifurcation angle, the branching number, the diameter of the zeroth branching level and the power exponent of power-law fluids. Both the phase permeabilities and the relative permeabilities are also derived and found to be a function of power exponent for the wetting phase and non-wetting phase, the saturation and other microstructural parameters and independent of the bifurcation angle.     

Volume Conservation of the Intermediate Phase in Three-Phase Pore-Network Models

Quasi-static rule-based network models used to calculate capillary dominated multi-phase transport properties in porous media employ equilibrium fluid saturation distributions which assume that pores are fully filled with a single bulk fluid with other fluids present only as wetting and/or spreading films. We show that for drainage dominated three-phase displacements in which a non-wetting fluid (gas) displaces a trapped intermediate fluid (residual oil) in the presence of a mobile wetting fluid (water) this assumption distorts the dynamics of three-phase displacements and results in significant volume errors for the intermediate fluid and erroneous calculations of intermediate fluid residual saturations, relative permeabilities and recoveries. The volume errors are associated with the double drainage mechanism which is responsible for the mobilization of waterflood residual oil. A simple modification of the double drainage mechanism is proposed which allows the presence of a relatively small number of partially filled pores and removes the oil volume errors.     

Nonaxisymmetric equilibrium shapes of a drop on a plane

A nonuniform temperature distribution, the presence of surface-active substances and impurities, and also other factors lead to a change in the wetting angle along a plane. A study is made of the influence of a small perturbation of the equilibrium contact angle on the shape of the free surface of the liquid. Two cases are considered: a surface of small slope in a gravity field and a nearly spherical shape under conditions of weightlessness. The equilibrium shapes of a liquid drop on an inclined plane under conditions of hysteresis of the wetting are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 164–167, July–August, 1983.I thank I. E. Tarapov and I, I, Ievlev for constant interest in the work and valuable comments.     

Deformation of liquid jets and drops injected into a gas stream

The process of deformation of liquid drops and jets is examined on a broad interval of two-phase flow parameters. The shape of a jet penetrating a gas stream directed at an angle to the jet-particle velocity vector is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–88, May–June, 1971.In conclusion the authors thank A. K. Simonovskii for his useful comments.     

On the stability margin of equilibrium states of a capillary liquid in a slit

The stability margin is determined for symmetric equilibrium shapes of the free surface of a liquid suspended in a slit and subject to gravity and surface tension. The calculations are made in the range of variation of the parameters, the wetting angle and the Bond number, adjoining the boundary of the stability region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 88–93, July–August, 1979.     

Effect of the shape of a blunt nose on the drag coefficient of a body in a hypersonic rarefied gas flow

The effect of the shape of a blunt nose of a body located in a hypersonic rarefied gas flow on the field of flow and on the aerodynamic characteristics is studied in the example of flow round ellipsoids of revolution at a zero angle of attack. The problem of the flow in the transition regime is solved on the basis of numerical analysis of the model kinetic Bhatnagar—Gross—Krook (BGK) equation for a monatomic gas. The good agreement of the results of the numerical calculations with the experimental data in a broad range of Mach numbers has shown [1, 2] that the numerical solution of the model kinetic equations is a reliable and effective means for studying flow problems. In the case when the problem is posed of determining the laws of the purely force interaction of a flow with the body, sufficiently good accuracy is given by the use of the model BGK equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 190–192, March–April, 1985.     

Percolation model of two-phase flow through porous media

A physical model of the process of two-phase flow of immiscible fluids through a porous medium is developed and used to make an analytical calculation of the dependence of the relative phase permeabilities on the saturation of the medium by one of the phases. The theory is compared qualitatively with experiment for a model capillary radius frequency function and quantitatively with numerical calculations made on a computer. In both cases good agreement is obtained. The pressure dependences of the phase permeabilities are analyzed. The question of residual saturation with the wetting fluid after completion of the displacement process is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 88–95, January–February, 1987.     

Application of the Density-Functional Method for Numerical Simulation of Flows of Multispecies Multiphase Mixtures

Numerical examples of application of the density functional used to describe isothermal flows of two-phase two-species mixtures are given. The following flows are calculated in a two-dimensional formulation: impact of a drop on a liquid layer, breakdown of a drop in the velocity field of the Couette flow, formation of the wetting angle of a drop on a solid surface, and development of the Rayleigh–Taylor and Kelvin–Helmholtz instabilities at the gas–liquid interface.     

Dynamics of a diverging liquid meniscus in a capillary,taking into account the specific properties of thin films

The theory of the diverging meniscus of a Newtonian liquid for capillary flow conditions at low meniscus velocities, in which the thermodynamic and Theological features of thin wetting films appear, is set forth. Two cases are considered: thermodynamically stable wetting film with high viscosity in the boundary layer on a completely wetted solid surface and a thermodynamically unstable film on a conditionally wetted solid surface exhibiting a liquid slip effect.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 72–82, May–June, 1976.The author wishes to express his appreciation to A. G. Grivtsov and V. S. Yushchenko for valuable assistance in the computer calculations.     

Evolution of bubble spectrum in the process of cavitational fragmentation by a shock wave reflected from a free liquid surface

Equations which describe the evolution of the bubble spectrum in the process of cavitational fragmentation by a shock wave reflected from a free liquid surface are formulated. As an example, the effect of artificial saturation of the initial fluid with large bubbles on the dispersity of a liquid-drop gas suspension focused by dispersion is investigated.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 51–58, May–June, 1992.     

Gas content of a foam bed at reduced pressures

The gas content of a foam bed has been experimentally investigated using a 50 × 80 mm² column at the following parameters: pressure P=0.1–1.0 bar, W=0.5-2.0 m/sec, H = 140–180 mm. In all cases the gas phase was air and the liquid phase was water and aqueous solutions of ethanol and glycerol. It has been established that reducing the pressure causes a considerable decrease in gas content, leading to an increase in the depth of the starting layer of liquid h₀. A formula that conforms with the experimental data to within ± 10% is obtained for the gas content.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 2, pp. 166–169, March–April, 1970.     

Micromodel Observation of the Role of Oil Layers in Three-Phase Flow

We have studied the flow of a non-aqueous phase liquid (NAPL, or oil), water and air at the pore scale using a micromodel. The pore space pattern from a photomicrograph of a two-dimensional section through a Berea sandstone was etched onto a silicon wafer. The sizes of the pores in the micromodel are in the range 3–30,m and are the same as observed in the rock from which the image was taken. We conducted three-phase displacement experiments at low capillary numbers (in the order of 10^-7) to observe the presence of predicted displacement mechanisms at the pore scale. We observed stable oil layers between the wetting phase (water) and the non-wetting phase (gas) for the water–decane–air system, which has a negative equilibrium spreading coefficient, as well as four different types of double displacements where one fluid displaces another that displaces a third. Double imbibition and double drainage are readily observed, but the existence of an oil layer surrounding the gas phase makes the other double displacement combinations very unlikely.     

Experimental investigation into the influence of polymer additives in water on the relative permeabilities of porous media

A method has been developed for investigating the relative permeabilities of porous media for oil and for aqueous solutions of polymers; experimental equipment has been developed for determining the phase permeabilities by a stationary method. Investigations were made of the influence of polyacrylamide additives on the change in the relative permeabilities for the simultaneous flow of water and a nonpolar hydrocarbon liquid. It was established that addition of the polymer can lead to a simultaneous reduction in the relative permeability for the wetting liquid and an increase for the nonwetting liquid. The phase permeabilities were obtained for oil and water moving behind a fringe of polymer substance. It was established that the phase permeability for the water phase is a function of the saturation and the amount of sorbate. A cycle of experimental investigations was made into the influence of the rate of pumping and the concentration of the dissolved polymer on the change in the relative permeabilities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 163–167, July–August, 1980.     

A Numerical Study of Micro-Heterogeneity Effects on Upscaled Properties of Two-Phase Flow in Porous Media

Commonly, capillary pressure–saturation–relative permeability (P ^c–S–K _r) relationships are obtained by means of laboratory experiments carried out on soil samples that are up to 10–12 cm long. In obtaining these relationships, it is implicitly assumed that the soil sample is homogeneous. However, it is well known that even at such scales, some micro-heterogeneities may exist. These heterogeneous regions will have distinct multiphase flow properties and will affect saturation and distribution of wetting and non-wetting phases within the soil sample. This, in turn, may affect the measured two-phase flow relationships. In the present work, numerical simulations have been carried out to investigate how the variations in nature, amount, and distribution of sub-sample scale heterogeneities affect P ^c–S–K _r relationships for dense non-aqueous phase liquid (DNAPL) and water flow. Fourteen combinations of sand types and heterogeneous patterns have been defined. These include binary combinations of coarse sand imbedded in fine sand and vice versa. The domains size is chosen so that it represents typical laboratory samples used in the measurements of P ^c–S–K _r curves. Upscaled drainage and imbibition P ^c–S–K _r relationships for various heterogeneity patterns have been obtained and compared in order to determine the relative significance of the heterogeneity patterns. Our results show that for micro-heterogeneities of the type shown here, the upscaled P ^c–S curve mainly follows the corresponding curve for the background sand. Only irreducible water saturation (in drainage) and residual DNAPL saturation (in imbibition) are affected by the presence and intensity of heterogeneities.     

Shock–Free Breakup of Droplets. Temporal Characteristics

In the present paper, we consider the shock–free breakup of droplets in their encounter with a layer (sheet) of a moving gas in the absence of pressure perturbations when the droplets are affected by a short U–shaped pulse of aerodynamic forces. Under a high pressure of the ambient gas medium p₀ = 20—80 bar, the droplets (ethanol or liquid oxygen) have a chance to break up after stay in a thing (2—5 mm thick) gas layer (jet) moving with a velocity of 1—10 m/sec. A distinctive feature of the process is that the characteristic time of droplet deformation and the period of natural oscillations coincide with the residence time for the droplets in the region of their interaction with the gas stream. Empirical formulas are proposed for determination of the total breakup time and the duration of the droplet disintegration stage in shock–free breakup.