Experimental investigation of pulsed stretching of cavitating media

A class of media whose structure develops into a foam state during pulsed volume stretching because of unrestricted growth of cavitational bubbles was determined experimentally. Among such media are low-viscosity Newtonian liquids, and disperse liquid media (emulsions, suspensions, and gels) with a low-viscosity liquid matrix. The results obtained are important for the development of a generalized rheological model for cavitating media. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 122–125, September–October, 1998.     

Motion of a gas inclusion in a capillary under the action of vibration

The motion of gas inclusions in a liquid-filled duct under the action of vibration for comparable cross-sectional dimensions of the inclusion and the duct is studied. Two limiting cases of inclusion motion differing with respect to the drag mechanism are considered. For low velocities, it is assumed that the drag is mainly determined by the capillary forces and the friction in the liquid film separating the gas inclusion from the duct wall. As the inclusion velocity increases, the main contribution to the drag is made by such mechanisms as flow separation, the formation of a low-pressure region in the wake, etc. It is demonstrated that due to the vibration a gas inclusion traveling in a capillary under the action of steady forces is halted at certain points of the capillary. The capillary behaves like a filter, impermeable for inclusions smaller than a certain threshold size. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 85–92, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No.96-01-01813).     

Influence of a sureactant on the instability of a falling liquid film

The hydrodynamic instability of a film flow of a weak solution containing a soluble volatile surfactant is investigated. Diffusion of the surfactant in the liquid, its evaporation into the boundary gas medium, and the adsorption and desorption processes in the near-surface layer are taken into account. A system of evolutionary equations is derived and a steady-state solution film flow along a vertical surface and the stability of this flow are investigated for the simultaneous action of body and capillary forces and the Marangoni effect. Hydrodynamic and diffusion instability modes are detected and their properties are investigated for constant and variable surfactant concentration in the adsorbed sublayer. Moscow, Madrid. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 56–67, July–August, 2000. The work was carried out with support from the Russian Foundation for Basic Research (project No. 97-01-00153) and the Spanish Ministry of Higher Education (program DGICYT (Spain), project No. PB 96-599).     

Stability Analysis of Uniform Equilibrium Foam States for EOR Processes

The use of foam for mobility control is a promising mean to improve sweep efficiency in EOR. Experimental studies discovered that foam exhibits three different states (weak foam, intermediate foam, and strong foam). The intermediate-foam state is found to be unstable in the lab whereas the weak- and strong-foam states are stable. The model of Kam (Colloids Surf A Physicochem Eng Asp 318(1–3): 62–77, 2008) is the only mechanistic foam model that can fit a variety of steady-state experimental data including multiple steady states. This model is modified from a previous mechanistic foam model to resolve the intrinsic instability of the strong-foam state. Simple finite-difference simulations have found that an arbitrary perturbation grows for the unstable intermediate foam but diminishes for the strong- and weak-foam states. The issue of the stability of foam states, especially the strong-foam state, is a serious concern in application of foam in EOR. Instabilities may rule out one or more states and consequently have considerable effect on reservoir sweep efficiency and injection pressure. Here, for the first time the stability of the various equilibrium foam states is investigated by an analytical stability-analysis method together with numerical simulations. We demonstrate the instability of most intermediate states, consistent with the laboratory observations. However, our analysis reveals an instability of the strong-foam state. We show that the diffusion, whether introduced artificially by the finite-difference scheme or representing physical dispersion, damps this instability. We obtain good agreement with finite-element simulations with and without additional diffusion. We also prove that all states are unconditionally stable for a local-equilibrium-foam model.     

Thermodynamics of the activated state of materials

The thermodynamics of irreversible processes is extended to deformable materials whose state and behavior under nonequilibrium conditions are determined by the value and evolution of the additional parameter — the activation parameter. General thermodynamic relations are presented. The concept of the time of existence of a nonequilibrium state is introduced, and the phase coexistence conditions are generalized taking into account the properties of the interface. Methods are described to generalize the relations for irreversible flows, thermodynamic forces, and the equations of state. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 141–152, January–February, 2009.     

Problem of filling of a spherical cavity in a Kelvin-Voigt medium

This paper is concerned with mathematical modeling and solution of the problem of the collapse of a spherical cavity in a viscoelastic medium under the action of constant pressure at infinity. A differential equation of motion for the cavity boundary is constructed and solved numerically. The existence of three modes of motion of the boundary is established, and a map of these modes in the plane of the determining parameters is constructed. Asymptotic forms of the solutions of the problem for all modes are constructed. The problem of cavity collapse with capillary forces taken into account is formulated and solved. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 93–101, September–October, 2008.     

Rheological model of volume stretching of newtonian liquids

An equation of state for a volumetrically stretched cavitating liquid medium that holds in the entire span of volume concentrations of bubbles ranging from cavitation nuclei to the stage of formation of a cellular foam structure is obtained based on a proposed macrorheological model. The dependence of the modulus of volume elasticity of a liquid on the volume concentration of bubbles is plotted, and a method for estimating the relaxation time for tensile stresses in cavitating liquid media is proposed. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 35–46, January–February, 1998.     

On a mechanical analogy in the ideal plasticity theory

The Cauchy problem of propagation of plastic state zones in a boundless medium from the boundary of a convex surface, along which normal pressure and shear forces act, is considered. In the case of complete plasticity, the Tresca system of quasi-static equations of ideal plasticity, which describes the stress-strain state of the medium, is known to be hyperbolic and to be similar to a system that describes a steady-state flow of an ideal incompressible fluid. This system is numerically solved with the use of a difference scheme applied for hyperbolic systems of conservation laws. Results of numerical calculations are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 74–80, July–August, 2008.     

Analysis of capillary interaction and oil recovery under ultrasonic waves

Although, the effects of ultrasonic irradiation on multiphase flow through porous media have been studied in the past few decades, the physics of the acoustic interaction between fluid and rock is not yet well understood. Various mechanisms may be responsible for enhancing the flow of oil through porous media in the presence of an acoustic field. Capillary related mechanisms are peristaltic transport due to mechanical deformation of the pore walls, reduction of capillary forces due to the destruction of surface films generated across pore boundaries, coalescence of oil drops due to Bjerknes forces, oscillation and excitation of capillary trapped oil drops, forces generated by cavitating bubbles, and sonocapillary effects. Insight into the physical principles governing the mobilization of oil by ultrasonic waves is vital for developing and implementing novel techniques of oil extraction. This paper aims at identifying and analyzing the influence of high-frequency, high-intensity ultrasonic radiation on capillary imbibition. Laboratory experiments were performed using cylindrical Berea sandstone and Indiana limestone samples with all sides (quasi-co-current imbibition), and only one side (counter-current imbibition) contacting with the aqueous phase. The oil saturated cores were placed in an ultrasonic bath, and brought into contact with the aqueous phase. The recovery rate due to capillary imbibition was monitored against time. Air–water, mineral oil–brine, mineral oil–surfactant solution and mineral oil-polymer solution experiments were run each exploring a separate physical process governing acoustic stimulation. Water–air imbibition tests isolate the effect of ultrasound on wettability, capillarity and density, while oil–brine imbibition experiments help outline the ultrasonic effect on viscosity and interfacial interaction between oil, rock and aqueous phase. We find that ultrasonic irradiation enhances capillary imbibition recovery of oil for various fluid pairs, and that such process is dependent on the interfacial tension and density of the fluids. Although more evidence is needed, some runs hint that wettability was not altered substantially under ultrasound. Preliminary analysis of the imbibition recoveries also suggests that ultrasound enhances surfactant solubility and reduce surfactant adsorption onto the rock matrix. Additionally, counter-current experiments involving kerosene and brine in epoxy coated Berea sandstone showed a dramatic decline in recovery. Therefore, the effectiveness of any ultrasonic application may strongly depend on the nature of interaction type, i.e., co- or counter-current flow. A modified form of an exponential model was employed to fit the recovery curves in an attempt to quantify the factors causing the incremental recovery by ultrasonic waves for different fluid pairs and rock types.     

Quasi-steady-state flows in a liquid film in a gas: Comparison of two methods of describing waves

The motion of thin films of a viscous incompressible liquid in a gas under the action of capillary forces is studied. The surface tension depends on the surfactant concentration, and the liquid is nonvolatile. The motion is described by the well-known model of quasi-steady-state viscous film flow. The linear-wave solutions are compared with the solution using the Navier-Stokes equations. Situations are studied where a solution close to the inviscid two-dimensional solutions exists and in the case of long wavelength, the occurrence of sound waves in the film due to the Gibbs surface elasticity is possible. The behavior of the exact solutions near the region of applicability of asymptotic equations is studied, and nonmonotonic dependences of the wave characteristics on wavenumber are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 103–111, May–June, 2007.     

Flow and instability of capillary jets interacting with the surrounding medium

The flow of an axially symmetric capillary jet of a viscous incompressible liquid in the space occupied by another liquid is investigated. The problem of stationary flow in the jet and in the surrounding medium under the action of viscosity, capillary forces, and gravity was obtained numerically. The instability problem of this flow to small perturbations in the form of running waves is stated and solved numerically. The values of the dimensionless Reynolds, Weber, and Froude numbers are explained, as well as the effect of the initial velocity profile in the jet, its instability, and subsequent jet decay into drops.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 50–59, November–December, 1978.     

Liquid flow in foams

A model equation for describing liquid motion in a foam of polyhedral structure is proposed. A dimensionless parameter characterizing the structure of the foam, namely, the ratio of the volume energy densities of the capillary and gravitational forces, is introduced. When the gravitational forces predominate over the capillary forces, the out-flow process may be regarded as a kinematic wave that can be described by the Burgers equation. In the opposite case, the capillary absorption can be described by a quasilinear parabolic equation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 103–108, March–April, 1988.The authors are grateful to A. V. Berlyand for discussing the problems associated with the solution of Eq. (3. 4).     

A Non-isothermal Pore Network Drying Model with Gravity Effect

The concept of immiscible displacement as an invasion percolation (IP) process driven by heat and mass transfer is used in a pore network model for convective drying of capillary porous media. The coupling between heat and mass transfer occurs at the liquid–gas interface through temperature-dependent equilibrium vapor pressure and surface tension as well as the phase change enthalpy (in evaporation and condensation). The interfacial effects due to capillary forces and gravity are combined in an invasion potential; viscous forces are neglected. Simulation results show stabilized invasion patterns and finite drying front width by the influence of gravity.     

Microdroplet absorption by two-layer porous media

Microdroplet absorption by two-layer porous media is studied both theoretically and experimentally. A two-dimensional model for liquid flow from a droplet into a porous medium is presented and veri.ed based on a simultaneous numerical solution of the Euler equations taking into account surface tension forces and the unsteady filtration equation. The effect of the structural parameters of the two-layer porous medium (pore size in the layers, and the thickness and porosity of the layers) on the droplet absorption is analyzed. It is shown that the presence of the second layer can have a significant effect on the droplet absorption rate and the liquid distribution in the medium. The pore size is found to be the main parameter that governs the effect of the second layer. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 121–130, January–February, 2007.     

On the basic laws of anisotropic viscoelasticity

The main aim of this work is to develop a consistent formulation of the rheological behavior for different anisotropic polymer systems. The unified theory of anisotropic viscoelasticity is developed based on the symmetry principles. The Maxwell rheological equation is extended to nonsymmetric anisotropic liquids. Transitions from the most general anisotropy to particular cases of anisotropy are established. It appears that the coupled relaxation of symmetric and antisymmetric stresses is a natural phenomenon in nonsymmetric viscoelasticity. Within the concept of an internal state variable, a stress–order relation is derived for a fully nonlinear case. The order tensor dynamics is also considered. A simple method of deriving the equation of the internal rotational motion is developed for the general macroscopic anisotropy. This paper was presented at the 3rd Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece     

An Analytical Model for Capillary Pressure–Saturation Relation for Gas–Liquid System in a Packed-Bed of Spherical Particles

Capillary pressure is considered in packed-beds of spherical particles. In the case of gas–liquid flows in packed-bed reactors, capillary pressure gradients can have a significant influence on liquid distribution and, consequently, on the overall reactor performance. In particular, capillary pressure is important for non-uniform liquid distribution, causing liquid spreading as it flows down the packing. An analytical model for capillary pressure–saturation relation is developed for the pendular and funicular regions and the factors affecting capillary pressure in the capillary region are discussed. The present model is compared to the capillary pressure models of Grosser et al. (AIChE J., 34:1850–1860, 1988) and Attou and Ferschneider (Chem. Eng. Sci., 55:491–511, 2000) and to the experiments of Dodds and Srivastava (Part Part Syst. Charact., 23:29–39, 2006) and Dullien et al. (J. Colloid Interface Sci., 127:362–372, 1989). The non-homogeneity of real packings is considered through particle size and porosity distributions. The model is based on the assumption that the particles are covered with a liquid film, which provides hydrodynamic continuity. This makes the model more suitable for porous or rough particles than for non-porous smooth particles. The main improvements of the present model are found in the pendular region, where the liquid dispersion due to capillary pressure gradients is most significant. The model can be used to improve the hydrodynamic models (e.g., CFD and cellular automata models) for packed-bed reactors, such as trickle-bed reactors, where gas, liquid, and solid phases are present. Models for such reactors have become quite common lately (Sáez and Carbonell, AIChE J., 31:52–62, 1985; Holub et al., Chem. Eng. Sci, 47, 2343–2348, 1992; Attou et al., Chem. Eng. Sci., 54:785–802, 1999; Iliuta and Larachi, Chem. Eng. Sci., 54:5039–5045, 1999, IJCRE 3:R4, 2005; Narasimhan et al., AIChE J., 48:2459–2474, 2002), but they still lack proper terms causing liquid dispersion.     

Self-similar problem of decomposition of gas hydrates in a porous medium upon depression and heating

We consider the specifics of decomposition of gas hydrates under thermal and depressive action on a porous medium completely filled with a solid hydrate in the initial condition. The existence of volumetric-expansion zones, in which the hydrate coexists in equilibrium with water and gas, is shown to be possible in high-permeable porous media. The self-similar problems of hydrate decomposition upon depression and heating are studied. Ii is shown that there are solutions according to which hydrate decomposition can occur both on the surface of phase transitions and in the volumetric region. We note that, in the first case, decomposition is possible without heat supply to a medium and even with heat removal. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen' 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 111–118, May–June, 1998.     

Fluidization of a granular medium in a viscous fluid under vertical vibration

The dynamics of a granular medium in a cavity filled with incompressible viscous fluid under harmonic vertical vibration are studied experimentally. The sand is fluidized in a relatively thin sublayer of the granular layer near the interface between the media. The fluidization is of the threshold type and is accompanied by intense parametric oscillations of the interface. For viscous fluids, the transition of the sand from a quasi-solid to a fluidized state and the reverse transition associated with a decrease in the oscillation rate occur with hysteresis. The nondimensional governing parameters determining the sand dynamics are established. The analysis is focused on the case of low nondimensional frequencies. Perm’, Paris. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 113–122, May–June, 2000.     

Model problem of instantaneous motion of a three-phase contact line

Hydrodynamic problems of fluid flow with three-phase contact lines (for example, solid body-liquid-gas or solid body and two nonmixing liquids) are of special interest. Much attention has been paid lately to steady and quasisteady flows. Significantly unsteady problems of this kind have almost escaped consideration. In the present paper, we study a model problem of a significantly unsteady motion of a finite volume of an incompressible fluid with a three-phase contact line. The static contact angle is assumed to be right and the initial free surface of the liquid is assumed to be cylindrical. One of the planes instantaneously begins to move toward the other with a constant finite velocity. Flows with high Reynolds numbers and small capillary numbers are considered. Mass forces are ignored in the problem. The basic result is the construction of a formal asymptotic of the solution at small times. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 51–61, July–August, 1999.