Konstantin G. Kornev

Foam in porous media: thermodynamic and hydrodynamic peculiarities

Abstract Thermodynamic and hydrodynamic properties of foams in porous media are examined from a unified point of view. We show that interactions between foam films (lamellae) and wetting films covering the pore walls play an important role in treating experimental data and constructing a general theory of foam residence and motion through porous media. Mechanisms of in situ bubble generation, foam patterning, and rheological peculiarities of foams in pores are discussed in detail. In particular, we clarify the difference between foam lamellae and liquid lenses, focusing on intermolecular forces in thin foam and wetting films. A consistent description of conditions of mechanical equilibrium of curved lamellae, including dynamic effects, is presented for the first time. This microlevel approach enables us to describe the dependence of the capillary pressure in the Plateau border on the current state of the pair ‘wetting film–foam lamella’. We review a theory of foam patterning under a load. Two driving forces are invoked to explain specific interactions between the solid skeleton and foams. The binding forces caused by bubble compressibility and the pinning forces due to capillarity determine a specific ordering of lamellae in porous media. The microscopic bubble train model predicts asymptotic expressions for the start-up-yield pressure drop. We consider key problems that underlay the understanding of physical mechanisms of anomalous foam resistance. Different micromechanical models of foam friction are thoroughly discussed. Brethertons (1961) theory of the forced, steady fluid–fluid displacement is reviewed in application to bubble transport through pore channels. The origins of disagreement of the theory and experiment are discussed. The Bretherton theory is augmented based on a new sailboat model, which accounts for thermodynamic coupling of foam lamellae and wetting films. Special attention is paid to studies of stick-slip motion of lamellae and bubbles in pores of varying diameter. Finally, we discuss macroscale models and analyze topical problems of foam behavior in porous media, including reservoirs, granular, and fibrous materials.

Capillary condensation as a morphological transition

The process of capillary condensation/evaporation in cylindrical pores is considered within the idea of symmetry breaking. Capillary condensation/evaporation is treated as a morphological transition between the wetting film configurations of different symmetry. We considered two models: (i) the classical Laplace theory of capillarity and (ii) the Derjaguin model which takes into account the surface forces expressed in terms of the disjoining pressure. Following the idea of Everett and Haynes, the problem of condensation/evaporation is considered as a transition from bumps/undulations to lenses. Using the method of phase portraits, we discuss the mathematical mechanisms of this transition hidden in the Laplace and Derjaguin equations. Analyzing the energetic barriers of the bump and lens formation, it is shown that the bump formation is a prerogative of capillary condensation: for the vapor-liquid transition in a pore, the bump plays the same role as the spherical nucleus in a bulk fluid. We show also that the Derjaguin model admits a variety of interfacial configurations responsible for film patterning at specific conditions.

Modeling of spontaneous penetration of viscoelastic fluids and biofluids into capillaries.

A theoretical model was developed to describe the dynamics of spontaneous penetration of viscoelastic fluids into capillaries. The model agrees quantitatively with recent experiments on absorption of droplets of polymer solutions by glass capillaries [A.V. Bazilevsky, K.G. Kornev, A.N. Rozhkov, A.V. Neimark, J. Colloid Interface Sci. (2003)]. The rate of penetration progressively reduces with the increase in fluid elasticity. Analysis revealed two main contributions to the viscoelastic drag of the liquid column: (i) viscous resistance, which is independent of fluid elasticity, and (ii) viscoelastic resistance, known as the Weissenberg effect. We analytically derived an augmented Bosanquet equation for the maximal velocity of penetration by balancing capillary, inertia, and viscoelastic forces. For slow creep of a liquid column, the Lucas-Washburn equation was modified by accounting for the Weissenberg effect. A series of numerical calculations were performed to demonstrate characteristic features of absorption of fluids at different conditions. This article also discusses some problems specific to absorption of biofluids. We show that deformations of cell membranes in the external converging flow may cause their rupture at the pore entrance.

Meniscus motion in a prewetted capillary

A conventional description of the effect of meniscus friction is based on the concept of the dynamic contact angle θ, which depends on the meniscus velocity V according to the Tanner law, θ∝V1/3. However, recent high-resolution experiments on spontaneous uptake of wetting fluids by capillaries have questioned the universality of the Tanner law. We analyze a mechanism underlying the phenomenological concept of meniscus friction, which finds experimental confirmation. As a case study system, we consider a forced flow of meniscus in a cylindrical capillary. It is assumed that the capillary is prewetted and the coating uniform film could coexist with the static meniscus. Numerical analysis is restricted to van der Waals fluids for which the disjoining pressure Π as a function of film thickness h has the form Π∝h−3. For these fluids, the equilibrium apparent contact angle is zero. Within the lubrication approximation of the film flow, we show that the nonzeroth dynamic contact angle first appears when the flui...

Spontaneous absorption of viscous and viscoelastic fluids by capillaries and porous substrates

We have developed a new technique to monitor spontaneous adsorption of fluids by porous substrates. The method is based on an optical electronic measuring system providing millisecond resolution. The method capabilities are demonstrated with the example of the absorption of millimeter-size droplets of water and aqueous solutions of polyethylene oxide and polyacrylamide by capillaries. It is shown that polymer additives even in a small amount reduce significantly the rate of adsorption. We have introduced a generalized Lucas-Washburn equation to account for the fluid elasticity. This equation is shown to explain the observed kinetics quantitatively without invoking adjustable parameters. We have derived a modified Bosanquet equation for the initial velocity of penetration, which accounts for the fluid elasticity. This simple formula gives a reasonable estimate of the rate of absorption of small droplets. We report visualization experiments on absorption of water and polymer solutions by sugar cubes as an example of porous substrates. Although the kinetics of droplet adsorption by porous substrates is similar to the kinetics of droplet adsorption by capillaries, the interpretation of experimental data is more complex and requires a plausible hydrodynamic model for lateral spreading in pores.

Surface stress-driven instabilities of a free film

We examine the effect of surface stress on the stability of free unconstrained solid films. We first determine the general thermodynamic criteria for film stability. Then, we show that two different morphological instabilities are possible, depending on the sign of the surface stress. The first corresponds to a self-induced Euler buckling mode and the second to an accordionlike wrinkling of the film surfaces.

Physical mechanisms of foam flow in porous media

Publisher Summary This chapter focuses on the physical mechanisms that govern foam flow in porous media. The motion of foams through porous media is a problem in physicochemical hydrodynamics. The basic mechanisms of foam transport reviewed contain some, but certainly not all, of the relevant physics of foam flow in porous media. Foam flow in porous media is a multifaceted process in which, on one hand, foam texture strongly governs foam rheology, and on the other, foam texture is in turn regulated by the porous medium through the capillary pressure. The chapter analyzes main features of this process with examples of foam motion in model pore channels. The modem theories of the foam lamella transport in pore channels of varying cross-section and the models of the weak foam flow are also discussed. Careful analyses of the flow on the scale of individual pores or channels are useful in exposing effects of various physical parameters on foam motion and in identifying flow-induced patterns. In addition, the basic physical mechanisms of foam microhydrodynamics underlie a variety of technological processes in oil recovery, groundwater/soil remediation, and textile manufacturing.