Some mechanisms of immiscible fluid displacement in small networks

We report experimental observations on immiscible displacement in two small networks using three different pairs of fluids, air-oil, air-water, and oil-water, to vary the wettability. The experiments were run for a wide range of capillary number, from 10⁻⁷ to 10⁻³. Various mechanisms are observed. These are film spreading and drainage, Haines' jump, free slip and stick-slip meniscus motion, contact angle hysteresis, snap-off, coalescence, and blocking of film and bubble. For the air-oil case, oil is perfectly wetting in the network. In imbibition, the displacement occurs first via thin film spreading, followed by snap-off of menisci, and then by piston-like displacement at low flow rates. As the flow rate increases, piston-like displacement dominates because film spreading is comparatively slow. Snap-off of menisci in the throats is a necessary condition for air trapping. In drainage, meniscus snap-off and coalescence are observed in one network. For both imbibition and drainage, during each snap-off or piston-like displacement event, all menisci move freely along the channels to adjust their curvatures, due to the lubrication of the wetting film. For the other two fluid pairs at low flow rates, this curvature readjustment through free slipping of meniscus is not observed, presumably due to the absence of wetting film during the displacement. At high flow rate, oscillation of menisci due to volumetric competition is observed. Neither wetting film spreading nor throat snap-off is observed. Stick and slip motion of meniscus is observed, probably due to the roughness and/or heterogeneous wettability of the solid surface. For the oil-water system the wettability seems to be time dependent. Coalescence between two menisci can occur in the throat, in the pore, or at the pore-throat boundary during displacement. Trapping of the displaced phase is due to its being bypassed or snapped off in the throat.     

Wetting: Inverse Dynamic Problem and Equations for Microscopic Parameters

Movement of a liquid meniscus in a low-diameter capillary while it is being filled or emptied is considered. The liquid is nonvolatile. Assuming low Reynolds number and low capillary number, the liquid-gas interface shape is studied. Angles of inclination of this boundary to the solid near the contact line are small. Consideration is given to the inverse problem in wetting dynamics: to establish an analytic expression for the universal constant that influences the dynamics of a three-phase contact line. Inverse relations for microscopic parameters in terms of macroscopic measured values obtained in experiments with a meniscus moving through a capillary are derived. The inverse relations are substantiated independently. To do so, numerical experiments for a van der Waals liquid have been carried out, using the de Gennes model of partial wetting. General formulas for microparameters agree well with numerical experiments. The article provides the similarity criterion which influences the wetting in the case of a van der Waals liquid meniscus. The inverse dynamic problem for both an advancing and a receding meniscus is solved. A relation for the critical speed of meniscus recession is proposed. Two contact angles for a meniscus are discussed. Behavior of dynamic contact angles in the vicinity of the critical speed is studied. One of the angles is shown to vanish at less than the critical speed, and the other one, exactly at the critical speed. In the case of an advancing meniscus the equations for microparameters are valid for both partial and complete wetting. The proposed inverse expression for complete wetting allows determination of the maximum precursor film thickness and its dependence on the motion speed (also determination of the Hamaker constant in the case of a van der Waals liquid). Copyright 2000 Academic Press.     

Investigation of Model Emulsion Films Stabilized by Solid Particles: Thickness of Films, Their Stability, and Interfacial Tension

The results of studying the thickness and stability in the gravitational field are presented for model emulsion films stabilized by solid particles of aluminum stearate and modified silica. The dependences of the capillary pressure on the thickness upon the creation of reduced pressure in a film (capillary pressure isotherms) are also given. The decrease in the water–oil interfacial tension because of solid particles is experimentally investigated.     

Liquid Entrainment from the Meniscus of a Liquid Wedge by a Moving Horizontal Plate

A hydrodynamic model is proposed for smear formation during the drawing of a film from the meniscus of a limited-volume liquid wedge. It was assumed that the regime of the flow is capillary and the characteristic time of the film formation is small compared to the characteristic time of the change in the meniscus curvature. At small time intervals, the film thickness was determined according to the Landau–Levich–Derjaguin method. At large time intervals, the curvature of the meniscus is described by a linear differential equation for the dynamics of the liquid wedge volume. Under these conditions, the film thickness changes along the plate according to a linear law with the tangent coefficient depending on the capillary number according to a power law, and the profile of the longitudinal section of the smear is close to a right triangle.     

Disjoining pressure measurements using a microfabricated groove for a molecularly thin polymer liquid film on a solid surface

A method for measuring disjoining pressure of a molecularly thin liquid film on a solid surface by using a microfabricated groove has been developed. The shape of the meniscus of a thin film in the microgroove was measured with an atomic force microscope, and the disjoining pressure was obtained from the capillary pressure obtained from the measured curvature of the meniscus. Our method is applicable to a film with a thickness greater than the diameter of gyration in the polymer molecule. Moreover, the method can detect the changes in the disjoining pressure caused by ultraviolet light irradiation, and it is effective in investigating the intermolecular interaction between a thin film and a solid surface.     

Spontaneous pattern formation by dip coating of colloidal suspensions on homogeneous surfaces

We study the slow withdrawal of a partially wet vertical plate at velocity U from a suspension of well-wet particles. Periodic horizontal striped assemblies form spontaneously at the three-phase contact line on energetically uniform surfaces. Stripe width and spacing depend on the withdrawal velocity U relative to a transition velocity Ut. Thick stripes separated by large spaces form for UUt, thin stripes separated by small spaces form. The stripe spacing is reduced by an order of magnitude and varies weakly with U until a maximum velocity is reached at which the stripes fail to form. A partially wet surface can entrain a meniscus. For UUt, we infer that a film of thickness h is entrained above the meniscus. When h is smaller than the particle diameter D, particles aggregate where the entrained film thickens to match up to the wetting meniscus. When an entrained particle becomes exposed to air by evaporation, it becomes the new pinning site from which the next film is entrained. The film thickness h increases with U; at some velocity, h becomes comparable to D. Particles flow into the film and deposit there in a disordered manner. A diagram summarizing particle deposition is developed as a function of D, U, and h.     

Rupture of wetting films caused by nanobubbles

It is now widely accepted that nanometer sized bubbles, attached at a hydrophobic silica surface, can cause rupture of aqueous wetting films due to the so-called nucleation mechanism. But the knowledge of the existence of such nanobubbles does not give an answer to how the subprocesses of this rupture mechanism operate. The aim of this paper is to describe the steps of the rupture process in detail: (1) During drainage of the wetting film, the apex of the largest nanobubble comes to a distance from the wetting film surface, where surface forces are acting. (2) An aqueous "foam film" in nanoscale size is formed between the bubble and the wetting film surface; in this foam film different Derjaguin-Landau-Verwey-Overbeek (DLVO) forces are acting than in the surrounding wetting film. In the investigated system, hydrophobized silica/water/air, all DLVO forces in the wetting film are repulsive, whereas in the foam film the van der Waals force becomes attractive. (3) The surface forces over and around the apex of the nanobubble lead to a deformation of the film surfaces, which causes an additional capillary pressure in the foam film. An analysis of the pressure balance in the system shows that this additional capillary pressure can destabilize the foam film and leads to rupture of the foam film. (4) If the newly formed hole in the wetting film has a sufficient diameter, the whole wetting film is destabilized and the solid becomes dewetted. Experimental data of rupture thickness and lifetime of wetting films of pure electrolyte and surfactant solutions show that the stabilization of the foam film by surfactants has a crucial effect on the stability of the wetting film.     

Dynamic Contact Angles of Water in Ultrathin Capillaries

Velocities of motion V of advancing meniscus of water in quartz capillaries with radii from 45 to 270 nm was directly measured using an optical microscope. In the case, when the meniscus advanced over the wetting film that is remained after the previous meniscus receding, hysteresis was not observed, and the wetting was complete. When the meniscus advanced over the yet unwetted surface, the dynamic contact angle _d greatly depended on V, this dependence was the more pronounced, the smaller the r value. As the velocity V increases to 10^–3 cm s^–1, the value of _d rises to 60°–70° reaching the plateau. Preliminary adsorption of water vapors on the capillary surface markedly decreases the values of _d. The results obtained cannot be explained in terms of hydrodynamic and barrier theories of the contact angle. It was assumed that the controlling factor is the kinetics of vapor adsorption on the capillary surface in front of advancing meniscus.     

Wetting of a particle in a thin film

When a particle is placed in a thin liquid film on a planar substrate, the liquid either climbs or descends the particle surface to satisfy its wetting boundary condition. Analytical solutions for the film shape, the degree of particle immersion, and the downward force exerted by the wetting meniscus on the particle are presented in the limit of small Bond number. When line tension is significant, multiple solutions for the equilibrium meniscus position emerge. When the substrate is unyielding, a dewetting transition is predicted; that is, it is energetically favorable for the particle to rest on top of the film rather than remain immersed in it. If the substrate can bend, the energy to drive this bending is found in the limits of slow or rapid solid deflection. These results are significant in a wide array of disciplines, including controlled delivery of drugs to pulmonary airways, the probing of liquid film/particle interface properties using particles affixed to AFM tips and the positioning of small particles in thin films to create patterned media.     

Kinetics of Gas Bubble Motion in a Capillary

Two flow regimes were discovered by measuring flow rate vof water through thin capillaries containing small gas bubble. The first regime is realized at a low pressure drop P, when the main resistance to flow is created by the wetting film. The estimate of its thickness makes it possible to determine the parameters of the isotherm of the electrostatic component of the disjoining pressure corresponding to the constant charge of the film–gas interface and potential of the quartz surface, which requires the application of a new calculation procedure. As Pincreases, an advancing meniscus forms contact angle of 50°–60° due to the film rupture when it reaches critical pressure in the thinnest part near the meniscus. In this case, the rate vis controlled by the flow in the filled part of a capillary, although some additional viscous drag is also created by the film moving in front of advancing meniscus. The longer the bubble, the greater this contribution.     

Spreading of non-Newtonian liquids over solid substrates

The spreading of drops of a non-Newtonian liquid (Ostwald-de Waele liquid) over horizontal solid substrates is theoretically investigated in the case of complete wetting and small dynamic contact angles. Both gravitational and capillary regimes of spreading are considered. The evolution equation deduced for the shape of the spreading drops has self-similar solutions, which allows obtaining spreading laws for both gravitational and capillary regimes of spreading. In the gravitational regime case of spreading the profile of the spreading drop is provided.     

Study of Salt Effects on the Micelle-Monomer Exchange Process of Octyl-, Decyl-, and Dodecyltrimethylammonium Bromide in Aqueous Solutions by Means of Ultrasonic Relaxation Spectroscopy

Spreading of a tiny macroscopic droplet of a nonvolatile, completely wetting liquid over a flat solid is considered. A liquid in creeping is subjected to capillary forces and long-range molecular forces. The droplet may be surrounded with a precursor wetting film. This paper deals with the problem of determining of the microscopic parameter that influences the interface shape near the apparent line of wetting; this is regarded as the inverse problem in the hydrodynamics of wetting. If the system includes a precursor film, the microscopic parameter coincides with the maximum thickness of the film. A series of inverse equations for the microparameter is obtained, which relate it to, first, the current geometric parameters of the macroscopic drop part and, second, the spreading time. A method for determining how the microparameter depends on the wetting line speed is proposed. The theory expands the opportunity to perform macroscopic measurements and reveals additional parameters. The inverse relations may be used to experimentally study the growth of the maximum thickness of a precursor film during drop spreading. Copyright 2000 Academic Press.     

Surface Tension and Dynamic Contact Angle of Water in Thin Quartz Capillaries

The surface tension of water has been measured in quartz capillaries with radii from 200 down to 40 nm. It appears that the surface tension does not differ from the known (bulk) values in the temperature range from 8 to 70 degrees C, within 1% experimental error. The dynamic contact angle, theta(d), vanishes when the capillary surface is covered with a wetting film left behind the receding meniscus. In the case of a dry surface, theta(d) depends on the velocity of the meniscus motion. The results obtained do not agree with presently available theoretical predictions from hydrodynamic theories of dynamic contact angles. Rather the kinetics of water vapor adsorption ahead of the moving meniscus seems to be the major controlling agent of the dynamic contact angle. Copyright 2000 Academic Press.     

Landau-Levich menisci

As shown by Landau, Levich and Derjaguin, a plate withdrawn out of a wetting bath at low capillary numbers deforms the very top of the liquid reservoir. At this place, a dynamic meniscus forms, whose shape and curvature select the thickness of the film entrained by the plate. In this paper, we measure accurately the thickness of the entrained film by reflectometry, and characterize the dynamic meniscus, which is found to decay exponentially towards the film. We show how this shape is modified when reversing the motion: as a plate penetrates the bath, the dynamic meniscus can "buckle" and present a stationary wavy profile, which we discuss.     

Universal Two-dimensional forces that Act on Particles at interfaces

This paper starts with a short tribute to the scientific legacy of Peter Kralchevsky and his role in the collaboration with the research group of Kuniaki Nagayama in Japan. Next it presents an overview of the lateral capillary forces, studied jointly by both authors and their groups. Analogies with some other forces in nature are highlighted where relevant. The lateral capillary forces emerge between objects dispersed at a liquid interface or in liquid film and act in direction parallel to the liquid interface, being caused by the liquid surface tension. The lateral capillary forces depend on the size of the objects and the wetting of the particle by the liquid and can be either attractive or repulsive. For fine particles the force–distance relationship follows an inverse-linear law. Their effect is seen in our everyday experience that dust particles and bubbles tend to aggregate on the water surface. These forces are universally acting between any objects regardless of scale and are described by equations similar to those describing the gravitational and electric forces in the two-dimensional (2D) world. The current KN & PK review article provides a didactic overview that is easy to digest as a 2D model of gravity in general relativity, because the origin of the latter force, namely the space distortion, can be clearly visualized.     

Fabrication of gradient colloidal topography

A rather simple but yet effective way to self-assemble polystyrene (PS) beads in gradient colloidal crystal topography is proposed. The PS bead concentration, solvent, and substrate have a big effect on the colloidal crystal topography. Whether the gradient-shaped crystals can form or not depends on the Bond number [Bo; the ratio of gravitational potential energy (G) to adhesive energy (E(a)), or gravitational to capillary forces]. When Bo < 1, that is, the capillary force dominates over the gravitational force, the liquid meniscus is stable. The gradient-shaped crystals can form. Otherwise, PS beads form a uniform multilayer structure.     

Shape of the capillary meniscus around an electrically charged particle at a fluid interface: comparison of theory and experiment

Here, we consider in detail the problem of the shape of the capillary meniscus around a charged colloidal particle, which is attached to a fluid interface: oil/water or air/water. The meniscus profile is influenced by the electric field created by charges at the particle/nonpolar fluid boundary. We digitized the coordinates of points from the meniscus around silanized glass spheres (200-300 mum in radius) attached to the tetradecane/water interface. The theoretical meniscus shape is computed in three different ways that give numerically coincident results. It is proven that for sufficiently small particles the meniscus profile can be expressed as a superposition of pure electric and gravitational deformations. Special attention is paid to the comparison of theory and experiment. A procedure for data processing is developed that allows one to obtain accurate values of the contact angle and surface charge density from the fit of the experimental meniscus profile. For all investigated particles, excellent agreement between theory and experiment is achieved. The results indicate that the electric field gives rise to an interfacial deformation of medium range and considerable amplitude.     

Spreading dynamics and dynamic contact angle of non-Newtonian fluids

The spreading dynamics of power-law fluids, both shear-thinning and shear-thickening fluids, that completely or partially wet solid substrate was investigated theoretically and experimentally. An evolution equation for liquid-film thickness was derived using a lubrication approximation, from which the dynamic contact angle versus the contact line moving velocity relationship was evaluated. In the capillary spreading regime, film thickness h is proportional to xi3/(n+2) (xi is the distance from the contact line), whereas in the gravitational regime, h is proportional to xi1/(n+2), relating to the rheological power exponent n. The derived model fit the experimental data well for a shear-thinning fluid (0.2% w/w xanthan solution) or a shear-thickening fluid (7.5% w/w 10 nm silica in polypropylene glycol) on a completely wetted substrate. The derived model was extended using Hoffmann's proposal for partially wetting fluids. Good agreement was also attained between model predictions and the shear-thinning fluid (1% w/w cmc solution) and shear-thickening fluid (10% w/w 15 nm silica) on partially wetted surfaces.     

Wetting Film Dynamics

The spreading of a tiny macroscopic drop of a nonvolatile, completely wetting liquid over a flat solid is considered, assuming no gravitation. A liquid, in creeping, is subjected to capillary forces and van der Waals forces. This nonstationary and nonlinear problem in the dynamics of the wetting film from a droplet is studied using numerical modeling. The precursor wetting film motion is described by an evolution equation with conditions at the moving boundaries. The wetting line is regarded as an unknown boundary to be determined in the course of solution. A simplified equation for the wetting line dynamics is analyzed. The difference between the wetting line radius and a fixed (nonzero) radius is described by a diffusion time law. Results of numerical experiments show the simplified law of wetting to be valid over a wide range of spreading times (or a wide range of radii of the wetting line). Copyright 2000 Academic Press.