Fine Structure of Meniscus of a Wetting Liquid

Equilibrium of a capillary meniscus near a wetting film on a solid in a gravitational field is considered. Unlike previous studies, the present study proves that the fine meniscus structure in a gravitational field is a universal feature—it takes place in a wide variety of problems. In the general case, the capillary meniscus is at a certain distance from the wetting film and does not intersect it. The relation for the minimum distance from the arbitrary meniscus to the solid generalizes the Derjaguin formula for a flat slit. An equation that optimally approximates the meniscus with due account of the contribution of the meniscus/film transition region is derived. A refined solution to the problem of a meniscus on a vertical plate is derived within the perturbation theory. Both gravity and nonuniformity of the vertical static film above a capillary–gravitational meniscus do not affect the minimum distance (the influence is less than 0.0001). A general method for solving sophisticated problems of capillary equilibrium in gravitational field is proposed.     

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As shown by Landau, Levich and Derjaguin, a plate withdrawn out of a wetting bath at low capillary numbers deforms the very top of the liquid reservoir.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.     

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.     

Additivity of the dynamic curvature of a thermocapillary depression and static curvature of a wetting meniscus

A thermocapillary depression is induced by a laser beam in a layer of a transparent liquid on an absorbing substrate. Two plane-parallel wettable plates are immersed in the liquid in symmetrical positions with respect to the point of incidence of the beam on the liquid. The diameters of the thermocapillary response formed by the laser beam on a screen are studied in their dependence on the curvature of the equilibrium liquid meniscus formed between the plates. The property of additivity is experimentally proved; according to this property, the curvature of the free liquid surface is equal to the algebraic sum of the static curvature of the wetting meniscus and the dynamic curvature of the thermocapillary depression.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 2, 2005, pp. 259–267.Original Russian Text Copyright © 2005 by Tarasov.     

Experimental investigation of evaporation and condensation in the contact line region of a thin liquid film experiencing small thermal perturbations

Image-analyzing interferometry technique is successfully used to study microscale transport processes related to a curved microfilm on a solid substrate. Digital image processing is used to analyze the images of interference fringes, leading to the evaluation of liquid (heptane) film thickness and curvature profiles at different inclinations on a high refractive index glass surface. The curvature profiles obtained at different inclinations clearly demonstrate that there is a maximum in curvature near the junction of the adsorbed film (of uniform thickness) and the curved film, and then it becomes constant in the thicker portions of the film. The adsorbed film thickness is measured for horizontal as well as inclined positions. Experimentally obtained values of the dispersion constants are compared to those predicted from the Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) theory, and reasonable agreements were obtained. A parameter alpha is defined and experimentally evaluated to quantify the closeness of the system to equilibrium. The nonequilibrium behavior of this parameter alpha is also observed with certain heat input at a particular inclination. A small thermal perturbation is used to force the liquid meniscus to undergo a cycle of alternating condensation and evaporation. High-speed video-microscopy and subsequent image analysis are used for data analysis. The numerical solution of a model that takes into account the balance between the suction and the capillary force is compared with the data to elicit new insights into the evaporation/condensation phenomena and to estimate the interfacial temperature differences for near-equilibrium situations.     

Spontaneous Liquid/Liquid Displacement in a Capillary

When a two-phase column consisting of paraffin oil and silicon oil is placed in an otherwise air-filled, horizontal glass capillary, the column starts moving spontaneously. Silicon oil displaces paraffin oil, which in its turn displaces air at atmospheric conditions; a stable film of silicon oil is left at the receding silicon oil/air meniscus. The driving force for the motion is the difference in capillary pressure at the free interfaces. However, the column moves considerably more slowly than predicted by the driving forces; it appears that the forces resisting the motion at the moving liquid/liquid/solid line are much larger than one would expect on the basis of the interfacial tension and the viscosities of the two phase system. Some considerations are made on the relationship of the theory of Fowkes to our system. Also, a method for measuring low interfacial tensions between immiscible liquids is proposed.     

Capillary force required to detach micron-sized particles from solid surfaces—Validation with bubbles circulating in water and 2 μm-diameter latex spheres

The adhesion forces holding micron-sized particles to solid surfaces can be studied through the detachment forces developed by the transit of an air–liquid interface in a capillary. Two key variables affect the direction and magnitude of the capillary detachment force: (i) the thickness of the liquid film between the bubble and the capillary walls, and (ii) the effective angle of the triple phase contact between the particles and the interface. Variations in film thickness were calculated using a two-phase flow model. Film thickness was used to determine the time-variation of the capillary force during transit of the bubble. The curve for particle detachment was predicted from the calculated force. This curve proved to be non-linear and gave in situ information on the effective contact angle developing at the particle–bubble interface during detachment. This approach allowed an accurate determination of the detachment force. This theoretical approach was validated using latex particles 2 μm in diameter.     

Modified Tilting-Plate Method for Measuring Contact Angles

The additivity of the dynamic curvature of a thermocapillary depression and the static curvature of liquid meniscus is experimentally confirmed. A high sensitivity of response shape to the static curvature of liquid surface is used to improve the tilting-plate method. The results of measuring contact angles by this method are well consistent with the data obtained by the sessile drop method. The behavior of meniscus is analyzed in the tilting of a plate with various positioning of its rotation axis in relation to the liquid–gas interface. The applicability limits of the modified method are indicated.     

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.     

Electric field enhanced spreading of partially wetting thin liquid films

Equilibrium and dynamic electrowetting behavior of ultrathin liquid films of surfactant (SDS) laden water over silicon substrate (with native oxide) is investigated. A nonobtrusive optical method, namely, image analyzing interferometry, is used to measure the meniscus profile, adsorbed film thickness, and the curvature of the capillary meniscus. Significant advancement of the contact line of the liquid meniscus, as a result of the application of electric field, is observed even at relatively lower values of applied voltages. The results clearly demonstrate the balance of intermolecular and surface forces with additional contribution from Maxwell stress at the interline. The singular nature of Maxwell stress is exploited in this analysis to model the equilibrium meniscus profile using the augmented Young-Laplace equation, leading to the in situ evaluation of the dispersion constant. The electrowetting dynamics has been explored by measuring the velocity of the advancing interline. The interplay of different forces at the interface is modeled using a control volume approach, leading to an expression for the interline velocity. The model-predicted interline velocities are successfully compared with the experimentally measured velocities. Beyond a critical voltage, contact line instability resulting in emission of droplets from the curved meniscus has been observed.     

Surface Tension of a Liquid under the Conditions of a Fast Surface Renewal during Evaporation

A new capillary method of measuring surface tension under the conditions of a fast surface renewal due to evaporation is considered. At the highest rates reached for n-pentane and water evaporation (0.6 and 0.14 kg m^–2 s^–1, respectively), the deviations of from its equilibrium values may be explained by a change in the meniscus shape under the conditions of intense heat exchange.     

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.     

On the thermodynamic theory of the strength of solids: 4. Capillary condensation and capillary evaporation in wedge-shaped crack

The processes of capillary condensation and capillary evaporation in a wedge-shaped crack are considered. Capillary evaporation is a comparatively new phenomenon that is opposite to capillary condensation and occurs upon the cleavage of a solid in a nonwetting liquid. For both cases, the positions of a meniscus inside a wedge-shaped crack have been calculated as functions of the meniscus curvature radius, liquid-contact angle, and crack-opening angle. The effect of temperature on the meniscus position has been analyzed; it has been established that the meniscus shifts from the gaseous toward the liquid phase as temperature rises. The regularities of meniscus displacements in the course of crack growth have been established: under the conformal mechanism of crack growth, the absolute position of the meniscus remains unchanged (i.e., the meniscus and the crack frontal line move at the same velocity), while, under the depth mechanism of growth, the relative position of the meniscus is retained.     

Performance of open tubular columns as a function of tube diameter and liquid phase film thickness

Summary Wall-coated, open-tubular (capillary) columns prepared from different diameter tubing, with different liquid phase film thickness, are compared with each other and with packed and support-coated open-tubular columns. The comparison is based on the variation of the phase ratio and the capacity factor, and includes column efficiency (HETP, theoretical plate number), resolution, retention time, and sample capacity. Problems associated with the evaluation of the sample capacity are outlined. The influence of temperature on column performance is discussed in detail. Finally, the possibilities of short, wide-bore open-tubular columns prepared with a thick liquid-phase film are demonstrated.Parts of this paper were presented at the 35th Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlantic City NJ, March 5–9, 1984, and at the 20th International Symposium on Advances in Chromatography, New York NY, April 16–18, 1984.     

Free-standing films of twist grain boundary TGBA and UTGBC* liquid crystals studied by fluorescence confocal polarizing microscopy

The director structures, meniscus profile, and defects in free-standing films of the twist grain boundary TGB_A and UTGB_C* liquid crystals were studied. The films were characterized by a combination of polarizing microscopy and fluorescence confocal polarizing microscopy. Five principal regions of meniscus were distinguished. When film thickness in the meniscus is much smaller then the TGB pitch, there is no difference between the free-standing films of TGB and ordinary smectic A liquid crystals. When the film thickness is larger than the TGB pitch, filamentary texture is observed. The 3D director pattern of the filaments are similar to the ground state director fields of TGB_A and UTGB_C* liquid crystals. In the intermediate thickness region of the meniscus, when the film thickness and TGB pitch are commensurate, a unique radial pattern is observed. Based on the fluorescence confocal polarizing microscopy studies of the director field, we propose a model for the 3D director structure in this part of the meniscus.     

Discontinuous meniscus location in tapered capillaries driven by pressure difference and dielectrophoretic forces

We calculate the meniscus location in tapered capillaries under the influence of pressure difference and dielectrophoretic forces with and without gravity. We find that the meniscus location can be a discontinuous function of the pressure difference or the applied voltage and that the meniscus can "jump" to one end or another of the capillary. Phase diagrams are given as a function of the pressure and voltage, depending on the geometrical parameters of the system. We further consider a revision of the dielectric rise under dielectrophoretic force in wedge capillaries and in the case of electrowetting, where the dielectrophoretic force is a small perturbation. Finally, we also find discontinuous liquid-gas interface location in the case of liquid penetration into closed volumes.     

Dewetting of a sol-gel-derived thin film

We report on the dewetting of a thin film produced by the sol-gel method. In the early stages of dynamic morphological instability, the drying stress in the capillary wave model determines the linearly scaling behaviors of the characteristic wavelength with the initial film thickness and the square law dependence of the number density of the dewetted holes on the film thickness. These power law dependences are weaker than those observed in the case of the spinodal dewetting of a polymer thin film. The wavelength determined in the early stages also dominates the scaling behaviors of the average length of the sides and number density of the polygons and the diameter of the droplets of the dewetting pattern with the film thickness in the final stages of the dynamic instability. We also observed that further drying eventually induces wrinkles in the droplets, rim, and film, which have a characteristic wavelength that can be theoretically predicted.     

Hydrodynamic interaction between spheres coated with deformable thin liquid films

In this article, we considered the hydrodynamic interaction between two unequal spheres coated with thin deformable liquids in the asymptotic lubrication regime. This problem is a prototype model for drop coalescence through the so-called "film drainage" mechanism, in which the hydrodynamic contribution comes dominantly from the lubrication region apart from the van der Waals interaction force. First, a general formulation was derived for two unequal coated spheres that experienced a head-to-head collision at a very close proximity. The resulting set of the evolution equations for the deforming film shapes and stress distributions was solved numerically. The film shapes and hydrodynamic interaction forces were determined as functions of the separation distance, film thickness, viscosity ratios, and capillary numbers. The results show that as the two spheres approach each other, the films begin to flatten and eventually to form negative curvature (or a broad dimple) at their forehead areas in which high lubrication pressure is formed. The dimple formation occurs earlier as the capillary number increases. For large capillary numbers, the film liquids are drained out from their forehead areas and the coated liquid films rupture before the two films "touch" each other. Meanwhile, for small capillary numbers, the gap liquid is drained out first and the two liquid films eventually coalesce.