Effect of dynamic contact angle on capillary rise phenomena

Capillary rise experiments of different liquids in glass capillaries and in columns of packed powders were carried out. The analysis of this rise was performed according to the classical Washburn’s equation in which the calculation of a constant term is needed in order to be able to determine contact angle of the considered liquid on the capillary wall or powders. However, it was observed that this constant term apparently varies as a function of the liquid used, in contradiction with Washburn’s approach. A more fundamental study of alkane rise into glass capillaries was carried out showing that this apparent variation is due to the variation of contact angles, which can take large values (up to 60°) as a function of velocity of the liquid front, although their expected value is 0°. Therefore, in the case of powders, different approaches to determine the real constant term with respect to particle size are proposed. Consequently, the use of Washburn’s equation for the determination of contact angles of liquids on these powders is also discussed.     

Filling kinetics of liquids in nanochannels as narrow as 27 nm by capillary force

We report the filling kinetics of different liquids in nanofabricated capillaries with rectangular cross-section by capillary force. Three sets of channels with different geometry were employed for the experiments. The smallest dimension of the channel cross-section was respectively 27, 50, and 73 nm. Ethanol, isopropanol, water and binary mixtures of ethanol and water spontaneously filled nanochannels with inner walls exposing silanol groups. For all the liquids the position of the moving liquid meniscus was observed to be proportional to the square root of time, which is in accordance with the classical Washburn kinetics. The velocity of the meniscus decreased both with the dimension of the channel and the ratio between the surface tension and the viscosity. In the case of water, air-bubbles were spontaneously trapped as channels were filled. For a binary mixture of 40% ethanol and water, no trapping of air was observed anymore. The filling rate was higher than expected, which also corresponds to the dynamic contact angle for the mixture being lower than that of pure ethanol. Nanochannels and porous materials share many physicochemical properties, e.g., the comparable pores size and extremely high surface to volume ratio. These similarities suggest that our nanochannels could be used as an idealized model to study mass transport mechanisms in systems where surface phenomena dominate.     

Dissolutive Capillary Penetration with Expanding Pores and Transient Contact Angles

The penetration kinetics of a cylindrical capillary and a capillary porous body with a temporally expanding capillary radius due to reactive dissolution ahead of the liquid front is modeled under conditions where the equilibrium contact angle is not attained during at least part of the penetration process. These effects cause deviations from the predictions of the Washburn equation, with the actual penetration kinetics depending upon the rate processes involved. Copyright 2000 Academic Press.     

A model of environmental craze growth in polymers

A model of environmental craze growth has been developed based on the customary meniscus (or Rayleigh-Taylor) instability model of craze propagation but allowing for the possibility that environmental plasticization may cause the active layer of material adjacent to the craze to be of significant thickness with respect to the fibril spacing. Initially, as the active layer thickness increases, the fibril growth rate increases at constant fibril spacing, but eventually the fibril spacing comes to be controlled only by the active layer thickness and not by the surface tension and stress. This model of craze growth has been coupled to a model of stress-enhanced case II diffusion that is itself based on the Thomas-Windle model. Two main regimes of craze thickness growth are distinguished. In one the craze growth rate is controlled by the velocity of the diffusion front, the meniscus instability growth rate is assumed to be relatively slow, so that a significant plasticized active layer exists whose thickness assures that the meniscus instability front travels at the same speed as the diffusion front. In the other regime the propagation of the craze front is sufficiently fast that it also forms the diffusion front, so the growth rate is controlled by a combination of the two processes: diffusion and meniscus instability.     

Prediction of coupled menisci shapes by Young-Laplace equation and the resultant variability in capillary retention

This paper shows how 2 coupled Young-Laplace equations can be solved to predict the shapes of two coupled menisci formed in a capillary system. Experiments are performed, which demonstrate that the equilibrium volume of liquid retained in a vertical capillary, can be variable, even when all the properties of the system are invariant. This variability in liquid retention also leads to different equilibrium shapes of the top and bottom menisci. A coupled form of the Young-Laplace equation is solved to predict the two coupled menisci shapes. The curvature of the top meniscus is fitted to the experimentally recorded meniscus shape. The coupled Young-Laplace equation solution is used to predict the shape of the bottom meniscus. The shape of the bottom meniscus thus obtained, is shown to match the experimentally recorded bottom meniscus shape reasonably well. This observed coupling of the menisci has a significant impact on some porosimetric techniques which are based on liquid extrusion and explains why the volume of liquid that can be retained in a capillary can vary, under invariant conditions. Retention of liquids in capillaries is of interest in several applications like fabric wash.     

Capillary rise of a meniscus with phase change

The Lucas-Washburn equation, describing the motion of a liquid body in a capillary tube, is extended to account for the effect of phase change - evaporation or condensation. The system is found to always possess a stable equilibrium state when the temperature jump across the interface is confined to a certain range. We show that phase change affects the equilibrium height of the meniscus, the transition threshold from monotonic to oscillatory dynamics, and the frequency of oscillations, when present. At higher mass transfer rates and/or large capillary radii, vapor recoil is found to be the dominant factor. Evaporation lowers the equilibrium height, increases the oscillation frequency and lowers the transition threshold to oscillations. For condensation, two regimes are identified: at high mass transfer rates similar trends to those of evaporation are observed, whereas the opposite is found for low mass transfer rates, resulting in an increased equilibrium height, lower oscillation frequencies and a shift of the transition threshold toward monotonic dynamics.     

Turbulent fronts in resonantly forced oscillatory systems

Phase fronts in the forced complex Ginzburg-Landau equation, a model of a resonantly forced oscillatory reaction-diffusion system, are studied in the 3:1 resonance regime. The focus is on the turbulent (Benjamin-Feir-unstable) regime of the corresponding unforced system; in the forced system, phase fronts between spatially uniform phase-locked states exhibit complex dynamics. In one dimension, for strong forcing, phase fronts move with constant velocity. As the forcing intensity is lowered there is a bifurcation to oscillatory motion, followed by a bifurcation to a regime in which fronts multiply via the nucleation of domains of the third homogeneous phase in the front. In two dimensional systems, rough fronts with turbulent, complex internal structure may arise. For a critical value of the forcing intensity there is a nonequilibrium phase transition in which the turbulent interface grows to occupy the entire system. The phenomena we explore can be probed by experiments on periodically forced light sensitive reaction-diffusion systems.     

Simultaneous imbibition-heat convection process in a non-Darcian porous medium

In the present work, the nonisothermal imbibition process in a porous medium was numerically analyzed using a non-Darcian model for the momentum equation and energy equations for the wetting and dry zones. In order to show the thermal character of the problem, we assume initially that the porous medium is found at a uniform temperature T0 and suddenly begins the imbibition process into the porous medium with a penetrating fluid at temperature T1. The physical influence of nondimensional parameters such as Peclet number, Pe, effective heat capacity number, beta(w), porous Reynolds number, Re(p), and the inertial coefficient of the porous medium, F, serve us to evaluate the position and velocity of the imbibition front as well as temperature profiles in both zones. In particular, for values of Re(p)F/beta(w)>1, we recover a type of nonisothermal Washburn law. The numerical predictions show that the imbibition front and the temperature fields strongly depend on the above nondimensional parameters, revealing a clear deviation of the simple Washburn law.     

Compressibility effects in packed and open tubular gas and supercritical fluid chromatography

The influence of the pressure drop on the efficiency and speed of analysis in packed and open tubular supercritical fluid chromatography (SFC) is described: methods previously developed to describe the effects of mobile phase compressibility on the performance of open tubular columns in SFC have been extended to packed columns. The Horvath and Lin equation has been used to elucidate the influence of variations in velocity, diffusivity, and capacity factor along the column on the overall efficiency of packed column SFC. In packed columns, in contrast with the situation in open tubular columns, because the increase in velocity is no longer compensated by an increase in diffusion coefficients, the increase in both linear velocity and capacity factor which result from a significant pressure drop cause the plate height to increase along the column. The effect of fluid decompression along the length of the column on the speed of analysis in SFC has been studied and numerical expressions derived which enable calculation of compressibility correction factors for the plate height. Both the f₁ and f₂ correction factors remain very close to unity for acceptable pressure drops, which means that the pressure drop has virtually no effect on the number of plates generated per unit time for an unretained component. For retained species, the decompression of the mobile phase across the column causes the capacity factor to increase and hence leads to increased analysis times.     

Shape of menisci in terrestrial dewetted Bridgman growth

Dewetted Bridgman is a crystal growth technique in which the crystal is detached from the crucible wall by a liquid free surface at the level of the solid-liquid interface, called liquid meniscus, which creates a gap between the crystal and the ampoule. Dewetting phenomenon was first obtained spontaneously in spatial experiments during the Bridgman solidification, and opened the possibility of reproducing experiments on the earth--obtained by applying a gas pressure difference Delta P=P cold-P hot between the cold and the hot sides of the sample. In order to understand the process which leads to a crystal with a constant radius on the ground, analytical and numerical studies of axisymmetric meniscus shapes are made and the dependence of the meniscus shape on the pressure difference is established. For this aim, starting from the Young-Laplace equation of a capillary surface in equilibrium in the presence of gas pressure, a mathematical model able to describe the meniscus surface z=z(r) and the angle theta=theta(r) between the tangent to the meniscus and the horizontal axis is presented. On the basis of this model, inequalities of the pressure intervals for which dewetting is feasible are established. Numerical results are performed for InSb crystals.     

Critical temperature measurements of liquids by means of differential thermal analysis

When studying crytalline substances and liquids in sealed off glass ampoules by differential thermal analysis the melting ranges but not the heat of evaporation of the liquids and fused substances are found, because inside the glass ampoule, there will always be the vapour pressure equillibrium which corresponds to the temperature. With liquids undergoing decomposition, it is possible to measure the range and heat of decomposition. Given a suitable quantity inside the ampoule the critical temperature, e.g., of water of ethanol can be measured for non-decomposing liquids. The measuring effect is based on the pronounced change of the liquid's specific heat at the critical temperature.Fundamental studies of the measurement of critical temperatures of liquids were carried out by the turn of the century. One the methods reported is the meniscus method, optimal measurement of the critical temperature, which comprises a liquid being filled into a glass tube which is then sealed by melting. The glass tube is heated while observing the meniscus. Its rise means that the critical volume has been exceeded, while a drop means that it has not yet been reached. The conditions are only met when that volume of liquid has been filled into the tube at which the meniscus neither rises nor falls on heating but rather remains, e.g. at mid level of the tube until it disappears. The tube contains the critical volume at the critical density when the critical temperature is reached. The critical pressure is then present. These conditions are obtained when the meniscus disappears and the liquid completely goes over into the vapour phase.The melting range (and the latent heat of fusion) are found when investigating a crystalline material under normal pressure by differential thermal analysis. Given a suitable arrangement the boiling temperature and, in rough approximation, the heat of evaporation are also found (Fig.1). The latent heat of fusion is found again when carrying out the same measurement in a closed system (glass tube sealed by melting). The heat of evaporation can no longer be measured since the vapour pressure equilibrium coresponding to the given temperature is present in the glass tube.     

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.     

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.     

Experimental investigation of contact angle, curvature, and contact line motion in dropwise condensation and evaporation

Image-analyzing interferometry is used to measure the apparent contact angle and the curvature of a drop and a meniscus during condensation and evaporation processes in a constrained vapor bubble (CVB) cell. The apparent contact angle is found to be a function of the interfacial mass flux. The interfacial velocity for the drop during condensation and evaporation is a function of the apparent contact angle and the rate of change of radius of curvature. The dependence of velocity on the apparent contact angle is consistent with Tanner's scaling equation. The results support the hypothesis that evaporation/condensation is an important factor in contact line motion. The main purpose of this article is to present the experimental technique and the data. The equilibrium contact angle for the drop is found experimentally to be higher than that for the corner meniscus. The contact angle is a function of the stress field in the fluid. The equilibrium contact angle is related to the thickness of the thin adsorbed film in the microscopic region and depends on the characteristics of the microscopic region. The excess interfacial free energy and temperature jump were used to calculate the equilibrium thickness of the thin adsorbed film in the microscopic region.     

Free release static coating of glass capillary columns; rapid coating at lower temperatures and elevated pressures

The coating speed upon static coating of glass capillary columans was evaluated in terms of inner diameter and length of the column, viscosity and pressure of solvent vapor, etc. From the equation obtained it can be shown that a smaller diameter of a microbore column restricts solvent vapor transfer to the orifice of the column drastically. To compensate for this restriction, a higher pressure at the meniscus is needed. As an alternative to using a higher coating temperature, application of more volatile solvents such as n-butane and isobutane is proposed. Several glass capillary columns (130 μm i.d.) were coated with SE-54 dissolved inpentane-acetone mixed with n-butane or isobutane and the column performances were evaluated. Selection of these solvents permitted free release static coating of ca. 100 μm columns at lower or even ambient temperatures and they were equally suitable as commonly applied solvents (e.g. pentane) to coat highly efficient columns.     

Co-current and counter-current imbibition in independent tubes of non-axisymmetric geometry

Experiments that illustrate and quantify the basics of co- and counter-current spontaneous imbibition have been conducted in a series of simple model pore systems. The fundamental pore geometry is a rod in an angled round-bottomed slot with the rod touching a capping glass plate. The capillaries thus formed by the surfaces of the slot, rod and plate do not have circular cross-sections but more complicated geometric structures with angular corners. The tubes formed at each side of the rod connect at both ends. A viscous, refined oil was applied from one end. For co-current experiments, the opposite end was left open to the atmosphere and oil imbibed into both tubes. For counter-current experiments the opposite end was sealed and connected to a sensitive pressure transducer. Oil imbibed into the smaller capillary and expelled air as a series of bubbles from the end of the larger capillary. Bubble snap-off was observed to be rate-dependent and occurred at a lower curvature than that of the cylindrical meniscus that just fits inside the tube. Only the corners of the larger capillary filled with oil during counter-current imbibition. Meniscus curvatures were calculated using the Mayer and Stowe-Princen method and were compared with actual values by measuring the capillary rise in the tubes; agreement was close. A simple model for co-current and counter-current imbibition has also been developed and the predictions compared with the experimental results. The model results were in agreement with the experiments. The experiments demonstrate that the capillary back pressure generated by the interfaces and bubbles in counter-current imbibition can slow the process significantly.     

Contact Angle Determined by Spontaneous Imbibition in Porous Media: Experiment and Theory

In this paper, a theoretical model was established to determine the contact angle by introducing a new defined effective capillary radius into the Lucas–Washburn equation. Based on the theoretical model, capillary rise experiments of water imbibed by different glass beads were carried out to measure the contact angle; the results were similar to the available data published in the literature. In addition, the model was modified to take account of the dynamic contact angle, according to the experimental data. The influence of the dynamic contact angle on the movement of the spontaneous imbibition was studied.     

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.     

The meniscus on a fibre

We describe the capillary rise along a vertical thin fibre. We first recall what the final height of the meniscus is, and give some predictions about the dynamics of the rise. Then we present an experiment, in a situation of complete wetting: a fibre is brought into contact with a reservoir of silicone oil, and the dynamic contact angle is measured, from 90° (just at the contact) to 0° (the equilibrium position). Most of the rising time is spent in a long regime of relaxation towards equilibrium, where θ(t) varies as 1/√t. A characteristic time τ is also measured, and studied as a function of the liquid viscosity.