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.     

On the derivation of Young's equation for sessile drops: nonequilibrium effects due to evaporation

Sessile liquid drops have a higher vapor pressure than planar liquid surfaces, as quantified by Kelvin's equation. In classical derivations of Young's equation, this fact is often not taken into account. For an open system, a sessile liquid drop is never in thermodynamic equilibrium and will eventually evaporate. Practically, for macroscopic drops the time of evaporation is so long that nonequilibrium effects are negligible. For microscopic drops evaporation cannot be neglected. When a liquid is confined to a closed system, real equilibrium can be established. Experiments on the evaporation of water drops confirm the calculations.     

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.     

Discontinuous liquid rise in capillaries with varying cross-sections

We consider theoretically liquid rise against gravity in capillaries with height-dependent cross-sections. For a conical capillary made from a hydrophobic surface and dipped in a liquid reservoir, the equilibrium liquid height depends on the cone-opening angle alpha, the Young-Dupré contact angle theta, the cone radius at the reservoir's level R(0), and the capillary length kappa(-)(1). As alpha is increased from zero, the meniscus' position changes continuously until, when alpha attains a critical value, the meniscus jumps to the bottom of the capillary. For hydrophilic surfaces the meniscus jumps to the top. The same liquid height discontinuity can be achieved with electrowetting with no mechanical motion. Essentially the same behavior is found for two tilted surfaces. We further consider capillaries with periodic radius modulations and find that there are few competing minima for the meniscus location. A transition from one to another can be performed by the use of electrowetting. Finite pressure difference between the two sides of the liquids can be incorporated as well, resulting in complicated phase-diagrams in the alpha-theta plane. The phenomenon discussed here may find uses in microfluidic applications requiring the transport small amounts of water "quanta" (volume < 1 nL) in a regular fashion.     

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.     

Influence of cyclohexane vapor on stick-slip friction between mica surfaces

Stick-slip friction between mica surfaces under cyclohexane vapor has been investigated with the Surface Force Apparatus. The dynamic shear stress decreased from 60 to 10 MPa with increasing relative vapor pressure (rvp) from 5% to 50%. Between a rvp of 50% and 80%, the shear stress remained at approximately 10 MPa, with a slight decrease on increasing the rvp. At a rvp greater than 80%, the values of shear stress were below 5 MPa. The stick-slip behavior was observed in the rvp range of 20% to saturation. When the rvp reached 20%, stick-slip appeared but faded out with sliding time. At a rvp greater than 50%, the stick-slip pattern was stable without fading. By taking into account the size of the meniscus formed by capillary condensation of the liquid around the contact area and the Laplace pressure, the dependence of shear stress and the stick-slip modulation on rvp suggests that the origin of the stick-slip observed in cyclohexane vapor is as follows: At a rvp greater than 50%, where stable sick-slip is observed, the stick-slip caused by the cyclohexane layering in the contact area is of essentially the same origin as that observed with mica surfaces sliding in bulk cyclohexane liquid. As with the bulk liquid experiment, decreasing the layer thickness (or the number of the layers) between the surfaces increases the shear stress at the onset of slip. In the vapor phase experiments, the stick-slip is enhanced by the increase of the negative Laplace pressure in the capillary condensed liquid, thereby forcing the surfaces toward each other more strongly with decreasing rvp. In the rvp range between 20% and 50%, where the fading stick-slip is observed, the condensate liquid seeps into the contact area under the influence of the applied tangential force and thus triggers the slip motion. Due to the small condensation volume, the liquid condensed around the contact area is exhausted in the process of repeating stick-slip. As the slip length is limited to the meniscus size, the stick-slip amplitude becomes smaller, and eventually the surfaces start sliding without stick-slip.     

A stochastic model in liquid penetration through fibrous media

The statistical genesis of the process of liquid penetration through fibrous media can be regarded as the interaction and the resulting balance among media and liquid cells that comprise the ensemble. A stochastic method, Ising's model, combined with Monte Carlo simulation, can therefore be employed in the study of liquid penetration through fibrous media. This process is driven by the difference of energy of the system after and before a liquid moves from one cell to the other. The energy of the system comprises the internal energy, work done by external force to the system, and the mechanical energy. For experimental verification, the process of water penetration through isotropic fiber mats, both spontaneously and under pressure, is examined. Simulation results are in good agreement with the experiments, indicating a good prospect of the method to be applied in this area.     

Stability and disturbance of coating films

In the studies of two-roll metering and application systems, two types of disturbances were observed. These were termed “ring type” and “irregular” disturbances. This research established that the physical reason for the appearance of the ring type instability is the competition between surface tension and centrifugal forces at the liquid-air interface. The rings are generated at the surface of the dynamic liquid meniscus, in the gap between the rolls, because of the very large centrifugal forces there. Considering conditions of a constant interfacial pressure difference (pressure jump), one can reduce the problem to one with only one free parameter, viz., the radius of the meniscus, and calculate the wavelength of the disturbances. There is no single formula which will adequately describe the dynamic meniscus. Its curvature depends on the rheological properties of the fluid and on the kinematic conditions in the process. Dimensional analysis is combined with experimental findings to yield a formula for the radius of the meniscus for fluids having a high yield stress for the case of two counter-rotating rolls.The rheological behavior of a flowing starch adhesive in the dynamical meniscus is analyzed. The theoretical and experimental studies show that systems using two counter-rotating rolls practically always produced ring-type instabilities with all types of fluids.The picture is more complex for co-rotating roll systems. When non-Newtonian adhesives are used, ring type disturbances are observed in one zone of roll speed ratios, and irregular disturbances are observed in another zone. The two zones are separated by a speed ratio zone (a “speed window”) where a more or less perfectly stable fluid layer is observed. When Newtonian oils are used, there are two such speed windows. The first one corresponds to very low metering roll speeds and a minimum of liquid transfer to the applicator roll. The second stable zone occurs at high metering roll speeds and yields a maximum of liquid transfer. The physical reason for the high transfer rate in the high speed “window” is considered and shown to be the thin air layer following the surface of the metering roll. The air pumped into the metering gap returns along the applicator roll and accelerates the film on the applicator roll in the process. Under these conditions the fluid-air interface may become unstable, leading to the “irregular” type of disturbance.     

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.     

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.     

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.     

Correction of flotation coefficients,derived from ultracentrifugation,for pressure and concentration

Flotation coefficients are usually determined from data obtained under high pressure (cell bottom) conditions. A power series expansion is proposed for correction to atmospheric pressure (meniscus) conditions. The same expansion may be applied to the concentration correction of flotation coefficients.     

Pressure induced transition between superhydrophobic states: configuration diagrams and effect of surface feature size

The stability of wetting states, namely the Cassie state (partial wetting) and the Wenzel state (complete wetting) of surfaces with protrusions, is determined by comparing the total free energy of a liquid drop in terms of their apparent contact angles for different protrusion features. It is found that when the area fraction of the topographical features and the intrinsic contact angle for a flat surface are large, the Cassie state is favored, but it can be either the metastable or stable state. It is shown that the transition from the Cassie state to the Wenzel state requires the application of a pressure to the meniscus between the surface protrusions. The critical transition pressure increases not only with increasing area fraction and intrinsic contact angle, but also with decreasing protrusion size. During the transition, a high-pressure gas can be trapped around the protrusions that can cause the Cassie state to be recovered after the release of the applied pressure. The analysis shows that a droplet can 'hang' upside-down when the protrusion size is very small; namely, the protrusions can pin the meniscus. These results are discussed relative to the advancing and receding contact angle.     

Inhibition of bubble coalescence: effects of salt concentration and speed of approach

Bubble coalescence experiments have been performed using a sliding bubble apparatus, in which mm-sized bubbles in an aqueous electrolyte solution without added surfactant rose toward an air meniscus at different speeds obtained by varying the inclination of a closed glass cylinder containing the liquid. The coalescence times of single bubbles contacting the meniscus were monitored using a high speed camera. Results clearly show that stability against coalescence of colliding air bubbles is influenced by both the salt concentration and the approach speed of the bubbles. Contrary to the widespread belief that bubbles in pure water are unstable, we demonstrate that bubbles formed in highly purified water and colliding with the meniscus at very slow approach speeds can survive for minutes or even hours. At higher speeds, bubbles in water only survive for a few seconds, and at still higher speeds they coalesce instantly. Addition of a simple electrolyte (KCl) removes the low-speed stability and shifts the transition between transient stability and instant coalescence to higher approach speeds. At high electrolyte concentration no bubbles were observed to coalesce instantly. These observations are consistent with recent results of Yaminsky et al. (Langmuir 26 (2010) 8061) and the transitions between different regions of behavior are in semi-quantitative agreement with Yaminsky's model.     

An oscillating molecular turnstile

An oscillating molecular turnstile based on a stator composed of a porphyrin core bearing two trans coordinating pyridyl units at the meso positions and a rotor equipped with a pyridyl group was designed. Whereas, in solution, the rotor freely rotates around the stator, in the presence of a silver cation behaving as an effector, the system oscillates between two stations. The oscillatory movement may be frozen upon cooling at -70 °C generating thus the closed state of the turnstile. The switching of the system between the open and closed states may be achieved using an external stimulus such as addition of Et(4)NBr.     

The geometry of primary drainage

We show that arc menisci configuration under primary drainage in capillary tube cross sections and, by extension, in throats in the void structure of rock and soil, can be understood in terms of the computational geometry theory of medial axis analysis. The solution for arc meniscus configuration is developed for cross sections of arbitrary, simply connected polygonal shape at both entry- and over-pressure values during primary drainage for arbitrary values of wetting angle. Using this solution technique, we have obtained highly accurate solutions of entry pressure arc meniscus radius for over 21,500 throats obtained from analysis of computed tomography images in a suite of 4 Fontainebleau core samples ranging from 7.5 to 22% porosity. We show that the ratio A/P, of throat area to throat perimeter, is an excellent predictor of entry pressure meniscus radius (and hence entry pressure) for primary drainage for real pores, while inscribed radius and area equivalent radius over-predict entry pressure meniscus radius by factors of 1.5-3, and are consequently poor predictors.     

Influence of the Meniscus at the Bottom of the Solid Plate on Imbibition Experiments

The analysis of the experiments on liquid imbibition into porous solids carried out by using the increase of weight technique proves the influence that meniscus formation has on the experimental increase of weight when the bottom of the porous layer is put in contact with the free surface of the liquid used to perform the penetration experiments. This process (meniscus onset) has a temporary dependence due to the change of the distance between the inferior base of the plate and the free surface of the liquid as a result of the imbibition. We have also found the proper experimental conditions under which such temporary dependence can be minimized after a short time after the start of contact between the porous layer and the free surface of the liquid utilized in the penetration procedure. Thus, the weight increase because of the meniscus formation can be assumed as a constant during the greatest part of the experiments, allowing the use of the proper mathematical form of Washburn's equation in order to describe the imbibition of the liquid into the pores of the solid. Copyright 2001 Academic Press.     

Adsorption-induced structural transition of an interpenetrated porous coordination polymer: detailed exploration of free energy profiles

Specific types of coordination polymers show an adsorption-induced structural transition, or so-called "gate adsorption", in which a host framework is said to change its structure from a "closed" nonporous phase to an "open" porous one for guest molecules. To identify the pathway for such a structural transition, we perform grand canonical Monte Carlo simulations for the adsorption of guest molecules in a host interpenetrated framework and calculate the free energy profiles of the structural changes in a complete three-dimensional space. In addition to the open phase found in our previous analyses along a fixed one-dimensional path, we reveal the existence of another open configuration. Each of the two open phases yields the status of global minimum to the other depending on the external pressure, resulting in a two-step isotherm. Moreover, the shape of adsorption hysteresis associated with the structural transition can change depending on the energy barrier between a metastable and a stable state that the system can overcome. Our simulations not only give a comprehensive understanding of stepped isotherms observed empirically but also suggest that isotherms with hysteretic gate adsorption is closely related to the thermal fluctuation of the system.     

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.     

Thickness-dependent autophobic dewetting of thin polymer films on coated substrates

We demonstrate that the wetting behavior of a thin liquid film, poly(4-bromostyrene) (PBrS), on top of a solid substrate may be effectively controlled with the insertion of a secondary liquid film, poly(4-vinyl pyridine) (P4VP), underneath the primary film. This secondary film remains stable under all conditions, and can be viewed as an extension of the substrate itself. On the basis of results from X-ray standing waves generated via total external reflection from an X-ray mirror, time-of-flight secondary ion mass spectroscopy, optical microscopy, and atomic force microscopy, we construct the full Helmholtz free energy versus PBrS thickness curve using existing theories that account for both long- and short-range interactions. The form of the free energy curve, which contains an inflection point and an absolute minimum at a nonzero PBrS thickness, accurately reflects our observation that thick PBrS films undergo autophobic dewetting on top of the stable P4VP, while sufficiently thin PBrS films remain stable. The thickness of the autophobic wetting layer is controlled by the range of the repulsive interaction between the film and the substrate, and is found to be ～4 nm for the PBrS/P4VP interface.