Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA)

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop). Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of original ADSA using a drop with an apex, it is still not as accurate as a surface tension measurement using a pendant drop suspended from a holder. In this article, the computational and experimental aspects of ADSA-NA were scrutinized to improve the accuracy of the simultaneous measurement of surface tensions and contact angles. It was found that the results are relatively insensitive to different optimization methods and edge detectors. The precision of contact angle measurement was enhanced by improving the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. To optimize the experimental design, the capillary was replaced with an inverted sharp-edged pedestal, or holder, to control the drop height and to ensure the axisymmetry of the drops. It was shown that the drop height is the most important experimental parameter affecting the accuracy of the surface tension measurement, and larger drop heights yield lower surface tension errors. It is suggested that a minimum nondimensional drop height (drop height divided by capillary length) of 1.7 is required to reach an error of less than 0.2 mJ/m(2) for the measured surface tension. As an example, the surface tension of water was measured to be 72.46 ± 0.04 at 24 °C by ADSA-NA, compared to 72.39 ± 0.01 mJ/m(2) obtained with pendant drop experiments.     

Analytical approach for the Lucas-Washburn equation

Porous media can be characterized by studying the kinetics of liquid rise within the pore spaces. Although porous media generally have a complex structure, they can be modeled as a single, vertical capillary or as an assembly of such capillaries. The main difficulties lie in separately estimating the effective mean radius of the capillaries and the contact angle between the liquid and the pore. In this paper we circumvent these obstacles by exploring another approach and suggest an analytical approach of the classical Lucas-Washburn equation (LWE). Specifically, we consider that the contact angle between the liquid meniscus and the inner surface of the capillary becomes a dynamic contact angle when the liquid front is in movement. It has previously been demonstrated that the resulting time dependence is due to frictional dissipation at the moving wetting front.     

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.     

Interfacial phenomena and dynamic contact angle modulation in microcapillary flows subjected to electroosmotic actuation

The dynamic evolution of an incompressible liquid meniscus inside a microcapillary is investigated, under the combined influences of viscous, capillary, intermolecular, pondermotive, and electroosmotic effects. In the limit of small capillary numbers, an advancing meniscus shape is shown to merge smoothly with the precursor film, using matched asymptotic analysis. A scaling relationship is also established for the dynamic contact angle as a nondimensional function of the capillary number and the applied electrical voltage. The analysis is further generalized by invoking a kinetic slip model for overcoming the constraints of meniscus tip singularity. The kinetic slip model is subsequently utilized to analyze the interfacial dynamics from the perspective of the results obtained from the matched asymptotic analysis. A generalization is achieved in this regard, which may provide a sound basis for controlling the topographical features of a dynamically evolving meniscus in a microcapillary subjected to electrokinetic effects. These results are also in excellent agreement with the experimental findings over a wide range of capillary number values.     

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.     

Capillary rise of a non-Newtonian power law liquid: impact of the fluid rheology and dynamic contact angle

The impact of non-Newtonian behavior and the dynamic contact angle on the rise dynamics of a power law liquid in a vertical capillary is studied theoretically and experimentally for quasi-steady-state flow. An analytical solution for the time evolution of the meniscus height is obtained in terms of a Gaussian hypergeometric function, which in the case of a Newtonian liquid reduces to the Lucas-Washburn equation modified by the dynamic contact angle correction. The validity of the solution is checked against experimental data on the rise dynamics of a shear-thinning cmc solution in a glass microcapillary, and excellent agreement is found.     

Impact of surface forces on wetting of hierarchical surfaces and contact angle hysteresis

The influence of the long-range surface forces on the wetting of multi-scale partially wetted surfaces is discussed. The possibility of partial wetting is stipulated by a specific form of the Derjaguin isotherm. Equilibrium of a liquid meniscus inside a cylindrical capillary is used as a model. The interplay of capillary and disjoining pressures governs the equilibrium of the liquid in the nano- and micrometrically scaled pores constituting the relief of the surface. It is shown that capillaries with a radius smaller than a critical one will be completely filled by water, whereas the larger capillaries will be filled only partially. Thus, small capillaries will show the Wenzel type of wetting behavior, while the same liquid inside the large capillaries will promote the Cassie-Baxter type of wetting. Consideration of disjoining/conjoining pressure allows explaining of the “rose petal effect”, when a high apparent contact angle is accompanied with a high contact angle hysteresis.     

Electrowetting-induced capillary flow in a parallel-plate channel

This paper investigated, theoretically and experimentally, the electrowetting-induced capillary rise in a parallel-plate channel. The measured equilibrium height of the meniscus was proportional to the square of the applied potential. A model, based on the kinetic equation of capillary flow with the consideration of an electrowetting dynamic contact angle, was established to simulate the capillary rise. The effects of the electrostatic charge and the contact-line friction were linearly added to describe the electrowetting dynamic contact angle. The model was found to be able to adequately describe the experimental data under different initial heights and applied voltages. The non-Poseuille flow effect had little influence in the meniscus rising phenomenon studied in this work.     

Influence of the Type of Contact between Particles Joined by a Liquid Bridge on the Capillary Cohesive Forces

The influence of the particle dimensions and type of interparticle contact on the magnitude of the capillary forces between the powder particles is studied on the basis of a model describing a capillary interaction of two particles joined by a liquid bridge. Various contact types were implemented using combinations of different particle shapes: spherical, conical, or plane. The meniscus of the bridge is described using a circular approximation; experimental results confirm that its use is justified. A method is developed for calculating the capillary forces and the amount of the liquid in the bridge with allowance for various parameters of the powder. The calculated results show that the dimensions of the particles and the type of their contact significantly affect the magnitude of the capillary forces.     

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.     

A micropump controlled by EWOD: wetting line energy and velocity effects

A Laplace pressure gradient between a droplet and a liquid meniscus was utilized to create an on-demand constant flow rate capillary pump. Electrowetting on dielectric was implemented to induce the pressure gradient in the microchannel. For an initial droplet volume of 0.3 μL and a power of 12 nW a constant flow rate of 0.02 μL s(-1) was demonstrated. The effects of the wetting line energy on the static contact angle and the wetting line velocity on the dynamic contact angle in the pump operation were studied. Sample loading on-demand could be achieved by regulating an electric potential.     

Effects of contact geometry on pull-off force measurements with a colloidal probe

This paper examines the effects of contact geometry on the pull-off (adhesion) force between a glass sphere (colloidal probe) and a silicon wafer in an environment with controlled relative humidity. An atomic force microscope is used to measure the pull-off force between the colloidal probe and the sample mounted at different tilt angles. The results show that the measured pull-off force is very sensitive to the tilt angle. Through the use of a newly developed direct scanning method, the exact contact geometry is determined for the zero-tilt angle case. The obtained digital image is then rotated to determine the contact geometry for the cases with other tilt angles. A detailed examination of the contact geometry, along with a magnitude analysis of the capillary force, suggests that the adhesion is most likely dominated by the capillary force from the meniscus formed between the probe and the sample. The strong dependence of the adhesion on the tilt angle may result from the change of meniscus dimensions associated with the probe-sample separation, which in turn is controlled by the highest peak on the probe sphere. Our observation emphasizes the combined role of microsurface shape near the contact and nanoroughness within the contact in determining the colloidal probe pull-off force and also microadhesion force in general.     

Modeling receding contact lines on superhydrophobic surfaces

We use mesoscale simulations to study the depinning of a receding contact line on a superhydrophobic surface patterned by a regular array of posts. For the simulations to be feasible, we introduce a novel geometry where a column of liquid dewets a capillary bounded by a superhydrophobic plane that faces a smooth hydrophilic wall of variable contact angle. We present results for the dependence of the depinning angle on the shape and spacing of the posts and discuss the form of the meniscus at depinning. We find, in agreement with ref 17 , that the local post concentration is a primary factor in controlling the depinning angle and show that the numerical results agree well with recent experiments. We also present two examples of metastable pinned configurations where the posts are partially wet.     

On the shape of a hydrostatic meniscus attached to a corrugated plate or wavy cylinder

The shape of a hydrostatic meniscus attached at a fixed contact angle to a vertical plate or circular cylinder with periodic corrugations is studied by analytical and numerical methods, and the effect of wall irregularities on the shape of the contact line and vertical component of the capillary force is discussed. An asymptotic analysis for a plate with small-amplitude sinusoidal corrugations is carried out to first order with respect to the corrugation amplitude, and a boundary-value problem is formulated and solved by a shooting method to determine the meniscus shape and elevation of the contact line. The meniscus attached to a corrugated plate with rounded corners produced by a Schwarz-Christoffel mapping function for a triangular wave is considered by numerical methods. The Laplace-Young equation determining the meniscus shape is solved in orthogonal curvilinear coordinates generated by conformal mapping using a finite-difference method. The numerical results are successfully compared with the predictions of the perturbation expansion for small amplitudes and discussed with reference to the rise of a meniscus inside a dihedral angle for large amplitudes. A companion asymptotic analysis is presented for a meniscus outside a vertical circular cylinder with small-amplitude sinusoidal corrugations. The analytical predictions are successfully compared with numerical solutions of the Laplace-Young equation for a meniscus outside an elliptical cylinder with aspect ratio near unity, regarded as a deformed circle.     

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.     

An experimental study about the imbibition of aqueous solutions of low concentration of a non-adsorbable surfactant in a hydrophilic porous medium

The imbibition of aqueous solutions of Triton X-100 in calcium fluoride columns has been studied in order to determine the influence of the interfacial adsorption of the surfactant in the capillary rise of the solutions. This system has been chosen because this surfactant behaves as non-adsorbable at the surface of this solid when it is in aqueous solution. The experiments have consisted of the measurement of the increase in the weight of the porous columns caused by the capillary rise of the solutions. The analysis of the results has been made through a modified expression of Washburn's equation that takes into account that the experimental increase in the weight is caused by the imbibition as well as by the development of a liquid meniscus around the bottom base of the columns. From this analysis, it has been deduced that the surfactant concentration does not influence on the imbibition rate, it being equal to the observed for water. However, it has been also proved that the contact angle depends on the surfactant concentration, taking decreasing values as the surface tension of the solutions decreases. In order to justify these findings, a study about the influence of the interfacial adsorption on the imbibition has been carried out. By means of them, it has been proved that the absence of adsorption at the solid-liquid interface is the reason that explains both the independence of the imbibition rate from the surfactant concentration and the decrease of the contact angle. Moreover, this fact indicates that the depletion of the surfactant molecules from the advancing meniscus, which has been normally adduced as the phenomenon causing the observed behaviour, has to be ruled out as the physical cause that justifies the behaviour found from the analysis of the imbibition experiments. As a corollary, it has been also stated that only if the adsorption at the solid interfaces happened, the imbibition of aqueous solution of surfactant in hydrophilic media could be influenced by the surfactant concentration.     

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.     

Surface functionalization of SBA-15 and a nonordered mesoporous silica with a 1,4-diazabicyclo[2.2.2]octane derivative: study of CuCl2 adsorption from ethanol solution

The equilibrium position of a spherical or prolate spheroidal particle resembling a needle floating at the interface between two immiscible fluids is discussed. A three-dimensional meniscus attached to an a priori unknown contact line at a specified contact angle is established around the particle, imparting to the particle a capillary force due to surface tension that is balanced by the buoyancy force and the particle weight. An accurate numerical solution for a floating sphere is obtained by solving a boundary-value problem, and the results are compared favorably with an approximate solution where the effect of the particle surface curvature is ignored and the elevation of the contact line is computed using an analytical solution for the meniscus attached to an inclined flat plate. The approximate formulation is applied locally around the nearly planar elliptical contact line of a prolate spheroid to derive a nonlinear algebraic equation governing the position of the particle center and the mean elevation of the contact line. The effect of the fluid and particle densities, contact angle, and capillary length is discussed, and the shape of the contact line is reconstructed and displayed from the local solution.     

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.     

Dynamics of a disturbed sessile drop measured by atomic force microscopy (AFM)

A new method for studying the dynamics of a sessile drop by atomic force microscopy (AFM) is demonstrated. A hydrophobic microsphere (radius, r ～ 20-30 μm) is brought into contact with a small sessile water drop resting on a polytetrafluoroethylene (PTFE) surface. When the microsphere touches the liquid surface, the meniscus rises onto it because of capillary forces. Although the microsphere volume is 6 orders of magnitude smaller than the drop, it excites the normal resonance modes of the liquid interface. The sphere is pinned at the interface, whose small (<100 nm) oscillations are readily measured with AFM. Resonance oscillation frequencies were measured for drop volumes between 5 and 200 μL. The results for the two lowest normal modes are quantitatively consistent with continuum calculations for the natural frequency of hemispherical drops with no adjustable parameters. The method may enable sensitive measurements of volume, surface tension, and viscosity of small drops.