Pressure dependence of the contact angle in a CO2-H2O-coal system

Carbon dioxide injection into coal layers serves the dual purpose to enhance coal bed methane production (ECBM) and to store CO2. The efficiency of this process is expected to be much higher if water is the non-wetting phase in the coal-water-gas system. Therefore, contact angles in the coal-water-CO2 system have been measured using the captive bubble technique in the pressure range between atmospheric pressure and 141 bar at a temperature of 45 degrees C. At atmospheric pressure the contact angle of a shrinking CO2 droplet increases with time, but stays below 90 degrees . At higher pressures (>2.6 bar) the contact angle increases beyond 90 degrees . The pressure dependence of the contact can be represented by theta=(111 degrees +/-10.5 degrees )+(0.17+/-0.14)P [bar]. The exceptional behavior at atmospheric pressure is possibly related to the stability of water patches on the coal surface. It is concluded that water is the non-wetting phase in this coal-water-CO2 system.     

Microscopic interpretation of the dependence of the contact angle on roughness

The macroscopic contact angle theta(m) of a liquid drop on a rough solid surface in the presence of a gas is calculated microscopically on the basis of a variational minimization of the total potential energy of the drop. Two limiting cases are considered: the liquid penetrates into the space between asperities (Wenzel regime) and the liquid resides on the top of asperities (Cassie-Baxter regime). Long-range as well as short-range interactions between the molecules of liquid, solid, and gas are taken into account. It was also assumed that small portions of insoluble gas are accumulated near the edges of the asperities during the formation of the droplet. The contact angle depends on several parameters involved in the microscopic interactions as well as on the fractions of solid surface between asperities, and of the surface of the asperities themselves, that are in contact with the liquid. It is shown that the theory can explain the nonlinear dependence of cos theta(m) on roughness observed by Krupenkin et al. [Krupenkin, T. N.; Taylor, J. A.; Schneider, T. M.; Yang, S. Langmuir 2004, 20, 3824].(1).     

Dynamic behavior of polymer surface and the time dependence of contact angle

The increased attention has been focused on the re-searches of soft materials proposed by Pierre-Gilles de Gennes, a Nobel Prize Laureate in Physics. A special issue of “Science” on soft surfaces was published in 2002 to review specific surface properti…     

Prediction of solid-water-hydrocarbon contact angle

The reliability of a recently developed solid-vapour and solid-liquid interfacial tension models has been investigated by applying them to predict liquid-vapour and liquid-liquid interfacial tension values. The impact of the geometrical molecular packing and the molecular orientations near the surface on the predicted values are discussed. The mutual solubility data are shown to be adequate for calculation of the interaction parameters in the solid-liquid model and a new equation, using this information, is developed for prediction of water-hydrocarbon interfacial tension. The model has been applied to recent data on water-methane-n-decane and water-methane-cyclohexane-n-decane interfacial tensions at elevated temperature and pressure and its reliability demonstrated. It is shown that the solid-liquid interfacial tension model is solely adequate for predicting the contact angle by applying it to mercury-water-benzene and stearic acid-water-n-decane systems.     

On the modelling of the dynamic contact angle

The dynamic contact angle is a value of great significance for characterizing wetting processes. Three strategies have been developed for modelling this value; empirical models, models based on molecular kinetics and models based on flow mechanics.Models based on molecular kinetics start from the fact that the dynamic contact angle appears immediately at the Une of wetting, and that the curvature of the liquid surface can be neglected. Models based on flow mechanics show that near the line of wetting the curvature is very strong. These models require the presence of the static contact angle at the line of wetting and give a model of the dynamic contact angle as the slope of the interface. In the present paper, models based on flow mechanics are extended in two directions. For the case of flow in a tubular capillary, the model represents the effect of the adsorption kinetics of surfactants on the dynamic contact angle, assuming the adsorption to be kinetically controlled. Another model is concerned with the effect of the flow of the third phase on the dynamic contact angle and on the boundaries of dynamic wetting. It is demonstrated that coating under an inert liquid is possible only for small working ranges.Symbols A dimensionless number of adsorption - B dimensionless number of adsorption - c concentration - C curvature - D diffusion coefficient - D _s surface diffusion coefficient - h, H height above the solid surface - K ₁ ,K ₂ rate constants - l length of slippage - p pressure - q mass flow density - r, R radius - R viscosity ratio - R _G gas constant - t time - U, v velocity - , , angle - viscosity - y dimensionless surface concentration - surface concentration - stream function - density - surface tension - _LF liquid-fluid interfacial tension - shearing stress - dimensionless radius - Ca capillary number     

The dynamic contact angle I. Dependence of the receding contact angle on velocity in the surfactant-containing three-phase system

Spontaneous three-phase contact (tpc) motion is investigated in order to determine the dependence of the static contact angle on tpc velocity in surfactant-containing systems after recession. To interpret the experimental results, the molecular-kinetic sitechanging theory and the hydrodynamic theory were considered. It is shown that, especially at very high tpc velocities, the experimental results are not thoroughly described by these theories. The deviations are explained as a surfactant transfer from the liquid/gas to the solid/gas interface which, under insufficient afterdiffusion, leads to an increase in surface tension and to a changed surface rheology. This mechanism could be governed by a model.     

Factors influencing the contact angle value. The contact angle,as a characteristic of the properties of solid surfaces

A survey of publications concerning the properties of solids in relation to wetting phenomena is presented. Factors influencing the contact angle value as well as problems of objective approach to research into wetting phenomena are discussed. Peculiarities of the direct and reverse processes during the formation of the solid—liquid—vapor three-phase contact and the inevitability of contact angle hysteresis for polar solids and liquids are analyzed. It is suggested that contact angle hysteresis is due to high energy of the interaction between the liquid and the solid and hence a long relaxation time of the three-phase contact system. Specific features of the response of a solid surface to all surface processes (“chemomechanics”) is discussed. Cleaning of solid surfaces as well as surface preparation for repeated measurements is considered. It is shown that good reproducibility of results is possible if conditions for sample preparation are met. The results of determination of the activation energy for wetting of glass surface with water are presented. The influence of the structure of solids (their hardness) on the contact angle values is demonstrated. Inevitability of the presence of different-type active sites characterized by different dissociation constants (pK_a) on the surface of solids is discussed. The pK_a values and content of these surface sites obtained from potentiometric titration and wetting data are estimated. The estimates thus obtained are in reasonable agreement with each other and can thus be used in practical applications. However, potentiometric titration is currently inappropriate for evaluating the content of individual surface sites as well as the surface charge.     

Contact angle interpretation: re-evaluation of existing contact angle data

We have recently shown that static contact angles measured by conventional goniometer techniques could be meaningless in the context of the Young equation. There is an abundance of contact angles in the literature that are of unknown status. Here, we explored whether one should completely neglect the literature contact angle data. Existing static contact angles for 34 different types of solid surfaces from Zisman and co-workers were evaluated in terms of their solid surface tensions using experimental contact angle patterns. A fortran computer program was implemented to automate these procedures. It was found that literature contact angles do not have to be discarded completely; they can be used to determine solid surface tensions, with caution. The surface tensions for the 34 solid surfaces from Zisman et al. are also reported.     

Pressure dependence of viscosity

We reanalyze the pressure dependence of viscosity of liquids of constant composition under isothermal conditions. Based exclusively on very general considerations concerning the relationship between viscosity and "free volume," we show that, at moderate values of pressure, viscosity increases, as a rule, with increasing pressure, provided the liquid is in stable or metastable (undercooled) equilibrium states. However, even if the behavior of the viscosity is governed by free volume effects, deviations from a positive pressure dependence are possible, when the liquid's thermal expansion coefficient is negative. We derive an equation that allows one to quantitatively determine the pressure dependence of viscosity, which requires, in the simplest case, only the knowledge of the temperature dependence of viscosity at constant pressure, the thermal expansion coefficient, and the isothermal compressibility of the liquid. As an example, the negative pressure dependence of water in the range of temperatures 0-4 degrees C and of several silicate liquids, such as albite, jadeite, dacite, basalts, etc., could be explained in such a way. Other glass-forming liquids initially (for moderate pressures) show a positive pressure dependence of viscosity that changes to a negative one when subjected to high (approximately GPa) isostatic pressure. A detailed analysis of water and already mentioned silicate melts at GPa pressures shows that, in addition to free volume effects, other pressure induced structural transformations may have to be accounted for in a variety of cases. By this reason, the theoretical analysis is extended (i) in order to describe the pressure dependence of viscosity for systems that are in frozen-in thermodynamic nonequilibrium states (glasses, i.e., undercooled liquids below the glass transition temperature Tg) and (ii) to systems which undergo, in addition to variations of the free volume, pressure induced changes of other structural parameters. In such cases a decrease of viscosity with increasing pressure may occur, in principle, even if the thermal expansion coefficient is positive. In this way, the present analysis grants a general tool to estimate the pressure dependence of viscosity and supposedly settles the controversy in the current literature.     

Constitutive modeling of contact angle hysteresis

We introduce a phase field model of wetting of surfaces by sessile drops. The theory uses a two-dimensional non-conserved phase field variable to parametrize the Gibbs free energy of the three-dimensional system. Contact line tension and contact angle hysteresis arise from the gradient term in the free energy and the kinetic coefficient respectively. A significant advantage of this approach is in the constitutive specification of hysteresis. The advancing and receding angles of a surface, the liquid-vapor interfacial energy and three-phase line tension are the only required constitutive inputs to the model. We first simulate hysteresis on a smooth chemically homogeneous surface using this theory. Next we show that it is possible to study heterogeneous surfaces whose component surfaces are themselves hysteretic. We use this theory to examine the wetting of a surface containing a circular heterogeneous island. The contact angle for this case is found to be determined solely by the material properties at the contact line in accord with recent experimental data.     

Surface heterogeneity and contact angle hysteresis

The effect of surface heterogeneity on contact angle hysteresis is studied by using the model of Neumann and Good of a vertical plate with horizontal heterogeneous strips. The results of this study explain well known, but not understood patterns of contact angle behaviour: On the one hand, the advancing contact angle on a carefully prepared solid surface is generally reproducible; on the other hand, even a very small amount of surface heterogeneity may cause the receding contact angle to be less reproducible and to depend on several non-thermodynamic factors.     

Nanodrop on a nanorough hydrophilic solid surface: contact angle dependence on the size, arrangement, and composition of the pillars

A two-dimensional nanodrop on a hydrophilic solid surface decorated with nanopillars is examined using a nonlocal density functional theory. It is shown that, in contrast to the commonly used Wenzel formula, even an extremely small roughness can considerably increase the contact angle. The contact angle depends on the distance between pillars, their height and width, as well as their composition. It was found that for all selected pillar heights and compositions, the largest contact angle is obtained when the distance between pillars acquires a size at which the liquid molecules can no longer penetrate between them. The further decrease in the interpillar distance decreases the contact angle, in qualitative agreement with the Cassie-Baxter formula. Considering pillars of various compositions, the role of the gradient of the fluid-solid interaction potential is examined. The presence of such a gradient does not allow the formation of a stable nanodrop on the surface. However, asymmetrical metastable nanodrops can be formed.     

Probing with a laser sheet the contact angle distribution along a contact line

An optical method for probing contact angle distribution along contact lines of any shape using a laser sheet is proposed. This method is applied to a dry patch formed inside a film flowing along an inclined plane, both liquid and solid being transparent. Falling normally to the plane, a laser sheet cuts the contact line and is moved along this line. Distortions of the sheet trace observed on a screen put below the plane allow us to extract the contact angle distribution and the local line inclination along the line. Our results show that the contact angle around a dry patch is nearly constant and equal to the static advancing angle, at least when the evolution of its shape is followed for increasing flow rates. This supports a model of dry patch shape recently proposed by Podgorski and co-workers. Preliminary results obtained for decreasing flow are also qualitatively observed.     

Lattice boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces

The moving contact line problem of liquid-vapor interfaces was studied using a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 2004, 69, 032602]. We have examined the static and dynamic interfacial behaviors by means of the bubble and capillary wave tests and found that both the Laplace equation of capillarity and the dispersion relation were satisfied. Dynamic contact angles followed the general trend of contact line velocity observed experimentally and can be described by Blake's theory. The velocity fields near the interface were also obtained and are in good agreement with fluid mechanics and molecular dynamics studies. Our simulations demonstrated that incorporating interfacial effects into the lattice Boltzmann model can be a valuable and powerful alternative in interfacial studies.     

Determining the contact angle between liquids and cylindrical surfaces

One of the simplest methods of measuring the quantities for estimating the adhesion properties of materials (i.e., the adhesion work, the surface energy, and the interfacial tension between certain liquids and a surface) requires the determination of the contact angle between the liquid and the surface. In the case of plane surfaces the determination of the drop dimensions makes it possible to calculate the contact angle by the sessile drop method, but in the case of cylindrical surfaces (such as the monofilaments), several methods were developed to improve the accuracy of the contact angle measurements. This paper presents a comprehensive method for precise evaluation of the contact angle between liquid drops and monofilaments by establishing a differential equation describing the drop contour. This equation makes it possible to accurately compute the contact angle using the dimensions of the drop. A comparison of the values of the contact angle calculated by our method and those obtained by other approaches is made. We applied our method in the case of polyamide-6 monofilaments treated using dielectric barrier discharge, knowing their medical applications in surgical sutures.     

Picoliter water contact angle measurement on polymers

Water contact angle measurement is the most common method for determining a material's wettability, and the sessile drop approach is the most frequently used. However, the method is generally limited to macroscopic measurements because the base diameter of the droplet is usually greater than 1 mm. Here we report for the first time on a dosing system to dispense smaller individual droplets with control of the position and investigate whether water contact angles determined from picoliter volume water droplets are comparable with those obtained from the conventional microliter volume water droplets. This investigation was conducted on a group of commonly used polymers. To demonstrate the higher spatial resolution of wettability that can be achieved using picoliter volume water droplets, the wettability of a radial plasma polymer gradient was mapped using a 250 microm interval grid.     

Prediction of solid-fluid interfacial tension and contact angle

Two simple equations have been developed using the lattice theory and the regular solution assumption to predict the solid-vapor and solid-liquid interfacial tension. The required parameters are the liquid critical temperature and volume, the solid melting temperature and the molar volume of liquid and solid compounds. To confirm the models, the predicted solid-fluid interfacial tension values have been used to predict the contact angle of the liquid drop on the solid surface applying Young's equation. Agreement of the predicted contact angle with the experimental data reveals the reliability of the developed models.