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.     

The possibility of different time scales in the dynamics of pore imbibition

To model the imbibition of liquids into porous solids, use is often made of the Lucas-Washburn equation, which relates the distance of penetration of a liquid at a given time to the pore radius, the viscosity and surface tension of the liquid, and the effective contact angle between the liquid and the solid. In this paper, we extend previous large-scale molecular dynamics simulations to show how this tool can be used to study the details of liquid imbibition, including the impact of the contact angle on the dynamics of penetration and the evolution of the internal flow field. In particular, we show that the asymptotic behavior of the contact angle versus time for a completely wetting liquid is given by approximately t(-1/4).     

On the evaluation of the surface free energy of porous and powdered solids from imbibition experiments: equivalence between height-time and weight-time techniques

A study of the equivalence between the height-time and weight-time experimental techniques, based on the imbibition of liquids into porous or powdered solids, has been carried out, determining under what conditions the deductions about the surface free energy of these solids made from the analysis of the experimental results obtained as weight versus time are similar to those deduced from the analysis of height versus time. Concretely, we have proved that only if the particular values of the porosity of the solid determined from the proper technique of imbibition, named the effective porosity, are taken into account, the analysis of both type of experimental measurements leads to the same conclusions about the surface free energy of the porous and powdered solids. In order to exemplify this, capillary rise measurements have been carried out by means of these two techniques with different liquids on silica gel layers.     

Surfactant solutions and porous substrates: spreading and imbibition

In Section 1, spreading of small liquid drops over thin dry porous layers is investigated from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. Drop motion over a porous layer is caused by an interplay of two processes: (a) the spreading of the drop over already saturated parts of the porous layer, which results in an expanding of the drop base, and (b) the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and an expanding of the wetted region inside the porous layer. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations has been derived to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters, one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate, and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments were used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters are determined. Experiments were carried out on the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer were monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactory for the experimental data. According to theory predictions [1]: (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function, and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in the system under investigation. These conclusions again are in good agreement with experimental observations [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. In Section 2, experimental investigations are reviewed on the spreading of small drops of aqueous SDS solutions over dry thin porous substrates (nitrocellulose membranes) in the case of partial wetting [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]. The time evolution was monitored of the radii of both the drop base and the wetted area inside the porous substrate. The total duration of the spreading process was subdivided into three stages-the first stage: the drop base expands until the maximum value of the drop base is reached; the contact angle rapidly decreases during this stage; the second stage: the radius of the drop base remains constant and the contact angle decreases linearly with time; the third stage: the drop base shrinks and the contact angle remains constant. The wetted area inside the porous substrate expends during the whole spreading process. Appropriate scales were used with a plot of the dimensionless radii of the drop base, of the wetted area inside the porous substrate, and the dynamic contact angle on the dimensionless time. Experimental data showed [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]: the overall time of the spreading of drops of SDS solution over dry thin porous substrates decreases with the increase of surfactant concentration; the difference between advancing and hydrodynamic receding contact angles decreases with the surfactant concentration increase; the constancy of the contact angle during the third stage of spreading has nothing to do with the hysteresis of contact angle, but determined by the hydrodynamic reasons. It is shown using independent spreading experiments of the same drops on nonporous nitrocellulose substrate that the static receding contact angle is equal to zero, which supports the conclusion on the hydrodynamic nature of the hydrodynamic receding contact angle on porous substrates. In Section 3, a theory is developed to describe a spontaneous imbibition of surfactant solutions into hydrophobic capillaries, which takes into account the micelle disintegration and the concentration decreasing close to the moving meniscus as a result of adsorption, as well as the surface diffusion of surfactant molecules [N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747]. The theory predictions are in good agreement with the experimental investigations on the spontaneous imbibition of the nonionic aqueous surfactant solution, Syntamide-5, into hydrophobized quartz capillaries. A theory of the spontaneous capillary rise of surfactant solutions in hydrophobic capillaries is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface [V.J. Starov, Colloid Interface Sci. 270 (2003)]. In Section 4, capillary imbibition of aqueous surfactant solutions into dry porous substrates is investigated from both theoretical and experimental points of view in the case of partial wetting [V. Straov, S. Zhdanov, M. Velarde, J. Colloid Interface Sci. 273 (2004) 589]. Cylindrical capillaries are used as a model of porous media for theoretical treatment of the problem. It is shown that if an averaged pore size of the porous medium is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants at any concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of the pure water. The critical radius is determined by the adsorption of the surfactant molecules on the inner surface of the pores. If an averaged pore size is bigger than the critical value, then the permeability increases with surfactant concentration. These theoretical conclusions are in agreement with experimental observations. In Section 5, the spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, M.G. Velarde, J. Colloid Interface Sci. 227 (2000) 185]. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid-vapor interfacial tension and hydrophilise the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by experimental observations. In Section 6, the process of the spontaneous spreading of a droplet of a polar liquid over solid substrate is analyzed in the case when amphiphilic molecules (or their amphiphilic fragments) of the substrate surface layer are capable of overturning, resulting in a partial hydrophilisation of the surface [V.M. Starov, V.M. Rudoy, V.I. Ivanov, Colloid J. (Russian Academy of Sciences English Transaction) 61 (3) (1999) 374]. Such a situation may take place, for example, during contact of an aqueous droplet with the surface of a polymer whose macromolecules have hydrophilic side groups capable of rotating around the backbone and during the wetting of polymers containing surface-active additives or Langmuir-Blodgett films composed of amphiphilic molecules. It was shown that droplet spreading is possible only if the lateral interaction between neighbouring amphiphilic molecules (or groups) takes place. This interaction results in the tangential transfer of "the overturning state" to some distance in front of the advancing three-phase contact line making it partially hydrophilic. The quantitative theory describing the kinetics of droplet spreading is developed with allowance for this mechanism of self-organization of the surface layer of a substrate in the contact with a droplet.     

Comparison of the Use of Washburn's Equation in the Distance-Time and Weight-Time Imbibition Techniques

Two experimental methods are usually employed to study liquid penetration in porous media. One of them is based on the measure of the height of the advance liquid front vs time, and the other one is based on the measure of the weight gained by the porous system due to the liquid penetration vs time. Generally, the experimental data obtained from these techniques are analyzed through Washburn's equation. However, depending on which of them is selected, different conditions, coming from the experimental method, are needed to be taken into account in order to get the correct application of Washburn's equation to the experimental data. Although these conditions are different for each method, we prove in this paper that only if these conditions are considered both techniques are equivalent to analyze imbibition experiments using Washburn's equation. Copyright 2001 Academic Press.     

Spreading of liquid drops over dry porous layers: complete wetting case

Spreading of small liquid drops over thin dry porous layers is investigated from both theoretical and experimental points of view. Drop motion over a porous layer is caused by an interplay of two processes: (a) the spreading of the drop over already saturated parts of the porous layer, which results in an expanding of the drop base; (b) the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and an expanding of the wetted region inside the porous layer. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations is derived to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters: one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments are used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters are determined. Experiments were carried out on the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer are monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactorily for the experimental data. According to our theory prediction, (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in our system. These conclusions again are in good agreement with our experimental observations.     

A Novel Method for Surface Free-Energy Determination of Powdered Solids

Interfacial solid/liquid interactions play a crucial role in wetting, spreading, and adhesion processes. In the case of a flat solid surface, contact angle measurements are commonly utilized for the determination of the solid surface free energy and its components. However, if such a surface cannot be obtained, then the contact angle can not be measured directly. Usually methods based on imbibition of probe liquids into a thin porous layer or column are applied. In this paper a novel method, also based on the capillary rise, is proposed for the solid surface free-energy components determination. Actually, it is a modification of the thin column wicking method; similar theoretical background can be applied together with that appropriate for the capillary rise method of liquid surface tension determination. The proposed theoretical approach and procedure are verified by using single glass capillaries, and then alumina and ground glass powders were used for the method testing. Thus obtained surface free-energy components for these solids, for both glass and alumina, agree well with the literature values.     

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.     

Influence of the interfacial adsorptions on the imbibition of aqueous solutions of low concentration of the non-ionic surfactant Triton X-100 into calcium fluoride porous medium

The imbibition of aqueous solution of Triton X-100 in porous columns of calcium fluoride has been carried out in order to investigate the surfactant influence on the capillary rise. Experiments have consisted of the measurement of the increase in the weight of the porous columns caused by the imbibition of the solutions. From their analysis, it has been found that the capillary rise velocity does not depend on the surfactant concentration, and that imbibition of these solutions behaves as in the case of water. This unexpected finding can not be attributed to depletion of the surfactant molecules from the advancing meniscus, since this effect can not be caused by the adsorption at the solid. This lack of surfactant adsorption on the solid is precisely the reason that justifies the observed behaviour. So, it has been proved that the driving force for the capillary rise movement will remain unaltered despite the surfactant addition whenever the free energies of the solid interfaces are not modified by the adsorption on the solid. Therefore, it is concluded from this study that only if adsorption on the solid happened, the imbibition could be influenced by the surfactant concentration.     

Co- and counter-current spontaneous imbibition into groups of capillary tubes with lateral connections permitting cross-flow

A model for co- and counter-current imbibition through independent capillaries has already been developed and experiments conducted to verify the theory [E. Unsal, G. Mason, N.R. Morrow, D.W. Ruth, J. Colloid Interface Sci. 306 (2007) 105]. In this paper, the work is extended to capillaries which are connected laterally and in which cross-flow can take place. The fundamental pore geometry is a rod in an angled round-bottomed slot with a gap between the rod and a capping glass plate. The surfaces of the slot, rod and plate form capillaries and interconnecting passages which have non-axisymmetric cross-sections. Depending on the gap size either (i) a large single meniscus, (ii) two menisci one on each side of the rod, or (iii) three menisci, one between the rod and the glass additional to the ones on each side can be formed. A viscous refined oil was applied to one end of the capillaries and co-current and counter-current spontaneous imbibition experiments were performed. The opposite end was left open to the atmosphere for co-current experiments. When the gap between the rod and the plate was large, the imbibing oil advanced into the tubes with the meniscus in the largest capillary always lagging behind the two menisci in the other two smaller capillaries. For counter-current imbibition experiments the open end was sealed and connected to a sensitive pressure transducer. In some experiments, the oil imbibed into the smaller capillaries and expelled air as a series of bubbles from the end of the largest capillary. In other experiments, the oil was allowed to imbibe part way into the tubes before counter-current imbibition was started. The meniscus curvatures of the capillaries have been calculated using the Mayer and Stowe-Princen method for different cell slot angles and gap sizes using a value of zero for the contact angle. These values have been compared with actual values by measuring the capillary rise in the tubes; agreement was very close. A model for co-current and counter-current imbibition has also been developed. The significance of this model is that some hydraulic/capillary properties are common for both co-current and counter-current imbibition. The experiments give an illustration of behavior expected in a real porous material and verify the importance of the 'perfect cross-flow' modification to the 'bundle of parallel tubes' model.     

Foam films stabilized with alpha olefin sulfonate (AOS)

Alpha olefin sulfonate (AOS) surfactants have shown outstanding detergency, lower adsorption on porous rocks, high compatibility with hard water and good wetting and foaming properties. These properties make AOS an excellent candidate for foam applications in enhanced oil recovery. This paper summarizes the basic properties of foam films stabilized by an AOS surfactant. The foam film thickness and contact angle between the film and its meniscus were measured as a function of NaCl and AOS concentrations. The critical AOS concentration for formation of stable films was obtained. The critical NaCl concentration for formation of stable Newton black films was found. The dependence of the film thickness on the NaCl concentration was compared to the same dependence of the contact angle experiments. With increasing NaCl concentration the film thickness decreases gradually while the contact angle (and, respectively the free energy of film formation) increases, in accordance with the classical DLVO theory.The surface tension isotherms of the AOS solutions were measured at different NaCl concentrations. They coincide on a single curve when plotted as a function of mean ionic activity product. Our data imply that the adsorption of AOS is independent of NaCl concentration at a given mean ionic activity.     

Effects of gas adsorption isotherm and liquid contact angle on capillary force for sphere-on-flat and cone-on-flat geometries

This paper explains the origin of the vapor pressure dependence of the asperity capillary force in vapor environments. A molecular adsorbate layer is readily formed on solid surface in ambient conditions unless the surface energy of the solid is low enough and unfavorable for vapor adsorption. Then, the capillary meniscus formed around the solid asperity contact should be in equilibrium with the adsorbate layer, not with the bare solid surface. A theoretical model incorporating the vapor adsorption isotherm into the solution of the Young-Laplace equation is developed. Two contact geometries--sphere-on-flat and cone-on-flat--are modeled. The calculation results show that the experimentally-observed strong vapor pressure dependence can be explained only when the adsorption isotherm of the vapor on the solid surface is taken into account. The large relative partial pressure dependence mainly comes from the change in the meniscus size due to the presence of the adsorbate layer.     

Analysis of the Silica Surface Free Energy by the Imbibition Technique

The surface free energy of silica and its components have been evaluated from imbibition experiments performed with liquids of differing surface properties by the distance–time method. Data were analyzed by a parabolic fit to Washburn's equation, because of the uncertainty in the exact position and time at which penetration begins in these kinds of experiments. In addition to the mathematical treatment of the experimental results, the influence of the components and parameters of the surface tension of the liquids used on the values of the solid surface free-energy components has been analyzed.     

Determination of contact angles on microporous particles using the thin-layer wicking technique

The properties of particle-stabilized emulsions, especially with regard to phase inversion, are very dependent on the contact angle that the particles experience at the oil-water interface. For the very small particles used for such emulsions (often a few tens of nm), it is impossible to measure this contact angle directly. Its value could be calculated if it were possible to determine the components of the solid surface free energy. To establish a method suitable for such particles, we have investigated the imbibition of five probe liquids into a porous bed of silica (commercial TLC plates) using the thin-layer wicking technique. For all liquids, the difference between wicking rate for bare plates and for those pre-contacted with the vapors is large but it is not due to an advancing angle effect on bare plates. Our analysis shows that it is due to the diversion of flowing liquid into blind pores which are already filled in the pre-contacted case. Thus a new model is proposed describing wicking in a porous medium with very small blind pores by introducing a parameter into the Washburn equation that corrects for this capillary condensation effect. The parameter needed is determined independently using gravimetric adsorption measurements. When this modified Washburn equation is used, the difference between advancing and receding contact angle is actually quite small. When the averages are used as the Young's contact angles, values for the surface energy components of silica are obtained that are completely consistent between the five liquids and have magnitudes expected for this type of silica surface.     

Some mechanisms of immiscible fluid displacement in small networks

We report experimental observations on immiscible displacement in two small networks using three different pairs of fluids, air-oil, air-water, and oil-water, to vary the wettability. The experiments were run for a wide range of capillary number, from 10⁻⁷ to 10⁻³. Various mechanisms are observed. These are film spreading and drainage, Haines' jump, free slip and stick-slip meniscus motion, contact angle hysteresis, snap-off, coalescence, and blocking of film and bubble. For the air-oil case, oil is perfectly wetting in the network. In imbibition, the displacement occurs first via thin film spreading, followed by snap-off of menisci, and then by piston-like displacement at low flow rates. As the flow rate increases, piston-like displacement dominates because film spreading is comparatively slow. Snap-off of menisci in the throats is a necessary condition for air trapping. In drainage, meniscus snap-off and coalescence are observed in one network. For both imbibition and drainage, during each snap-off or piston-like displacement event, all menisci move freely along the channels to adjust their curvatures, due to the lubrication of the wetting film. For the other two fluid pairs at low flow rates, this curvature readjustment through free slipping of meniscus is not observed, presumably due to the absence of wetting film during the displacement. At high flow rate, oscillation of menisci due to volumetric competition is observed. Neither wetting film spreading nor throat snap-off is observed. Stick and slip motion of meniscus is observed, probably due to the roughness and/or heterogeneous wettability of the solid surface. For the oil-water system the wettability seems to be time dependent. Coalescence between two menisci can occur in the throat, in the pore, or at the pore-throat boundary during displacement. Trapping of the displaced phase is due to its being bypassed or snapped off in the throat.     

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

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

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.     

Problems of contact angle and solid surface free energy determination

The current general problems of formulation and determination of surface free energy are discussed. So far several theories and approaches have been proposed, but formulation of surface and interfacial free energy, as regards its components, is still a very debatable issue. However, as long as no method for determination of real surface free energy quantities is known, even relative values charged with many simplified assumptions are useful for better understanding of the wetting processes. In this paper special focus is concentrated on powdered solids for which direct measurement of the contact angles is not possible. For such solids the porous layer imbibition techniques are most frequently applied. Then, using the wicking results the contact angle is calculated from Washburn's equation. However, such a procedure leads to overestimated contact angle values in comparison to those measured directly on smooth surfaces of the same solid, if such surface can be obtained at all. As a consequence, the solid surface free energy components calculated via such overestimated contact angles are significantly lower than those obtained from contact angles measured directly. Methodologies to avoid this problem are also described.