The validity of Cassie's law: a simple exercise using a simplified model

The contact angle of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model which can lead to the augmented Young-Laplace equation. Droplets under the condition of constant volume as well as constant vapor pressure are considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy of the interface displacement model, we derive an equation which is similar but different from the well-known Cassie's law. Our modified Cassie's law is essentially the same as the formula obtained previously by Marmur [J. Colloid Interface Sci. 168 (1994) 40]. A few consequences from this modified Cassie's law are briefly described in the following sections of this paper. Several sets of recent experimental results seem to support the validity of our modified Cassie's law.     

Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model. First, the apparent contact angle of a droplet on a heterogeneous surface under the condition of constant volume is considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy, we derive an equation for the apparent contact angle, which is similar but different from the well-known Cassie's law. Next, using this modified Cassie's law as a guide to predict the behavior of a droplet on a heterogeneous striped surface, we examine several scenarios of contact angle hysteresis using a periodically striped surface model. By changing the volume of the droplet, we predict a sudden jump of the droplet edge, and a continuous change of the apparent contact angle at the edge of two stripes. Our results suggest that as drop volume is increased (advancing contact lines), the predominant drop configuration observed is the one whose contact angle is large; whereas, decreasing drop volume from a large value (receding contact lines) yields drop configuration that predominantly exhibit the smaller contact angle.     

A topography/chemical composition gradient polystyrene surface: toward the investigation of the relationship between surface wettability and surface structure and chemical composition

In this paper, we have prepared of a topography/chemical composition gradient polystyrene (PS) surface, i.e., an orthogonal gradient surface, to investigate the relationship between surface wettability and surface structure and chemical composition. The prepared surface shows a one-dimensional gradient in wettability in the x, y, and diagonal directions, including hydrophobic to hydrophilic, superhydrophobic to hydrophobic, superhydrophobic to superhydrophilic gradients, and so forth. These one-dimensional gradients have different gradient values, gradient range, and contact angle hysteresis, which lie on both the surface roughness and the surface compositions. From the trend of variation of contact angle hysteresis, it can be concluded that the transition from the Cassie's model to the Wenzel's model occurs both by decreasing surface roughness and by increasing surface hydrophilic compositions. Moreover, the transition is more effective via changing surface chemical composition than changing surface roughness herein.     

Droplet spreading on microstriped surfaces

When a droplet of fluid is deposited on a surface with chemical and/or topological patterns, its static shape is highly dependent on the 2D distribution of the patterns. In the case of chemical stripes, three distinct spreading regimes have been observed as a function of wettability contrast between the two kind of stripes. For low wettability contrast, the droplet spreads with the same [corrected] velocity normal and parallel to the stripes [corrected] and the macroscopic contact angle is close to Cassie's contact angle. When the wettability contrast is intermediate/high, the resulting shape of the droplets is elongated. In the intermediate wettability contrast regime, an ideal situation shows stick and slip behavior of the contact line, during which the contact line jumps from one stripe to another. For a high wettability contrast, the confinement of the fluid between two chemical stripes leads to a 2D spreading.     

Ag-SiO2 core-shell nanorod arrays: morphological, optical, SERS, and wetting properties

Using the hydrolysis of tetraethylorthosilicate, a uniform and conformal layer of porous SiO(2) with controlled thickness has been coated onto the oblique angle deposited Ag nanorod (AgNR) array to form an aligned AgNR-SiO(2) core-shell array nanostructure. The morphology, optical property, SERS response, and surface wettability of the AgNRs with different SiO(2) shell thicknesses have been obtained by multiple characterization techniques. The morphological characterization shows that each AgNR on the array is coated with a uniform and porous silica shell independently and the growth of shell thickness follows a linear function versus the coating time. Thickening of the shell induces a monotonic decrease of the apparent contact angle, red-shift of the transverse mode of the localized surface plasmon resonance peak, and makes the SiO(2) shell more compact. The SERS response of 4-Mercaptophenol on these substrates exhibits an exponential decay behavior with the increasing coating time, which is ascribed to the decreasing Ag surface coverage of core-shell nanorods. Under the assumption that the Ag surface coverage is proportional to the SERS intensity, one can estimate the evolution of SiO(2) coverage on AgNRs. Such coverage evolution can be used to qualitatively explain the LSPR wavelength change and quantitatively interpret the contact angle change based on a double Cassie's law.     

Influence of surface charge on wetting kinetics

The wettability of a titania surface, partially covered with octadecyltrihydrosilane, has been investigated as a function of solution pH. The results show that surface charge affects both static wettability and wetting kinetics. The static contact angle decreases above and below the point of zero charge of the titania surface in a Lippman-like manner as the pH is altered. The dependence of dynamic contact angle on velocity is also affected by pH. The molecular-kinetic theory (MKT) is used to interpret the dynamic contact angle data. The frequency of molecular displacement κ(0) strongly varies with surface charge, whereas the mean molecular displacement length λ is essentially unaffected. There is an exponential dependence of contact-line friction upon work of adhesion, which is varied simply by altering the pH.     

Influence of the dynamic contact angle on the characterization of porous media

It has been shown recently that the classical Lucas-Washburn equation, often used to model the dynamics of liquid penetration into porous media, should be modified to take account of the dynamic contact angle between the liquid and the pore. Here we show how neglect of this effect can lead to significant errors in estimation of the effective pore radius.     

The influence of pore wettability on the dynamics of imbibition and drainage

Using large-scale molecular-dynamic (MD) simulations, we have shown previously that the classical Lucas–Washburn equation commonly employed to describe capillary imbibition and drainage should be modified to include dynamic contact-angle effects. In addition, we have demonstrated how these effects can be accounted for using the molecular-kinetic theory of dynamic wetting. In a further publication, we presented theoretical arguments and experimental evidence that the velocity of wetting depends on the intrinsic wettability of the solid surface in such a way that there exists an optimum contact angle at which the velocity of wetting is a maximum. Here, we combine these ideas to show how the maximum speeds of capillary imbibition and drainage are affected both by the pore wettability and the pressures used to drive capillary displacement. In particular, we introduce the concept of dynamic wetting transitions (DWTs) and discuss how these limit displacement efficiency and can be manipulated by controlling pore wettability. The results of this work may be beneficial in optimising the performance of capillary processes such as those involved in oil recovery.     

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).     

纳米结构表面浸润性质的分子动力学研究

采用分子动力学方法研究了氩纳米液滴在铂金属及其模型固体表面的浸润现象,获得了液滴在平滑表面和三角纳米结构阵列表面的接触角和展布特性.研究表明,液滴与壁面的势能作用较强时,液滴与纳米结构表面为均匀浸润,但是由于迟滞效应,接触角受表面纳米结构的影响不明显;势能作用较弱时,纳米结构间隙中存在类似蒸汽的低密度相,液滴与纳米结构表面为非均匀浸润,接触角受纳米结构的影响而增大;表面纳米结构可以使表面具有超疏水性.     

How Wenzel and cassie were wrong

We argue using experimental data that contact lines and not contact areas are important in determining wettability. Three types of two-component surfaces were prepared that contain "spots" in a surrounding field: a hydrophilic spot in a hydrophobic field, a rough spot in a smooth field, and a smooth spot in a rough field. Water contact angles were measured within the spots and with the spot confined to within the contact line of the sessile drop. Spot diameter and contact line diameter were varied. All of the data indicate that contact angle behavior (advancing, receding, and hysteresis) is determined by interactions of the liquid and the solid at the three-phase contact line alone and that the interfacial area within the contact perimeter is irrelevant. The point is made that Wenzel's and Cassie's equations are valid only to the extent that the structure of the contact area reflects the ground state energies of contact lines and the transition states between them.     

Dissipative particle dynamics simulation of contact angle hysteresis on a patterned solid/air composite surface

We have studied two types of topological substrates--the continuous solid substrates (CSS) and the discontinuous solid substrates (DSS)--by using the dissipative particle dynamics (DPD) method for a better understanding of the contact angle hysteresis on two such substrates. After the validation of DPD in the system, we found that DSS has a different distribution of the metastable states from that of CSS and that DSS has relatively larger contact angle hysteresis at lower temperature. Obtained results also show that CSS is more suitable for making an ultrahydrophobic or ultralyophobic surface than DSS from the point of view of dynamic wettability.     

Control over wettability of polyethylene glycol surfaces using capillary lithography

We demonstrate that wettability of poly(ethylene glycol) (PEG) surfaces can be controlled using nanostructures with various geometrical features. Capillary lithography was used to fabricate PEG nanostructures using a new ultraviolet (UV) curable mold consisting of functionalized polyurethane with acrylate group (MINS101m, Minuta Tech.). Two distinct wetting states were observed depending of the height of nanostructures. At relatively lower heights (< 300 nm for 150 nm pillars with 500 nm spacing), the initial contact angle of water was less than 80 degrees and the water droplet easily invaded into the surface grooves, leading to a reduced contact angle at equilibrium (Wenzel state). At relatively higher heights (> 400 nm for 150 nm pillars with 500 nm spacing), on the other hand, the nanostructured PEG surface showed hydrophobic nature and no significant change in contact angle was observed with time (Cassie state). The presence of two wetting states was also confirmed by dynamic wetting properties and contact-angle hysteresis. The wetting transition from hydrophilic (bare PEG surface) to hydrophobic (PEG nanostructures) was described by the Cassie-Baxter equation assuming that enhanced hydrophobicity is due to the heterogeneous wetting mediated by an air pocket on the surface. The measured contact angles in the Cassie state were increased with increasing air fraction, in agreement with the theoretical prediction.     

Wetting of β-casein layers adsorbed at the solid–aqueous interface

The wetting by water of the adsorbed layer of β-casein on hydrophobised silica and pure (hydrophilic) silica surface was investigated by dynamic contact angle measurements based on the Wilhelmy plate principle. The results are discussed in relation to adsorption data obtained for the protein on similar surfaces by in situ ellipsometry. β-casein adsorption on a hydrophobic surface leads to a significant decrease of the contact angle, in particular in terms of the receding contact angle, which decreased by about 70°. This indicates a strong shielding of the hydrophobic surface by the hydrophilic domain of β-casein. Adding a specific enzyme, endoproteinase Asp-N, which previously has been proposed to remove a large fraction of the hydrophilic segments, results in a significantly decreased wettability of the solid surface. The layer is now more hydrophobic and the hysterises is much smaller. The receding contact angle after the proteolysis is roughly 70°. The results are consistent with the hypothesis that β-casein adsorbs at the hydrophobic surface to form a monolayer with the hydrophobic part of the protein anchored at the surface, leaving the hydrophilic segments dangling into the solution. Less dramatic effects are observed in terms of changes of the wettability on the hydrophilic surface. The surface is still quite hydrophilic both after adsorbing β-casein and exposing the layer to endoproteinase Asp-N. These results confirm the differences in the structure of β-casein layers on the hydrophobic and hydrophilic surface.     

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.     

Influence of the work of adhesion on the dynamic wetting of chemically heterogeneous surfaces

The velocity dependence of the dynamic contact angle for a glycerol-water mixture wetting two different chemically heterogeneous surfaces (mixed thiols on gold and partially methylated titania, 16 samples in all) was studied. The molecular kinetic theory (MKT) of wetting was used to interpret the dynamic contact angle data. The equilibrium displacement frequency ( K 0) was predominantly determined by the viscous contribution from the bulk liquid, with a minor contribution from the surface. The mean distance between surface sites (lambda) decreased with increasing work of adhesion. The contact line friction coefficient zeta 0 was found to vary exponentially with the work of adhesion, enabling the unit flow volume of the liquid to be obtained.     

Modification of the wettability of a polymeric substrate by pH effect. Determination of the surface acid dissociation constant by contact angle measurements

The wetting properties of a substrate can be changed by chemical reaction. Here, we studied simple materials with acid-base properties, by preparing poly(vinyl chloride) films containing lauric acid. These substrates constitute simple polymeric surfaces the wettability of which can be easily controlled by the acid-base equilibrium. The roughness of the material was then varied by adding Aerosil (hydrophobic fumed silica). We then studied the wettability of these materials toward aqueous buffer solutions between pH 2 and 12 from contact angle measurements. The variation of the contact angle of a droplet of buffer solution with the pH of the solution was described by a simple thermodynamic model requiring only two parameters. Thus, we could characterize the acid polymer by an effective surface acid dissociation constant the value of which was consistent with those obtained with a similar surface. We showed that the behavior of any substrate could be described even if the surface geometry was not well-known.     

Particle-surface capillary forces with disjoining pressure

A new, atomic force microscopy (AFM) based experimental setup for the continuous acquisition of friction force data as a function of humidity has been developed. The current model of interactions between wet contacts under the influence of capillary effects, has been amended to include a vertical component due to the disjoining pressure and takes into account the influence of liquid films adsorbed on the surface. This is a 'switching' model, i.e. the contact between nanometer-sized sphere and a flat surface can exist in two distinct states due to capillary bridge formation/destruction as the humidity is varied. The model has been qualitatively verified on samples of differing wettability produced by UV-ozone treatment of polystyrene (PS). Results of AFM analysis of the friction vs. vapor pressure curves collected from the surface are presented. Correlation between important surface properties such as wettability, adsorption, and contact angle and friction force under varying humidity were found and discussed.     

Contact-line friction of liquid drops on self-assembled monolayers: chain-length effects

The static and dynamic wetting properties of self-assembled alkanethiol monolayers of increasing chain length were studied. The molecular-kinetic theory of wetting was used to interpret the dynamic contact angle data and evaluate the contact-line friction on the microscopic scale. Although the surfaces had a similar static wettability, the coefficient of contact-line friction zeta0 increased linearly with alkyl chain length. This result supports the hypothesis of energy dissipation due to a local deformation of the nanometer-thick layer at the contact line.     

WETTABILITY OF DRUG LOADED POLYMER MATRICES

Drug release is to a large extent influenced by penetration of a dissolution liquid into a polymer matrix. If an aqueous medium does not wet a matrix, its penetration into the polymer bulk and the resulting drug extraction would be considerably hindered. It is therefore of extreme importance to study not only the physical state of drug loaded matrices but also their wettability and their penetration by an aqueous medium.

In the present review paper we describe the results of two investigations, performed in our laboratory and having direct relevance to the medical and pharmaceutical fields: the estimation of wettabilities of polymer tablet formulations and of drug loaded polymer films. For tablet formulations it was clearly demonstrated that the use of high-viscosity polyols for contact angle and penetration experiments yielded incorruptible data which enabled to determine mean pore size of tablets from the Washburn equation. For drug-loaded cast films, as exemplified for SIBA (a cytostatic drug)-loaded ethylcellulose cast films, the choice of the solvent appeared to play a determinant role on the wettability and heterogeneity of films.