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Depending on the contact angle, liquids can be classified as nonwetting ({{90}^{\circ }}<\theta <{{180}^{\circ }}), partially wetting ({{0}^{\circ }}<\theta <{{90}^{\circ }}), or completely wetting (\theta ={{0}^{\circ }}). When a small amount of liquid is brought into contact with an initially dry solid surface, the liquid behaves in one of two ways: (1) if the liquid does not wet the solid it may break up into small droplets, or (2) if the liquid wets the solid it may spread over the solid surface and form a thin liquid film. Wettability can be attributed to a strong intermolecular attractive force near the interface between the solid and liquid. The thermodynamic definition of surface tension, eq. (2.212), establishes that there is a significant decrease in the surface free energy per unit area in a wetting liquid. Spreading of a liquid on a solid surface can be described by the spreading coefficient Sp, defined as

S{{p}_{\ell s}}={{\sigma }_{sv}}-{{\sigma }_{\ell v}}-{{\sigma }_{s\ell }}


which is a measure of the ability of a liquid to spread over a solid surface. The spreading coefficient defined by eq. (1) is difficult to evaluate, because data for σsv and {{\sigma }_{s\ell }} are not available for most substances. Substituting eq. (10) into eq. (1), one obtains

S{{p}_{\ell s}}=-{{\sigma }_{\ell v}}(1-\cos \theta )


For a partially wetting liquid ({{0}^{\circ }}\le \theta \le {{90}^{\circ }}), \cos \theta \le 1 and the spreading coefficient S{{p}_{\ell s}} is always negative, which means that the liquid will partially wet the solid surface and an equilibrium contact angle can be established.

The discussion thus far has treated the three phases – solid, liquid, and vapor – as though their boundaries were sharply-delineated lines or surfaces. This idealization, which serves as a useful analytical device at the macroscopic level, does not hold at the microscopic level. At that level, the interfaces between phases appear as regions over which properties vary continuously, rather than as lines or surfaces with discontinuous property changes. Intermolecular forces of both repulsion and attraction influence how material in the various phases is distributed throughout these interfacial regions. Adsorption – which is one of the consequences of this intermolecular action – occurs when a liquid or solid phase adjacent to a second phase (solid, liquid, or gas) retains molecules, atoms, or ions of the second phase at the shared interface. Adsorption affects the wetting process because it alters the interfacial tension of the solid-liquid interface. Introducing the surface pressure of the adsorbed material on the solid surface, ps:

ps = σsv − σsv,a


where σsv,a is the interfacial tension with the absorbed substance present. Young’s equation, eq. (10), can be rewritten as

{{\sigma }_{\ell v}}\cos \theta =({{\sigma }_{sv}}-{{p}_{s}})-{{\sigma }_{s\ell }}

Figure 1 Capillary phenomenon in an open tube (Faghri, 1995; Reproduced by permission of Routledge/Taylor & Francis Group, LLC).
Figure 1 Capillary phenomenon in an open tube (Faghri, 1995; Reproduced by permission of Routledge/Taylor & Francis Group, LLC).

which indicates that adsorption changes equilibrium contact angles and surface tension.

Surface tension, equilibrium contact angles, and capillary pressure determine the behavior of liquids in small-diameter tubes, slots, and porous media. The best example is the capillary rise of a wetting liquid in a small tube (see Fig. 1), in which case the capillary force is balanced by gravitational force. The pressure difference across the liquid-vapor interface in such tube is given by eq. (11). For tubes with a very small radius, the two radii of curvature RI and RII are the same, i.e.,

{{R}_{I}}={{R}_{II}}=\frac{r}{\cos \theta }


Substituting eq. (5) into eq. (11), one obtains the pressure difference between liquid and vapor at point C

{{({{p}_{v}}-{{p}_{\ell }})}_{C}}={{p}_{cap,C}}=\frac{2\sigma }{r}\cos \theta


The pressure at the flat surface A [see Fig. 1 (a)] is related to the vapor pressure by

pA = pv + ρvgH


where H is the height of the meniscus above the flat surface A. The pressure at point B inside the tube must be equal to that at point A because they are on the same horizontal surface, i.e.,

{{p}_{B}}={{p}_{v}}+{{\rho }_{\ell }}gH-{{p}_{cap,C}}={{p}_{A}}


Combining eqs. (6) – (8), one obtains

\frac{2\sigma \cos \theta }{r}=({{\rho }_{\ell }}-{{\rho }_{v}})gH


Capillary rise phenomena can be observed when the liquid wets the tube wall (\theta <{{90}^{\circ }}). If the liquid cannot wet the tube wall (\theta >{{90}^{\circ }}), the capillary rise H obtained by eq. (9) is negative, which indicates that there is a capillary depression, as shown in Fig. 1b.

In general, solid materials have only two types of behavior when they interact with water. They are either hydrophobic or hydrophilic. Hydrophobic materials have little or no tendency to absorb water, while hydrophilic materials have an affinity for water and readily absorb it. The criteria for hydrophobic or hydrophilic properties of a material is based on its contact angle {{\theta }_{Hydrophilic}}<\frac{\pi }{2},{{\theta }_{Hydrophobic}}\ge \frac{\pi }{2}

Hydrophobic materials can be observed as beading of water on a surface, such as a freshly waxed car surface. Hydrophilic materials allow water to wet its surface forming a film or coating. Hydrophilic materials are usually charged or have polar side groups to their structure that attract water.

There are many cases of hydrophobic surfaces in nature, including some plant leaves, butterfly wings, duck feathers and some insects’ exoskeletons. There are many synthetic hydrophobic materials available including waxes, alkanes, oils, Teflon, and Gortex. There are numerous applications for using these materials such as protection of stone, wood, and cement from the effects of rain, waterproofing fabrics and the removal of water from glass surfaces, such as a windshield, to increase transparency. Hydrophobic materials are also used for cleaning up oil spills, removal of oil from water and for chemical separation processes to remove nonpolar from polar compounds.

A hydrophilic material’s ability to absorb and transport water gives it numerous applications in cleaners, housings, cables, tubes and hoses, waterproofing, catheters, surgical garments, etc. A hydrophilic coating on a tube or hose eliminates the need for other lubricants, which is useful to prevent cross-contamination. Hydrophilic coatings on plugs and o-rings increase their ability to stop leaks; this is the basis for water-stop and sealants.

Another use for hydrophobic and hydrophilic materials is the storage and distribution of water and methanol in miniature direct methanol fuel cells (DMFCs). For the distribution of methanol, a material is chosen that wets methanol but is hydrophobic to water. This type of a material is a preferential wicking material. This allows neat methanol to be stored and distributed in a DMFC without water diffusing into the methanol storage layers. The water storage layer at the anode of the fuel cell is a hydrophilic material. It is not preferential to either water or methanol and provides a layer in which they can mix.


Additional Equations

\cos \theta =\frac{{{\sigma }_{sv}}-{{\sigma }_{s\ell }}}{{{\sigma }_{\ell v}}}


{{p}_{cap}}=\Delta p=\sigma \left( \frac{1}{{{R}_{I}}}+\frac{1}{{{R}_{II}}} \right)=\sigma ({{K}_{1}}+{{K}_{2}})



Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA.

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