In particular, when dealing with the interaction between a liquid and a solid phase, the term adhesion is used to describe the attraction between the particles of both phases, and cohesion refers to the attractive forces between the particles within one phase. Cohesive forces arise due to electric interactions between particles and are often called Van der Waals forces, named after their discoverer. These can be very strong in polar substances like water or significantly weaker in non-polar substances, where induced dipoles arise due to collisions between particles, leading to temporary charge separations.
If adhesion is stronger than cohesion, the liquid spreads out and completely wets the surface. If cohesion is stronger, the liquid is repelled from the surface, forming spherical droplets. Electrical attractive forces between particles play a key role in adhesion as well. Adhesive forces depend on the chemical and physical properties of both substances involved.
Let us now analyze these interaction processes between different materials in more detail. In addition to the interface between liquids and gases discussed in the previous section, we must now consider the more general case of interfaces between solid (1), liquid (2), and gaseous (3) phases. For each of these interfaces, an interfacial tension $\sigma_{i,j}$ is introduced, which is equal to the specific interfacial energy $\varepsilon_{i,j}$.
The indices $i$ and $j$ can each take on integer values from 1 to 3. For example, $\varepsilon_{2,3} = \sigma_{2,3}$ represents the surface tension of a liquid. As with water, $\varepsilon_{2,3}$ must always be positive to maintain stability; otherwise, the particles would escape into the gas phase.
The interfacial energy $\varepsilon_{1,2}$ is directly linked to the adhesive forces between the liquid and the solid. The interactions between the gas and solid phase are described by $\varepsilon_{1,3}$. These three interfacial tensions $\sigma_{i,j}$ result in tangential forces at the interfaces, causing a deformation — imperceptible in solids, but more pronounced in liquids — such that the net force at the contact point of all three phases vanishes.
By projecting $\sigma_{2,3}$ onto the tangential direction of the solid interface, we obtain the Young's equation:
$$
\boxed{\sigma_{1,2} + \sigma_{2,3}\cos\varphi - \sigma_{1,3} = 0}
$$
or, rearranged for $\cos\varphi$:
$$
\cos\varphi = \frac{\sigma_{1,3} - \sigma_{1,2}}{\sigma_{2,3}}
$$
If $\sigma_{1,3} > \sigma_{1,2}$, then $\cos\varphi > 0$ and thus $\varphi < 90^\circ$. The liquid forms a concave curved surface and wets the surface — e.g., water in a glass container with a contact angle of about $20^\circ$. This curved surface is known as a meniscus. When reading a scale in such a container, one must always read from the bottom of the meniscus to avoid incorrect volume readings.
In the opposite case, $\sigma_{1,3} < \sigma_{1,2}$, the angle $\varphi > 90^\circ$, resulting in a convex curved surface. An example is mercury in a glass container, where increasing the solid–gas interface area is energetically more favorable.
If a thin tube (called a capillary) with inner radius $r$ is placed in a liquid, the liquid rises inside the tube to a height $h$ above the external liquid level due to interfacial tension. This phenomenon is known as capillarity.
The corresponding increase in potential energy is:
$$
\Delta E_\mathrm{pot} = mgh = V\varrho g \Delta h
$$
With the volume of the cylinder $V = \pi r^2 h$, we get:
$$
\Delta E_\mathrm{pot} = \pi r^2 \varrho g h \Delta h
$$
At the same time, the surface energy changes according to the cylindrical surface area $A = 2\pi r h$:
$$
\Delta E_\mathrm{O} = - (\sigma_{1,3} - \sigma_{1,2}) 2 \pi r\Delta h
$$
Using Young's equation and knowing that $\sigma_{2,3} = \sigma$ (the surface tension), this simplifies to:
$$
\Delta E_\mathrm{O} = 2\pi r \sigma \cos{\varphi} \Delta h
$$
A stable height is reached when $\Delta E_\mathrm{pot} = -\Delta E_\mathrm{O}$. Solving for $h$ yields:
$$
\boxed{h = \frac{2\sigma\cos\varphi}{r g \varrho}}
$$
By measuring the height and the contact angle, the surface tension of a liquid can be easily determined.