Solution (source code)

= Solution

<Wetting> concerns how a liquid covers a solid in contact with another phase, such as its vapor. For an ideal flat homogeneous surface, balance of the three interfacial tensions gives <Young's equation>
$$
\boxed{\gamma_{SV}-\gamma_{SL}=\gamma_{LV}\cos\theta,}
$$
where the <contact angle> $\theta$ is measured through the liquid. Small angle means favorable contact; partial wetting gives a finite angle. The spreading coefficient $S=\gamma_{SV}-\gamma_{SL}-\gamma_{LV}$ compares a covered surface with a dry one. Positive $S$ favors <complete wetting>, while negative $S$ permits a finite-angle droplet in the partial-wetting regime.

A sessile-drop experiment images the tangent at the contact line on a clean level substrate. Varying drop volume slowly distinguishes advancing and receding angles; their difference is <contact-angle hysteresis> from pinning and heterogeneity, so a single observed angle need not equal the ideal equilibrium value. A capillary-rise experiment gives a second consequence: the <Young–Laplace equation> and hydrostatic balance predict $h=2\gamma_{LV}\cos\theta/(\rho g r)$ in a narrow circular tube when meniscus-volume corrections are negligible. A wetting liquid rises, whereas a sufficiently nonwetting one is depressed.