Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 2 / Section A(iii) / 18 / i / Solution

At a straight contact line, take forces per unit transverse length and measure the contact angle $\theta$ through the liquid. Solid–vapor surface tension pulls outward along the solid, solid–liquid surface tension pulls inward, and the liquid–vapor force has horizontal component ${\gamma }_{LV}\cos \theta$. Tangential equilibrium givesThis is Young's equation. The substrate supplies the normal reaction balancing the vertical capillary component. The original force sketch labels directions at a right-hand contact line. The result assumes smooth, chemically uniform, rigid surfaces in partial-wetting equilibrium, with negligible pinning and line tension.