Capillary Phenomena – Part II: Explicit Analytical Expression for Capillary Rise and Depression

In this second part, we present the explicit analytical expression of the framework introduced in Part I. The formulation yields closed-form predictions for capillary rise and depression in cylindrical geometries and extends naturally to a wide range of configurations. It shows that the contact angle, rather than being a primitive parameter, emerges as a measurable consequence of adhesive and cohesive forces. The resulting expression quantitatively links wettability to material properties, gravity and geometry, without recourse to empirical fitting parameters. Several interfacial phenomena are revisited within this unified description.