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

Building on the work presented in Part I, which detailed the theoretical development leading to a new fundamental formula for the study and characterization of capillary phenomena, this second part introduces the explicit analytical form of that formula. This expression enables the treatment of nearly all problems related to capillary rise and depression. The analysis of capillary behavior within this new theoretical framework reveals that the concept of contact angle is, in fact, merely the manifestation of a more fundamental parameter, referred to here as the capillary range. Beyond its hypothetical nature, the contact angle proves to be a purely qualitative construct. An analytical expression for this angle is established, thereby allowing highly precise numerical values to be assigned to it. The proposed formulation explicitly accounts for the effects of the intrinsic nature of both the solid and the liquid, gravity, and the geometry of the capillary cross-section, without relying on arbitrary parameters. One of its principal strengths lies in its ability to quantify wettability with high accuracy. Other equally significant interfacial phenomena are also addressed within this same unified theoretical framework.