Capillary phenomena: New fundamental formula

TL;DR

This paper introduces a new fundamental formula for capillary phenomena that unifies thermodynamic and mechanical perspectives, incorporating factors like adhesion, cohesion, and geometry to better predict liquid behavior in capillaries.

Contribution

It presents a more general and coherent formula for capillary rise, linking apparent contact angle to physical parameters, and offers a method to measure surface tension without substrate effects.

Findings

The new formula aligns with classical results in specific cases.

It enables direct measurement of liquid-solid adhesive forces.

Provides a method for substrate-independent surface tension measurement.

Abstract

This study proposes a new fundamental formula that describes in a more coherent way, the rise and fall of liquids in capillaries. The variation of the contact angle classically associated with these phenomena appears to be the indirect result of a more authentic physical parameter, which we call the apparent capillary range. This range depends on factors expected to affect the contact angle, such as liquid-solid adhesion forces, liquid-liquid cohesion forces, liquid density, gravitational forces and the geometric shape of the capillary section. Our main objective in this work is not to criticize the classical theory, a task that has been largely accomplished, but to present a more general and coherent approach, which perfectly reconciles the thermodynamic and mechanical points of view and makes the interpretation of various configurations clearer. This new perspective can serve as a platform to guide researcher's efforts toward more promising results. In the first part of this work, we discuss the theoretical basis of the new formula using common examples. In the second part, we introduce the more explicit form of this formula, thus allowing a more precise quantification of wettability by providing access to the direct measurement of liquid-solid adhesive forces. The third part proposes a method for measuring static surface tension without the adverse effects of the substrate.