How to Compute the Contact Angle inside an Opaque Capillary Tube: A Universal Equation

Capillarity is a ubiquitous and important phenomenon in nature. The Jurin's law establishes a relationship between the contact angle and the liquid rising height inside a capillary tube and is widely employed to evaluate the wettability of transparent tubes since 1717. However, it fails once encounters the opaque counterparts because of the invisible rising height. Here, an idea that correlates the contact angle with an intrinsic property of a matter, i.e., the mass is proposed. A universal equation is thus established to compute the contact angle using the liquid mass inside the capillary tube. The equation is systematically verified against the height measurement method adopting a series of quartz capillary tubes, where a good agreement is attained. An in situ approach of high sensitivity is hence derived and demonstrated to evaluate the capillary tubes regardless of the wettability, transparency, or materials. A theoretical basis is provided to assess the surface wettability inside capillary tubes in a more general way and thus a new avenue is opened to investigate the heat and mass transfer under spatial limitation with well-defined surfaces for portable devices, flexible electronics, etc.

Automated summary

This study proposes a universal equation based on liquid mass to calculate the contact angle inside a capillary tube, and verifies its validity through experiments. The method is not affected by the transparency, wettability, or material of the capillary tube, providing a new and highly sensitive in situ method for evaluating capillary tubes. The study provides a theoretical basis for investigating heat and mass transfer under spatial limitation with well-defined surfaces in portable devices, flexible electronics, etc.