How to Compute the Contact Angle inside an Opaque Capillary Tube: A Universal Equation. Issue 5 (25th January 2022) - Zhao, Kaiqi; Sun, Lidong
Abstract: 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. Abstract : A universal equation is established to compute the contact angle inside capillary tubes. A feasible and facile approach is hence developed with the equation and exhibits less limitations to contact angle measurements, such as wettability, transparency, and materials. The findings broaden the spectrum of available capillary tubes for fundamental studies bridging the practical applications.