Science China Physics, Mechanics and Astronomy

, Volume 55, Issue 11, pp 2158-2166

First online:

A new look on wetting models: continuum analysis

  • JianLin LiuAffiliated withSchool of Pipeline and Civil Engineering, China University of Petroleum Email author 
  • , Re XiaAffiliated withSchool of Power and Mechanical Engineering, Wuhan University
  • , XiaoHua ZhouAffiliated withDepartment of Mathematics and Physics, Fourth Military Medical University

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In this study, we considered the wetting phenomenon on a general substrate from a new viewpoint of continuum mechanics. The analyses first show how the Wenzel and the Cassie models deviate the practical results in some special substrates, and then elucidate the mechanism of the triple contact line (TCL) moving. Based upon variational theory of the total free functional dealing with the movable boundary condition, we show that the macroscopic contact angle (MCA) expression is the corresponding transversality condition. It manifests that the MCA depends only on the chemical and geometric property at the TCL, and is not affected by the gravity of the droplet and the contact area beneath the liquid. Our continuum model also shows the exploration of the pinning effect on a sharp wedge or the interface between two different phases. This investigation will help designing super-hydrophobic materials for novel micro-fluidic devices.


continuum field energy functional transversality condition mechanism-based model triple line moving