Simulating contact angle hysteresis using pseudo-line tensions
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esearch Letter
Simulating contact angle hysteresis using pseudo-line tensions Ping He
and Chun-Wei Yao, Department of Mechanical Engineering, Lamar University, Beaumont, TX 77710, USA
Address all correspondence of modeling and simulations to Ping He at [email protected] Address all correspondence of experiments to Chun-Wei Yao at [email protected] (Received 23 May 2019; accepted 27 June 2019)
Abstract Pseudo-line tensions are used in a continuum approach to simulate contact angle hysteresis. A pair of pseudo-line tensions in the receding and advancing states, respectively, are utilized to represent contact line interactions with a substrate because of the nanoscale topological and/or chemical heterogeneity on the substrate. A water droplet sitting on a horizontal or inclined substrate, whose volume is 4–30 µL, has been studied experimentally and numerically. Our simulation model predicts consistent hysteresis at four different droplet sizes compared with experiments. Meanwhile, the critical roll-off angles captured in simulations match well with experiments.
Introduction Contact angle hysteresis (CAH) is defined as the difference between the advancing and receding contact angles of a liquid droplet, which is immersed in a gas environment (normally the air), advancing or receding on a solid substrate. In general, CAH is understood to be mainly caused by the topological roughness, defects, and/or chemical heterogeneity of the substrate.[1] A specific study of water–ethanol mixtures on micropatterned substrates reveals that at different conditions of surface tensions and micro-patterns: (i) the advancing contact angle does not change much, and however, (ii) the receding contact angle largely varies because the receding mode is greatly affected by the formation process of the micro-capillary bridges connecting the nearby micro-structures.[2] More experimental results indicate that the advancing and receding processes are not the reverse of each other, but are quite different events that correspond to totally different activation energies.[3] Because of the topologically and chemically heterogeneous complexity involved in CAH, modeling the phenomena of CAH is a challenge. The original Young’s equation can only predict the equilibrium contact angle based on force balance at the contact line:
gLV cosuY = gSV − gSL
(1)
where θY is the equilibrium contact angle, also called the Young’s angle, and γ is the surface tension between two substances. The subscript L represents liquid, S solid, and V vapor. (In latter parts of this paper, σ is also referred to γLV for simplicity.) Gibbs et al.[4] suggested that line tension, in the same manner of surface tension, is the free energy along the contact line. Based on Gibbs’ concept, Boruvka and
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Neumann[5] modified the Young’s equation with an additional term of line tension to compute a non-equilibrium contact angle under the influence of line tension:
gLV cosu = gSV − gSL − gSLV kgs
(2)
where θ is the non-equilibrium contact angle, γSLV is the line tension (in units of joules
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