A recently published experimental study by Xia and Steen examines the connection between the contact line velocity and contact angle of liquid drops on an oscillating substrate that display contact angle hysteresis. Of particular interest in this experimental study is the analysis of the dependence of contact angle deviation on contact line velocity. Indeed it is found that for small angular displacements, there is a linear relationship between the two. Moreover, the oscillating drop exhibits contact angle hysteresis that is much greater than that measured from quasi-static experiments. Here we use a phase-field model of dynamic wetting which directly includes the contact angle hysteresis to simulate the results of the aforementioned authors. A thorough derivation of the governing equations is presented, starting from the pioneering work of Cahn and Hilliard. Our model is unique due to the explicit inclusion of contact angle hysteresis, a phenomenon that has proven quite difficult to model. We demonstrate that by choosing appropriate parameters, our model can achieve very good agreement with experimental data. Further, we compare to our results to those computed using another model, further validating our method. We then investigate the effects of contact line friction and the hysteresis window, which are otherwise very difficult to explore experimentally. / Master of Science / When a drop of liquid comes into contact with a solid surface, it forms a semi-spherical cap having a fixed contact angle defined as that between the wall and the line tangent to the liquid drop, at the point where the liquid meets the solid. In recent decades, researchers in fields as varied as mathematics, physics, chemistry and materials science have studied the spreading and contraction of liquid drops on solid surfaces of various chemical compositions. Of particular interest to this paper is a phenomenon called `contact angle hysteresis' (CAH), in which a liquid drop can remain stationary at multiple distinct contact angles. The presence of hysteresis in physical systems significantly complicates the analysis of the physical problem and has been a motivating factor for the development of mathematical models that can contend with CAH. Here we present a model for describing the motion of liquid drops which explicitly takes CAH into account.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/110413 |
| Date | 02 June 2022 |
| Creators | Candelaria, Ariel Zachary |
| Contributors | Mathematics, Yue, Pengtao, Iliescu, Traian, Borggaard, Jeffrey T. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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