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Given the importance of dynamic contact angle, its numerous applications andthe complexity and difficulty of use of available approaches, here we present anew simple semi-empirical models for estimation of dynamic contact angle'sdependence on the wetting line velocity. These models should be applicable toany geometry, a very large range of capillary numbers and static contact anglesand all solid-liquid-gas systems without requiring further experiments. Twosimple equations are intuitively derived from the most promising theoreticaldynamic contact angle models, the hydrodynamic and the molecular-kineticmodels. Then the models, along with the basic form of the Hoffman model, arefitted to a large pool of data. The data are extracted from numerous studiesand cover over 5 decades of capillary number, include static contact angles upto the superhydrophobic region and comprise of various geometries. Theresulting models are compared to each other where the hydrodynamic model'spredictions are found to be superior to the other two models by all statisticalmeasures. Then, noting that the molecular forces become dominant at lowercapillary numbers we separate the data into low and high capillary regions andrepeat the process. There was only a minuscule difference between the resultsobtained for general models and high capillary models ($\textrm{Ca}>10^{-4}$)but the empirical approach resulted in the most accurate model at low capillarynumbers ($\textrm{Ca}<10^{-4}$).

Simple Model for Estimation of the Influence of Velocity on Advancing Dynamic Contact Angles