Dynamic Meniscus Profile Method for determination of the dynamic contact angle in the Wilhelmy geometry

We present here a real time hybrid experimental/numerical method for the determination of the angle of the stationary meniscus slope in the Wilhelmy geometry: a plate or a cylinder is immersing/withdrawing at constant speed in a bath of liquid. This method, which we call the Dynamic Meniscus Profile Method is based on the general hydrodynamic model of Voinov (Fluid Dyn. 11 (1976), 714) which takes into account all three contributions: the capillary, the gravitation and the viscous pressure terms in the determination of the shape of the stationary meniscus. From Voinov's equation, imposing as boundary condition the experimentally determined meniscus height at certain distance to the cylinder/plate, one obtains numerically with high precision the shape of the stationary dynamic meniscus profile in the whole system domain. From the dynamic meniscus profile as function of the distance to the plate one obtains the angle of the meniscus slope. We apply the suggested method using experimental data and demonstrate its effectiveness. We show that the obtained contact angles by the Dynamic Meniscus Profile Method versus capillary number agree very well with the experimental results obtained by the Tangent line method and this is quite evident for all values of the capillary number Ca. In order to illustrate the advantages of the suggested method we compare the obtained solutions for the meniscus profile and the dynamic contact angle with the results of the often used so far static approximation methods and with asymptotic solutions of Voinov's equation. The comparison reveals that the effect of the viscous pressure is not negligible. The use of the static approximation methods and the asymptotic solutions for the determination of the dynamic contact angle is not justified even for not very high values of Ca.

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► A method for precise determination of the dynamic contact angle is presented.
► Its effectiveness is demonstrated using experimental data.
► A comparison is made with the results of other methods.