# Dynamic Meniscus Profile Method for Determination of the Dynamic Contact Angle in the Wilhelmy Geometry CCCCCCC

We have presented in  a real time hybrid experimental /numerical method for determination of the macroscopic dynamic contact angle in the Wilhelmy geometry: a vertical homogeneous solid cylinder/plate is moving vertically with constant velocity U in a tank of liquid in the partial wetting regime as shown in the figure. This method is based on the hydrodynamic model of Voinov which takes into account the viscous pressure in the determination of the shape of the stationary meniscus [2,3]. It allows one to obtain numerically with high precision the stationary shape of the dynamic meniscus profile (and from there the angle of the meniscus slope) via Voinov's equation using the experimentally determined meniscus height H0=Z(X0) at certain distance X0 to the cylinder /plate in the macroscopic region.

Schematic drawing of the experimental system in the Wilhelmy  geometry

The numerical code for solving Voinov's equation is posted on this page in C++. Also a Java-application is posted for obtaining the meniscus profile and the angle of the meniscus slope in the neighborhood of X0 which just needs the following input parameters: the dynamic viscosity η given in mPa . s, the surface tension γ in mN/m, the density ρ in kg/m3, the velocity of the plate U in mm/s, the height H0 in mm at X0 in μm. In the case of a cylinder one needs also the radius of the cylinder r in  mm. The initial values given in the boxes are the values of the corresponding quantities used in the experiment in .

For a plate:

start the Java-application (DMPM.html)

For a cylinder:

1. Stanimir Iliev, Nina Pesheva, Dynamic meniscus profile method for the determination of the dynamic contact angle in the Wilhelmy geometry, (submitted to Col. Surf. A).
2. Voinov, O. V. Fluid Dyn. 1976, 11, 714.;
3. Maleki, M.; Reyssat, E.; Quéré, D.; Golestanian, R. Langmuir, 2007, 23, 10116.
4. Forsythe, G. E.; Moler, C. B. Computer Methods for Mathematical Computations, Prentice-Hall: Englewood Cliffs, NJ, 1977.
5. Lee, H.J.; Schiesser, W.E. Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB, Chapman & Hall/CRC Press, Boca Raton, 2004.

Modified date:22-03-2011