Dynamics of Partial Wetting

Abstract

The kinetics of partial wetting was investigated for the case of spreading of cylindrical and axisymmetric drops over a horizontal solid surface under the action of capillary forces. The Brochard-Wyart and de Gennes (1992) relation, having a cut off of molecular size below which the continuum theory breaks down, is used to provide a dynamic contact angle boundary condition. The dynamic contact angle relation and the viscous dissipation are shown to be valid even in the case of axisymmetric spreading when using the approximation of a wedge flow pattern near the leading edge. To obtain an analytical solution for the dynamics of spreading, the departure of the outer region solution from the spherical cap profile, near the inflection point, was neglected, and the accuracy of the approximation was examined. The analytical solution obtained is a powerseries expression. Simple short-time and long-time asymptotic solutions are also provided. The model for the dynamics of partial wetting does not require any fitting parameter. The results are found to agree favorably with the available published experimental data even at dynamic contact angles as large as about 90°, which is beyond the range of applicability of the lubrication theory. The model matches very closely the dynamics of spreading obtained with a previous model by Chebbi (2010), in which a numerically similarity solution was used to account for the deviation from the spherical cap profile near the inflection point.