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.

Dynamics of Thermocapillary-Driven Motion of Liquid Drops

“…24 The ultimate splitting of the drop suggests that the method can be a compelling substitute to other methods. 24 Chebbi 26,27 used Brochard-de Gennes dynamic boundary conditions 4,16 to model the partial wetting of drops on the solid surface using (i) an analytical approach assuming a nearly circular profile 27 and (ii) a numerical approach to account for deviations from the spherical cap. 26 Both approaches gave very close results with good agreement with experimental data from three different publications, including data from Hocking and Rivers.…”

Onset of Area-Dependent Dissipation in Droplet Spreading

“…For a system with a well-defined volume Ω the relaxation time τ of the exponential decay is a function of Ω, θ e , and the fluid viscosity η. In the limit of small contact angles, there are several different predictions for τðΩ; θ e ; ηÞ [32,[34][35][36][37][38][39], but there is a dearth of experimental systems where τ can be systematically probed as a function of all three variables. The lack of experiments is largely due to the fact that contact angle pinning is the bane of careful dynamics measurements especially at small contact angles [40] and can occur at even dilute concentrations of defects [41].…”

“…The relaxation time, however, does depend on whether the droplet is advancing or receding towards θ e . Previous studies [32,[34][35][36][37][38][39] predict that, because the dominant mechanism for dissipation is viscous dissipation near the contact line, τ ∝ Ω 1=3 [see Eq.…”