APPROXIMATE SOLUTION FOR THE SPREADING OF A DROPLET ON A SMOOTH SOLID-SURFACE

The same approach used by Boender, Chesters, and van der Zanden in the context of an advancing liquid-gas meniscus in a capillary tube is ex tended to the case of spontaneous spreading of a droplet on an ideal s olid surface. The result is an ordinary differential equation for the droplet profile which can be solved if the meniscus inclination phi(0) , is specified at some distance lambda from the solid. As in the capil lary-tube case, good agreement is obtained with experimental data obta ined by the authors and by others if phi(0), is set equal to the stati c contact angle (zero in cases investigated experimentally), taking la mbda of the order of a molecular dimension (1 nm). A comparison of pre dicted dynamic contact angles in the spreading-drop and capillary-tube cases for given values of the capillary number indicates only a weak dependence of the behavior on the system geometry. De Gennes and co-wo rkers have predicted that during the final stages of spreading the inn er length scale lambda should be determined by the effects of disjoini ng pressure in the thin film adjacent to the contact line rather than by molecular dimensions. The lambda value implied by their model is de rived, thereby establishing the regime of spreading in which such effe cts should be dominant. The observed behavior in this regime is found to correspond somewhat better with a lambda value of the order of a mo lecular dimension, although the differences are small. Although the ex planation probably lies in the nonideality of even the smoothest surfa ces, this result suggests that the simplest model, based on a single l ambda value of the order of 1 nm, should provide an excellent predicti ve tool. (C) 1998 Academic Press.