A study of the advancing interface

Abstract A molecular model has been developed which predicts the dependence of the dynamic contact angle upon the capillary number when a liquid moves to displace a gas. As a basis for this analysis we have assumed that molecules at the contact line between the advancing liquid and the solid substrate move forward by two different mechanisms. One involves the diffusion of liquid molecules across the solid substrate. This process is dominant when the dynamic contact angle is less than 120°, and the rate of surface diffusion increases with increasing values of the dynamic contact angle. The other process involves a “tank tread” motion of the liquid molecules normal to the solid substrate; this latter mechanism predominates when the dynamic contact angle is 180°. At contact angles between 120 and 180°, both processes come into play. From the model used in this analysis one finds that there are several molecular parameters which have some influence on the relationship between the dynamic contact angle and the capillary number. Although the effect of these parameters may be secondary in nature, it is likely that a universal correlation for the dynamic contact angle which is valid for all fluids and solid substrates must include these variables along with the capillary number and the static contact angle.