Here, we concentrate on the influence of small (physical We consider a simplified model for the line pinning of a contact roughness) defects on the uncoated substrate and in particuline on a single (physical) spherical heterogeneity, and we show lar the so-called line-pinning effect (3) which such defects that this problem is related to the capillary problem of pushing a exert on the free surface as it passes over them. small spherical object through a liquid/gas interface. The model In (4), the microscopic pinning of a contact line on a predicts that the contact line pins, distorts, and finally slides across single heterogeneity (5) was investigated in a series of carethe defect and is in agreement with experimental results. Furtherfully conducted experiments. A variety of phenomena was more, it gives an explicit criterion for the onset of sliding. The observed including sticking, stretching, and jumping of the associated sphere/interface problem shows similar characteristics.
contact line. Some of the results were compared with approx-We suggest that further modeling of line pinning phenomena should concentrate on modeling the capillary aspects as accurately imate models (3, 6) based on the assumption of small contact as possible, a numerical approach being unavoidable if the essenangle and point heterogeneity. In the experiments described tially three-dimensional problem is to be modeled properly. แญง 1996 in (4), the contact angle was in fact about 90ะ, but a little Academic Press, Inc.
reflection will confirm the fact that, regardless of the value Key Words: line-pinning; capillarity; surface tension; perturbaof the contact angle, for a phase boundary in contact with tion.
a sphere there are always configurations for which the slope of the liquid/gas interface is not small (see also boundary condition [5] in the next section). Both models (3, 6) are of the substrate is also taken into consideration (with subse-