# Application Note: Running Off

Droplets stuck on roughness

Some people run off to pursue their dreams, politicians have run-off elections, copy machines run off multiple copies; and when things are going good, water runs off your roof without causing damage. You want water to run off your clothes when being worn but to wet them in the wash. We could run on with more run offs, but it’s more interesting to ponder the last on-off problem.

How does one control liquid running on or off a surface? Certainly surface tension and liquid-solid adhesion are properties that strongly influence wettability. Another is the geometrical structure of the surface, that is, whether it is rough or smooth. Surfaces that look smooth to the eye often have ridges and grooves several microns (10-6m) deep. Such small features would not seem to be important, until one realizes that surface forces increase in importance compared to other forces with decreasing physical size. For example, surface tension forces in water at micron scales are typically orders of magnitude larger than viscous and gravitational forces.

Consider the classical dilemma faced by researchers trying to understand how a liquid moves across a solid surface. It is argued that it should not be possible for liquid to move onto dry solid because viscous stress requires the liquid velocity at the solid surface to be zero. A rough surface, however, can smooth the way by accommodating liquid stuck on rough protuberances while allowing flow across the grooves. From a macroscopic point of view, the liquid appears to “slip” over the surface.

Another dilemma resolved by roughness is how small drops of water are seen to remain stationary on a clean window. On a smooth surface the adhesion force between the liquid in a drop and the window cannot affect the net force on the drop since it acts uniformly in all directions. Roughness can explain this behavior as shown in the FLOW-3D simulation at the side of this article.  The water drop (left frame) has a contact angle of 60° and remains stuck on a vertical surface with 2mm grooves (middle frame) because the contact lines cannot bridge the gaps between ridges. On a smooth surface (right frame) the drop slides downward.

The importance of surface tension at the micron scale explains why an accurate treatment of surface tension is crucial for modeling what goes on in micro-mechanical-electrical-systems (MEMS). Get into the running with your MEMS ideas by running them through FLOW-3D.