Dynamics of Total Wetting

Lellah and Marmur performed a different but equivalent set of measurements. They monitored the increase in the horizontal radius R t) of a wet spot. The spreading lasts typically from a few hours for ordinary liq- 

FIGURE 6.9,. Spreading of a drop on a solid surface in total wetting regime. With the naked eye, an observer can see the drop, but not the precursor film. 

The results can be expressed in terms of a contact angle Oq which depends on the spreading time t. When surfaces are smooth and clean, and for non-volatile liquids, the law is remarkably universal. It is known as Tanner s law  

The explanation for this puzzle is related to another experimental fact, which Hardy observed long ago. It turns out that ahead of the drop is a precursor film a few nanometers thick, which extends much farther out than the drop itself. Hardy detected the existence of this film with very clever techniques. In one of them, he used a tiny glass rod resting on the substrate at a finite angle. As long as the surface remained dry, friction held the rod in place. But as soon as the liquid film reached the rod, its lubricating effect loosened the contact and caused the rod to fall. For a detailed review of these phenomena, the reader is invited to consult the literature. 

The precursor film is evidence of the great force F acting on its boundary. The liquid is rapidly drawn toward the periphery in the form of a film whose thickness is roughly the pancake thickness defined in chapter 4. But behind the film, where Tanner physically saw the edge of a drop, the forces involved are quite different. Within the drop are the forces of traction —7sl — y cos Od) whereas in the film proper (characterized by a zero angle) are the forces 75L + 7- The net force acting on the drop is then only 

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