Running Drops on a Solid Planar Surface

We now return to the case of reactive wetting. The capillary example described above is relatively straightforward to analyze. Unfortunately, it is quite a challenge to obtain good, clean surfaces (free of hysteresis) inside a capillary tube. That is the reason why running drops were first observed and studied on planar, horizontal surfaces. 

The ingredients remain the same, although the hydrodynamics is slightly more complicated to handle. We can use the same framework as developed while analyzing the behavior of drops in a wettability gradient, the only difference being that here the drop itself imprints its own gradient S  

We expect the result to be U oc y/lc, where c is the surfactant concentration, which controls r via equation (10.42). These predictions are reasonably well borne out by the experiments reported in reference 14. 

A breathing mode, whereby the drop remains centered on a fixed point but changes its degree of spreading. 

A polar mode, whereby the center of gravity moves. This mode is unstable and gradually spawns a translational motion that ultimately reaches a constant velocity. 

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