For around a number of years* I have been fascinated by droplets that are in gradients (shown in the movie by a colour gradient of the background), and are an undersaturated solution so are dissolving. They have been some cool experiments done that see droplets zipping along gradients and dissolving as they do so, in particular by Hajian and Hardt. But it is a hard system to model and to understand.
One question for a droplet that is dissolving in a gradient is: Does it dissolve into nothingness in place, i.e., without moving in place. Or does it zip along the gradient and only then dissolve, as in the movie above. There are two timescales here, one for dissolution, and one for movement along the gradient. Yhe behaviour depends on which timescale is longer.
There are two lengthscales in the problem: the length of the gradient (above, the width of the frame) and the size of the droplet. The droplet is always much smaller than the length of the system, and this tends to make the dissolution timescale smaller. The droplet radius has less far to go to hit zero. So the speed of the droplet along the gradient needs to be much faster than that of the droplet-solution interface.
This can be done if the droplet is somehow very fast moving, or if the droplet interface is very slow moving. The motion of the droplet surface can be controlled by the flux of molecules leaving it, which depends on the solubility of whatever molecules make up the droplet. If the solubility is very low then the flux off is small and dissolution can be slow enough for the droplet to move a long way before it dissolves, as it does above.
Chance & Necessity 