23 research outputs found
A model for the behaviour of fluid droplets based on mean curvature flow
During his experiments W. D. Ristenpart made a very remarkable discovery. If
two oppositely charged droplets of fluid are close enough, at first they
attract each other and touch eventually. Surprisingly after that the droplets
are repelled from each other, if the initial strength of the charges is high
enough. Otherwise they coalesce and form a big drop, as one might expect. We
present a theoretical model for this observation, using mean curvature flow.
With the help of appropriate barriers for the flow we can predict the observed
droplet behaviour. This shows that, contrary to general belief, decreasing
surface energy can explain the phenomenon. The barrier construction includes a
new proof for the existence of multiple mean curvature flow evolutions of
certain double cones, first discovered by Angenent, Chopp and Ilmanen. Our
proof yields a slightly stronger result