Discussion of the Question 12/02
CHARGED DROPThe question was:
The shape of a freely suspended liquid drop is kept spherical (with radius R) by the surface tension g. [For simplicity we assume weightlessness.] Assume that the liquid is conducting and it is being gradually charged. What will happen as the charge Q increases?
(6/05) Y. Kantor: Finally we have some progress on the problem. We got (2/6/2005) a suggested solution from J.I.I. de la Torre (e-mail nacho@usal.es). (His solution can be found in the following PDF file.) He compares the total energy (electrostatic energy+surface energy) for two cases: a single spherical drop, and two spherical drops with total volume equal to the volume of the original (single) drop. He finds that when the charge Q exceeds certain value that is defined by the volume of the original drop and the surface tension, the system would prefer to be split into two spherical drops.
What does it mean? It means that single drop solution is NOT a global minimum if the charge is too large. At this point, however, it is not clear whether for even smaller charges one can find geometrical configurations that have a lower energy than a single drop. Moreover, it has been shown that for certain charges the single drop geometry is not a global minimum. But is it a local minimum? I.e., is the spherical configuration locally stable?
(7/05) Later (27/7/2005) we recieved an extension of the solution mentioned above. It can be found in the following PDF file. This work shows that for sufficiently high charge the configurations should be unstable. It, however, does not consider all possible modes of local instability.
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