The discussion revolves around the free surface problem in electrohydrodynamics, specifically addressing the relationship between bulk charge density in an electrified fluid and the potential existence of surface charge. Participants explore theoretical implications, mathematical relationships, and the behavior of electric fields in and around the fluid.
Participants do not reach a consensus on whether a surface charge necessarily arises from a bulk charge density. Multiple competing views exist regarding the relationship between bulk charge, surface charge, and the behavior of electric fields.
Participants note that the assumptions regarding charge distribution and fluid motion may affect the conclusions drawn about surface charge. The discussion also highlights the complexity of the problem, with references to different scenarios and mathematical approaches that may yield varying results.
I don't know. It's certainly something that I'm not going to be concerned about when I deal with variable charge density, although I am curious where the term ##\rho_{v}\mathbf{u}## comes from. That would couple the variable charge density very nicely.renormalize said:So do you agree that the authors meant to write ##\nabla## and that their eq.(2) is therefore not nonsense?