Recent content by hunt_mat

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.

I'm familiar with Fickian diffusion.

The question remains, as my model includes electric fields, fluid velocity and a free surface, what equation do I add to close the system for surface charge?

I had a look at their paper, and it looks like nonsense to me. In their equation (2), they seem to mix vectors and scalars in a single equation. However, if one makes the simple assumption of Ohm's law, [\itex]\mathbf{J}=\sigma\mathbf{E}[/itex] then you're led down a rather odd route. I thank...

The surface is also moving. So could it theoretically move with the charge, so no surface charge forms?

My MHD paper is apparently too large to upload.

I am familiar enough to have written a paper on free surface flows in MHD in the Journal of Plasma Physics, so I'm fairly familiar with that particular aspect of the MHD literature. I have enclosed the paper in question. I have also included a copy of my paper on EHD without any charges. I am...

I have written down the set up of the problem I'm interested in here.

If I'm considering only small perturbations from the equilibrium, then it's still a good assumption?

So I can ignore surface charge for my problem, then?

Isn't the normal component of the \mathbf{D}=\epsilon\mathbf{E} continuous across the boundary if there is no surface charge?

Surely only the tangential part of the electric field is continuous at the boundary. You have to make a calculation for the normal component of the electric field. If the forces aren't too large, then should there be no surface charge? Or, at the very least, the assumption of no surface charge...

Yes. I have solved the result when there is no electric charge, I thought that the next logical step(for a mathematician that is) is to look at the case where there is a constant charge density within the fluid.

Unfortunately, the fluid is infinite in extent.

That is something to be found as part of the solution. I'm connecting the Euler equations with Maxwell's equations to find the resulting shape of the free surface.