I want to comment with you this imaginary problem. I have not formulated it yet. But I would want your qualitative opinion about this. It is not anything new or revolutionary, because electromagnetic control of boundary layers have been proved yet. But I would want to understood mathematically the proccess. I hope this thread have more success than others usually un-answered, I'm starting to feel myself "understood". I am thinking seriously of moving into differential equation forum. Last times I have more success there. There's a free air stream subsonic (Ma<<<1) over a plain surface. The initial data line is u=uo; v=0. (stream parallel to surface). Well, surely you know that it exists some methods for avoiding flow separation. One of them was improved by Von Karman, he proposed a flow suction trough the porous wall of the surface. Thus, it can be demonstrated by the Von Karman integral equation that such suction pushes forwards the critical point of separation. After this introduction, and under the hypothesis I have no idea of Magneto-Hidrodinamics at all (I'm only 22, sure it will be time for it), let's imagine next experiment. The surface, which would be an airfoil one, is connected to a DC electrical battery. One of its electrodes, the positive one, is connected to mass, and the other is connected to airfoil surface. Then, the complete airfoil has a negative potential respect to mass. Because of Maxwell Equations, a potential field V is generated over the infinite semiplane above the surface. If fluid freestream has electrical conductivity, its electrical charges would sense such potential, and eventually positive charges would experiment an atraction force to the airfoil surface, avoiding at first glance the flow separation. First of all, I'm not able to formule the problem. Since I do not understood which equations govern this event, I am not capable of judge its behaviour. Is the electrical field generated by the surface being perturbated by the flow?. I mean, does it exists a convective transportation of electrical field or something like this?. It can be resumed if I'm allowed to use the Laplace equation (derived from 1st Maxwell equation) in order to solve the static electrical potential field. And another question is: the air would be ionized passing over the surface, but what occurs with negative charges?. They would esperiment a repulsion force, wouldn't they?. I want to simulate this proccess numerically, I think maths here are easy enough, because integration of the Parabolized Navier-Stokes equations are not a problem yet, but I'm not capable of seeing the link between Navier-Stokes and Maxwell equations. Surely there is some coupling between them.
Hmm... to start with - don't really understand what you're talking about and what you're asking and why all the math. I'll try to answer something, charges - electrons can be released from a surface when they are supplied with enough energy- overcome a certain potential barrier. This can be achieved if there's a high enough potential drop - which happens in a conductor, and air is also a conductor, though a poor one, and due to surface impacts which provide enough energy for the charges to escape (could also be chemical reactions which lower the potential barrier). Live long and prosper.
The fact of I'm saying something with no sense is perhaps one of the solutions of my problem. But to be honest, I think this is the trivial solution. I hope for a non-trivial solution.