Migration of an ion in a non-conductive medium Someone asked me why, when performing DNA electrophoresis we need to put the gel inside a conducting buffer. Couldn't we just run it in distilled water?
My answer was that if we had distilled water we would not be able to close the circuit between the anode and the cathode of the electrophoresis apparatus, no current (or very little) would flow and no movement would be possible.
The next question then was: why do we need a current to pass through the system in order to have movement of the DNA (or, in general, any charged particle) towards the anode? What physical forces enter into play?
In other words: if we had a bath of distilled water, we put two electrodes connected to a generator at each end and put a charged molecule in the middle of the bath, would it be able to migrate? Why? Which forces would be involved?
I found this document which essentially confirms my first answer:

Electrophoresis Buffer: Several different buffers have been recommended for electrophoresis of DNA. The most commonly used for duplex DNA are TAE (Tris-acetate-EDTA) and TBE (Tris-borate-EDTA). DNA fragments will migrate at somewhat different rates in these two buffers due to differences in
  ionic strength. Buffers not only establish a pH, but provide ions to support conductivity. If you mistakenly use water instead of buffer, there will be essentially no migration of DNA in the gel! Conversely, if you use concentrated buffer (e.g. a 10X stock solution), enough heat may be generated in the gel to melt it.

However, I have not been able to find a proper explanation of the physical forces involved in the process.
PS: of course in a real DNA electrophoresis the charged molecule is trapped in a gel, which itself has been made using a conducting buffer, so the question becomes probably a tad more tricky...
 A: The problem with the conductivity explanation:
    The logic is this: adding more ions will increase the conductivity so ions (including DNA) will flow more easily. Although more ions means more total current, it does not mean the ions will move any faster. You put more cars on the freeway but didn't change the speed limit. If we maintain a voltage, the electric field will be the same, so the force on each ion (including ours) will be the same. In fact, the velocity of each ion will drop slightly at high concentrations because of increased viscosity and screening (the charge attracts counter charges which reduces it's average net charge). This "traffic jam" effect is apparent in the plot of resistivity vs salt concentration; there is a small departure from linearity at dead-sea concentrations:
http://gasstationwithoutpumps.files.wordpress.com/2012/08/resistivity_nacl.jpg
My best guess (an expert in this field should elaborate):
The ionic strength (weighted concentration of ions) of the solution changes how the DNA behaves. The gel is an obstacle course for the DNA. The basic idea is that the DNA in distilled water vs salt water will be structured differently. It could be more balled up and too big to fit through the pores, or less soluble so it tends to bind to the gel in distilled. See http://www1.lsbu.ac.uk/water/hofmeist.html
for the physics of ionic effects on solubility (unfortunately, they don't discuss DNA). 
It is also possible that the ionic strength affects the gel's structure itself when the gel is prepared.
A: In Wikipedia's article it is stated:

The negative charge of its phosphate backbone moves the DNA towards the positively-charged anode during electrophoresis.

It is clear that Coulomb interaction is the responsible for the attraction of the DNA (or charged particle). Basically opposite charges attract.
From what I understood, the gel plays an important role here: if there was no gel, there would be no separation (all charged molecules would go straight to the anode, all together). 
The fact that the gel has viscosity could make the longer molecules to "flow" through the gel harder than the shorter molecules. Also, the molecules which are more charged will suffer a higher acceleration towards the anode. These mechanisms should be taken into account when justifying the separation of molecules, but, citing Wikipedia 

however the precise mechanism responsible the separation is not entirely clear.

Concluding, you need a conductive buffer to allow the charged particles to flow and interact with the molecules.  If a medium is more conductive, that means it can transport a charge more easily. Let that charge be your DNA or another charged particle. The gel plays an important role to separate the molecules despite the fact that the mechanisms that allow it are not fully understood.
