Initially, the DNA is brought near the pore through diffusive (brownian) motion + any small attraction it'll have to the membrane. Close to the pore it uses a combination of the electrophoretic and electro-osmotic effects to draw the DNA molecules through. The application of an external magnetic field will cause the charged DNA molecules to migrate along the field (electrophoresis). This is independent of the fluid, and happens to any ions under voltage. The electro-osmotic flow, on the other hand, is a motion of the fluid itself, pulling the DNA molecules along with it. EOF is a really interesting phenomenon which is caused by the interaction between the surface chemistry (vis-a-vis charge distribution) and the concentration gradient of charge carriers in the fluid. I'd recommend Fundamentals and Application of Microfluidics by Nguyen et al if you're looking for a good primer on electrically induced flows in microfluidics.