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If I run a small agarose DNA gel and use a voltage of 90V, the DNA migrates the length of the gel in about an hour. If I use a medium size gel I have to use a voltage of 140V to move the same DNA the same distance (the equivalent of the small gel) in the same amount of time. For a large gel it takes about 170V. What is it exactly that requires a higher voltage to maintain the same speed of DNA movement?

I think this is more of an electrochemistry question than a biology questions so I put it here.

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    $\begingroup$ It’s not an electrochemistry question, more like an electrophysics question. $\endgroup$ – Jan Jun 16 '16 at 10:20
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It's actually a physics question. The speed of the particle in the gel is proportional to the force that acts on it. The force that acts on the charged particle is proportional to the strength of the electric field $E$. The strength of the electric field is proportional to the voltage $U$ and inverse proportional to the length of the gel $d$.

$$E = \frac{U}{d}$$

So if you want to have the same strength of the electric field you have to double the voltage if you double the length of the gel.

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