DNA electrophoresis in designed channels
We present a simple description on the electrophoretic dynamics of polyelectrolytes going through designed channels with narrow constrictions of slit geometry. By analyzing rheological behaviours of the stuck chain, which is coupled to the effect of solvent flow, three critical electric fields (permeation field $E^{(per)} \sim N^{-1}$, deformation field $E^{(def)} \sim N^{-3/5}$ and injection field $E^{(inj)} \simeq N^0$, with $N$ polymerization index) are clarified. Between $E^{(per)}$ and $E^{(inj)}$, the chain migration is dictated by the driven activation process. In particular, at $E>E^{(def)}$, the stuck chain at the slit entrance is strongly deformed, which enhances the rate of the permeation. From these observations, electrophoretic mobility at a given electric field is deduced, which shows non-monotonic dependence on $N$. For long enough chains, mobility increases with $N$, in good agreement with experiments. An abrupt change in the electrophoretic flow at a threshold electric field is formally regarded as a nonequilibrium phase transition.