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A novel Biased Reptation model with Electroosmosis (BRE) is proposed for long-chain DNA electrophoresis in microchannels with sub-micron pillar array. The BRE model incorporates effective electroosmosis into the classical BRM model. In addition, the electrophoretic mobilities of different sizes of long-chain DNA, T4 DNA and lambda DNA, at different electric fields were measured. In comparison with the experimental results and classical BRM model, the BRE model shows excellent agreement with the experimental results.