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We present simulation results from a new computational model of DNA flow in microfluidic devices. This work is important because computational models are needed to design miniaturized biomedical devices that are becoming the state-of-the-art in many significant applications including pathogen detection as well as continuous monitoring and drug delivery. Currently advanced algorithms in design tools are non-existent but necessary to understand the complex fluid and polymer dynamics involved in biological flow at small scales. Our model is based on a fully coupled fluid-particle numerical algorithm with both stochastic and deterministic components in a bead-rod polymer representation. We have applied this work to DNA extraction configurations in a microfluidic PCR chamber used in a pathogen detection system. We demonstrate our method on the test problem of flow of a single DNA molecule in a 2D packed array microchannel. We are also investigating mechanisms for molecular "sticking" using short range forces.