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Principles and applications are described for a Fourier-Bessel series model that predicts the transport of bionanoparticles driven by a dielectrophoretic (DEP) force and randomized by Brownian motion. The model is applicable for a dielectrophoretic force that spatially decays from the electrode array according to a reciprocal-law; that is, in the near field of a planar interdigitated array or in the far field where other long range forces assist DEP transport, e.g., ac electro-osmosis. Capabilities of the model are demonstrated for estimating and decomposing data typical of dielectrophoretic bionanoparticle collection experiments. An important approximation, for moderately strong DEP forces, is that a collection can largely be described by a single exponential profile with a square-law dependence on microdevice chamber height. Applications of the model demonstrate transformation and representation of time-dependent bionanoparticle transport in the frequency domain and prediction of a modulation bandwidth that concurs with experimental observations.