Abstract We model the dielectrophoretic response of E. coli bacterial cells and red blood cells, upon exposure to an electric field. We model the separation, capture, and release mechanisms under flow conditions in a microfluidic channel and show under which conditions efficient separation of different cell types occurs. The modelling work is aimed to guide the separation electrode architecture and design for experimental validation of the model. The dielectrophoretic force is affected both by the geometry of the electrodes (the gradient of the electric field), the Re{CM(ω)} factor, and the permittivity of the medium ϵ_m. Our modelling makes testable predictions and shows that designing the electrode structure to ensure structure periodicity with spacing between consecutive traps smaller than the length of the depletion zone ensures efficient capture and separation. Such electrode system has higher capture and separation efficiency than systems with the established circular electrode architecture. The simulated, modelled microfluidic design allows for the separated bacteria, concentrated by dedicated dielectrophoretic regions, to be subsequently detected using label-free functionalized nanowire sensors. The experimental validation of the modelling work presented here and the validation of the theoretical design constraints of the chip electrode architecture is presented in the companion paper in the same issue (Weber MU et al 2022 Chip for dielectrophoretic Microbial Capture, Separation and Detection II: Experimental Study).