We present a microfluidic device where micro- and nanoparticles can be continuously functionalized in flow. This device relies on an element called particle exchanger, which allows for particles to be taken from one medium and exposed to some reagent while minimizing mixing of the two liquids. In the exchanger, two liquids are brought in contact and particles are pushed from one to the other by the application of a dielectrophoretic force. We determined the maximum flow velocity at which all the particles are exchanged for a range of particle sizes. We also present a simple theory that accounts for the behaviour of the device when the particle size is scaled. Diffusion mixing in the exchanger is also evaluated. Finally, we demonstrate particle functionalization within the microfluidic device by coupling a fluorescent tag to avidin-modified 880 nm particles. The concept presented in this paper has been developed for synthesis of modified particles but is also applicable to on-chip bead-based chemistry or cellular biology.