We characterise computationally and experimentally a three-dimensional (3D) microfluidic passive mixer for various Reynolds numbers ranging from 1 to 100, corresponding to primary flow rates of 10-870 mu l min(-1). The 3D mixing channel is composed of multiple curved segments: circular arcs situated in the substrate plane and curved nozzle/diffuser elements normal to the substrate plane. Numerical simulation provides a detailed understanding of the mixing mechanism resulting from the geometrical topology of the mixer. These Comsol software-based simulations reveal the development of two secondary flows perpendicular to the primary flow: a swirling flow resulting from tangential injection of the flow into the nozzle holes and Dean vortices present in the circular arcs. These phenomena are particularly important at a Reynolds number larger than 30, where mixing occurs by chaotic advection. Experimentally, the 3D mixer is fabricated in a monolithic glass substrate by powder blasting machining, exploiting eroding powder beams at various angles of impact with respect to the substrate plane. Experimental mixing was characterised using two coloured dyes, showing nearly perfect mixing for a microfluidic footprint of the order of a few mm(2), in good agreement with the simulations.