Mixing in microscale flows, where turbulence is inherently difficult to generate, has been a challenging issue owing to its laminar flow characteristics. Either the diffusion-based mixing process, or the convective mixing based on the cross-stream secondary flow, has been exploited as a passive mixing scheme that does not require any external force field. However, these techniques suffer from insufficient mixing or complicated channel design step. In this study, we propose an efficient mixing scheme by combining inertio-elastic flow instability in a viscoelastic dilute polymer solution and a modified serpentine channel, termed a gear-shape channel, which has side wells along the serpentine channel. We achieved highly efficient mixing in the gear-shaped channel for a significantly wider range of flow rates than in a conventional serpentine channel. Further, we applied our novel mixing scheme to the continuous synthesis of silica nanoparticles, which demonstrated the synthesis of nanoparticles with more uniform size distribution and regular shape, than those in a Newtonian fluid. In addition, the adsorption of inorganic materials on the channel walls was significantly suppressed by the flow instability of the viscoelastic dilute polymer solution in the gear-shaped channel.