Optimizing fluid mixing in channel flow using wall-mounted flexible structures

In channel mixers with two parallel streams of fluid, mixing is achieved by either laminar diffusion at low Reynolds numbers or from flow agitation due to geometric variations. Traditionally, rigid obstructions or textures are used in various spatial arrangements to improve fluid mixing. In our work, we have numerically investigated the mixing performance of a passive scalar in a two-dimensional channel flow accompanied by wall-mounted flexible plates as obstructions for a wide range of low Reynolds numbers ($Re$). The thin plates are arranged on opposite walls of the channel, and the distance between them is varied in the range $0h$ to $2h$, where $h$ is the channel lateral width. The different arrangements result in corresponding flow paths, thereby affecting fluid mixing and flow rate due to the pressure head losses. We assessed the mixing performance in the channel via the mixing index and the head loss. Our results show that the channel with the two plates when arranged exactly opposite the walls (without a separation gap), offers the highest mixing with significant pressure drop. In contrast, either a single plate or two plates widely separated result in nearly similar levels of mixing index with a lower head loss. We devised a performance index based on a cost-benefit analogy by comparing the flexible plate configurations with the plane channel (i.e, without any obstruction) so as to assess the mixing effectiveness and found that a single flexible plate in the channel in the flow conditions with $Re\approx 400$ suit the best for the mixing of two fluid in the channel.