Optimisation of the net flow generated by artificial cilia performing tilted conical motion in confined micro-channels

Cilia exist ubiquitously in nature, and they are very effective in generating flow in a low Reynolds number environment. Inspired by nature, various artificial cilia have been invented for microfluidic applications, and a nature-mimicking tilted conical motion was often used for flow generation due to its simplicity and effectiveness. However, the current theoretical model for predicting the net flow rate generated by the tilted conical motion fails when the cilia are in close confinement, i.e. when the tips of the cilia are close to the ceiling of their channel or chamber, which is, in reality, the most practical way to enhance flow rate generation. Moreover, numerical simulations are very expensive for optimisation of such designs. In this study, we derive a new theoretical model, taking into account the tilting and opening angles of the cone, the height of the chamber and the length of the cilia. The results differ significantly from when the ceiling is not considered, and counter-intuitively in some cases the flow can even reverse. These unexpected results have important implications for artificial cilium design and applications. We validate the model with both numerical simulations and experiments using magnetic artificial cilia, and show that the flow optimisation based on tilted conical cilium motion can now be performed accurately in a realistic and practical manner. This study not only offers a simple tool for optimising designs of artificial cilium-based systems for microfluidic applications, but it also provides fresh insights for understanding natural cilium-driven flows.