Artificial Micro-Devices: Armoured Microbubbles and a Magnetically Driven Cilium
Micro-devices are developed for uses in targeted drug delivery and microscale manipulation. Here we numerically and analytically study two promising devices in early stages of development. Firstly, we study Armoured Microbubbles (AMBs) which can self-propel as artificial microswimmers or facilitate microfluidic mixing in a channel when held stationary on a wall. Secondly, we study an artificial cilium, which due to its unique design, when placed in an array, easily produces a metachronal wave for fluid transportation. The Armoured Microbubble was designed by our experimental collaborators (group of Philippe Marmottant, University Grenoble Alpes) and consists of a partial hollow sphere, inside which a bubble is caught. Under ultrasound the bubble oscillates, generating a streaming flow in the surrounding fluid and producing a net force. Motivated by the AMB but considering initially a general setup, using matched asymptotic expansions we calculate the streaming flow around a spherical body undergoing arbitrary, but known, small-amplitude surface shape oscillations. We then specialise back to the AMB and consider its excitation under ultrasound, using a potential flow model with mixed boundary conditions, to identify the resonant frequencies and mode shapes, including the dependence of the resonance on the AMB shape parameters. Returning to our general streaming model, we applied the mixed boundary conditions directly to this model, calculating the streaming around the AMB, in good agreement with experiments. Using hydrodynamic images and linear superposition, this model was extended to incorporate one wall, and AMB compounds. We then study the streaming flows generated by arrays of AMBs in confined channels, by modelling each AMB as its leading order behaviour (with corrections where required) and superposing the individual flow fields of all the AMBs. We identified the importance of two confining walls on the streaming flow around the array, and compared these flows to experiments in five cases. Motivated by this setup, we theoretically considered the extension of a two fluid interface passing through an AMB array to quickly identify good AMB arrays for mixing. We then studied the second artificial micro-device: an artificial cilium. Tsumori et. al. produced a cilium of PDMS containing aligned ferromagnetic filings, which beat under a rotating magnetic field. We modelled a similar cilium but assumed paramagnetic filings, using a force model balancing elastic, magnetic and hydrodynamic forces identifying the cilium beat pattern. This agreed with our equilibrium model and asymptotic analysis. We then successfully identified that the cilium applies the most force to the surrounding fluid at an intermediate value of the two dimensionless numbers quantifying the dynamics.