Simulation of Micro-fluidic Mixing Using Artificial Cilia

Our recently developed micro-mixer based on artificial cilia shows good mixing over relatively short lengthscales[1], which was unexpected. In this paper we present a numerical tool and use it to simulate the micromixerto explain the observed effects. The tool consists of a fully coupled fluid-solid interaction model, which issolved with a finite element method, and a particle tracking scheme. The former computes the motion of fluid andsolid for one actuation cycle of the cilia and the latter tracks the position of passive particles for several cyclesusing the calculated velocity field. Two parameter sets are computed, one including and one excluding fluidinertia. The obtained particle distributions after fifty cycles show that net fluid motion is in the direction of therecovery part of the cycle for the inertialess case and in the direction of the actuation part of the cycle for theinertial case. This implies that by controlling the cilium velocity, which controls the Reynolds number, the flowdirection can be controlled for a given system. The simulated intermediate particle distributions agree very wellwith optical coherence tomography data for the inertial case, whereas the inertialess simulations showcompletely different behaviour. Therefore it is concluded that inertial effects play a crucial role in the efficientmixing in this micro-mixer, which was not expected since the dimensions are in the sub-millimetre range.[1] Toonder, J.M.J. den, Bos, F.M., Broer, D.J., Filippini, L., Gillies, M., Goede, J. de, Mol, G.N.,Talen, W., Wilderbeek, J.T.A., Khatavkar, V., & Anderson, P.D. (2008).Artificial cilia for activemicro-fluidic mixing, Lab Chip, 8, 533-541