Transport and mixing by artificial cilia

Microfluidic analysis devices are becoming more common as a tool for clinical analysis. In these devices fluid transport and mixing of multiple components are common tasks. A possible way of achieving these tasks can be found in nature, where small hairs, named cilia, are found on micro-organisms and surfaces. These hairs move the surrounding fluid, or move the micro-organism through the fluid. As in micro-fluidics, the generated flows are inertialess in general. By mimicking natural cilia, several successful microfluidic actuators for pumping and mixing have been developed recently [1–8]. In order to understand the working principles of these devices and improve their design, a numerical model is presented in this thesis. With this model, we studied the fluid-structure interaction of the cilium with the surrounding fluid. Since cilia are very thin beams which show large deformations, a model which can cope with large deformations is required. We therefore chose to model the fluid on a fixed Eulerian grid and the solid on a moving Lagrangian grid. Initially we used a fictitious domain/Lagrange multiplier technique to couple both domains. Simulations showed however, that this technique is inaccurate near the moving interface of the fluid and the cilium. This inaccuracy stems from two causes, namely the fictitious fluid domain and the discretization of the Lagrange multiplier. The first cause is eliminated by removing the fictitious domain with the eXtended Finite Element Method (xfem). The second cause is removed by applying coupling in a weak manner, without the need of a Lagrange multiplier. This method gave accurate results for Newtonian, generalized Newtonian and viscoelastic fluids in combination with an elastic solid. The major advantages of this method are its accuracy, optimal convergence rates, without including problem dependent parameters. In Chapter 4, the new numerical model is used to study the influence of the actuation frequency on the transport and mixing efficiency of one or two artificial cilia. It is shown that there exists a frequency for which the flow rate is maximum. The reason for this maximum is the fact that a fluid-structure interaction problem has an intrinsic time-scale, which makes the system frequency dependent, even when fluid and solid inertia are absent. At the optimal flow rate, the amount of displaced fluid per cycle is not optimal. So using the latter as an objective may not lead to the largest flow rate possible in the system. For the mixing analysis two cilia were modeled, each having a different intrinsic time-scale. Both were actuated by the same actuation force, thus showing different motion. This led to a phase difference between the two cilia, which has been shown to enhance mixing [9]. The mixing performance was measured by tracking a blob in time, which was initially placed in between the cilia. The stretch of this blob is a measure for the local mixing efficiency, and an exponential increase indicates chaotic mixing. A length stretch increase was observed in all cases. Changing the cilium thickness of one of the cilia has a clear beneficial effect on mixing. For mixing the amount of fluid moved by the cilia is also important, as the mixing performance at low actuation frequency is much better than at high actuation frequency, where the movement of the cilia, and hence the induced flow, is less. In order to perform simulations of artificial cilia in a non-Newtonian fluid, the numerical model proposed in Chapter 4 has been extended in Chapter 6. In addition a local mesh refinement scheme was developed in order to make accurate simulations within a shorter time-frame feasible. Both the mesh refinement scheme and the viscoelastic fluid-structure interaction scheme were tested, and shown to be stable and accurate. The numerical model of this chapter is used in Chapter 7 for the simulation of generalized Newtonian and viscoelastic fluid flow by artificial cilia. It is shown that by making use of the typical time-scale of the cilia system and the time-scale of the generalized Newtonian fluid, the net fluid flow of a generalized Newtonian fluid had a higher dependence on the actuation force than for a Newtonian fluid. In the final chapter conclusions and recommendations for future work are given.