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Micro-Mixing and the Role of Multiple Rotating and Bending Flaps
Ruth A. Lambert and Roger H. Rangel

We explore the role of thin elastic flaps in enhancing fluid mixing in a microchannel. At the micro-scale, viscous diffusion dominates and the Reynolds number for typical processes is of order 1. A numerical fluid-and-solid interaction model is developed using the fictitious domain method. Distributed Lagrange Multipliers are used to couple the fluid and solid equations. Fluid flow is generated by the actuation of flexible flaps using an applied surface load. The influence of the modulus of elasticity and the wall endpoint condition on fluid mixing for both single and multiple flaps is considered. Mixing in the fluid is determined by solving the mass transport equation for a solute and calculating a mixing fraction. The results show that for single flap motion, flap effectiveness changes with the applied load. The results of multiple flap motion show that single flaps are equally effective in enhancing fluid mixing as multiple flaps since an additional flap can act as a barrier to fluid recirculation. An additional flap can enhance mixing if the flaps oscillate out of phase with a phase angle of φ = 0 or in some cases φ = π/2.

Keywords: Fluid mixing, fictitious-domain method, micro-cantilever, micro-fluidics, fluid-solid interaction, multiple-flap motion

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