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Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/2916
Title: Experimental study and nonlinear dynamic analysis of time-periodic micro chaotic mixers
Authors: Lee, Yi-Kuen
Shih, Chiang
Tabeling, Patrick
Ho, Chih-Ming
Keywords: Chaotic mixing
Lyapunov exponent
Micro mixer
Poincaré section
KAM curves
Issue Date: Mar-2007
Citation: Journal of fluid mechanics, v. 575, March 2007, p. 425-448
Abstract: The efficiency of MEMS-based time-periodic micro chaotic mixers was experimentally and theoretically investigated in this study. A time-periodic flow perturbation was realized using digitally controlled solenoid valves to alternately activate a source and sink, acting together as a pair, with different driving frequencies. Working fluids with and without fluorescent dye were used in the micro mixing experiments. The spatiotemporal variation of the mixing concentration during the mixing process was characterized at different Strouhal numbers, ranging from 0.03 to 0.74, under fluorescence microscopy. A simple kinematical model for the micro mixer was used to demonstrate the presence of chaotic mixing using different methods. The specific stretching rate, Lyapunov exponent, as well as local bifurcation and Poincaré section analyses were used to identify the emergence of chaos. Two different numerical methods were employed to verify that the maximum Lyapunov exponent was positive in the proposed micro mixer model. A simplified analytical analysis of the effect of Strouhal number was presented. Kolmogorov–Arnold–Mose (KAM) curves, which are mixing barriers, were also found in Poincaré sections. From a comparative study of the experimental results and theoretical analysis, a Finite-Time Lyapunov exponent (FTLE) was shown to be a more practical mixing index compared to the classical Lyapunov exponent because the time spent in mixing is the main concern in practical applications, such as bio-medical diagnosis. In addition, the FTLE takes into account both fluid stretching in terms of the stretching rate and fluid folding in terms of curvature.
Rights: '© Cambridge University Press 2007. This paper was (will be) published in Journal of fluid mechanics and is reprinted with permission.'
URI: http://hdl.handle.net/1783.1/2916
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