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Experimental study and nonlinear dynamic analysis of time-periodic micro chaotic mixers

Published online by Cambridge University Press:  07 March 2007

YI-KUEN LEE ,
CHIANG SHIH ,
PATRICK TABELING  and
CHIH-MING HO
YI-KUEN LEE
Affiliation:
Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
CHIANG SHIH
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA
PATRICK TABELING
Affiliation:
MMN, ESPCI, 10, rue Vauquelin, 75005 Paris, France
CHIH-MING HO
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
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Abstract

The efficiency of MEMS-based time-periodic micro chaotic mixers is experimentally and theoretically investigated in this study. A time-periodic flow perturbation was realized using digitally controlled solenoid valves to activate a source and sink alternately, acting together as a pair, with different driving frequencies. Working fluids with and without fluorescent dye were used in the micromixing experiments. The spatio-temporal variation of the mixing concentration during the mixing process was characterized at different Strouhal numbers, ranging from 0.03 to 0.74, using fluorescence microscopy. A simple kinematical model for the micromixer was used to demonstrate the presence of chaotic mixing. Specific stretching rate, Lyapunov exponent, and 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 micromixer model. A simplified analytical analysis of the effect of Strouhal number is 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 than 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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 425 - 448
Copyright
Copyright © Cambridge University Press 2007

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