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Technical Briefs

Added-Mass Effect in Modeling of Cilia-Based Devices for Microfluidic Systems

[+] Author and Article Information
J. Kongthon, B. McKay, D. Iamratanakul, K. Oh, J.-H. Chung, J. Riley

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195-2600

S. Devasia1

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195-2600devasia@u.washington.edu

1

Corresponding author.

J. Vib. Acoust 132(2), 024501 (Feb 12, 2010) (7 pages) doi:10.1115/1.4000766 History: Received January 31, 2008; Revised November 25, 2009; Published February 12, 2010; Online February 12, 2010

This article shows that the added mass due to fluid-structure interaction significantly affects the vibrational dynamics of cilia-based (vibrating cantilever-type) devices for handling microscale fluid flows. Commonly, the hydrodynamic interaction between the cilia-based actuators and fluid is modeled as a drag force that results in damping of the cilia motion. Our main contribution is to show that such damping effects cannot explain the substantial reduction in the resonant-vibrational frequency of the cilia actuator operating in liquid when compared with the natural frequency of the cilia in air. It is shown that an added-mass approach (that accounts for the inertial loading of the fluid) can explain this reduction in the resonant-vibrational frequency when operating cantilever-type devices in liquids. Additionally, it is shown that the added-mass effect can explain why the cilia-vibration amplitude is not substantially reduced in a liquid by the hydrodynamic drag force. Thus, this article shows the need to model the added-mass effect, both theoretically and by using experimental results.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

(a) Experimental setup for testing the resonant-vibrational frequency of cilia. (b) Image of a cilium excited by piezostage. (c) Nominal cilium dimensions are length L=800 μm, depth D=10 μm, and height H=45 μm.

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Figure 2

Frequency response of cilia with nominal dimensions L×H×D=800×45×10 μm3 in (a) air and (b) DI water. The dots represent the experimental data (mean value of six cilia), and the bars represent the standard deviation ±σ. The lines represent the response of the model in Eq. 2 with the fitted parameters in Tables  12.

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Figure 3

Contour plot for normalized resonant-vibrational frequency ω¯r in Eq. 44

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Figure 4

Frequency response prediction in water for models of cilia (with different lengths): (a) with the added-mass effect (solid lines) and (b) without the added-mass effect (dashed lines). Experimentally measured data points are shown in the left plot.

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