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TECHNICAL PAPERS: Fluids/Heat/Transport

Oscillatory Flow in a Cone-and-Plate Bioreactor

[+] Author and Article Information
C. A. Chung, M. R. Tzou, R. W. Ho

Department of Mechanic Engineering,  National Central University, Jhongli 320, Taiwan, ROC

J Biomech Eng 127(4), 601-610 (Dec 01, 2004) (10 pages) doi:10.1115/1.1933964 History: Received March 04, 2004; Revised December 01, 2004

Motivated by biometric applications, we analyze oscillatory flow in a cone-and-plate geometry. The cone is rotated in a simple harmonic way on a stationary plate. Based on assuming that the angle between the cone and plate is small, we describe the flow analytically by a perturbation method in terms of two small parameters, the Womersley number and the Reynolds number, which account for the influences of the local acceleration and centripetal force, respectively. Working equations for the shear stresses induced both by laminar primary and secondary flows on the plate surface are presented.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of the cone-and-plate bioreactor showing the coordinate system and nomenclature. The cone rotates sinusoidally with the angular speed of ωcos(Ωt).

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Figure 2

The analytic and numerical solutions of primary flow for α=0.05 and δ=0.1. (a) The contours of velocity amplitude, (b) the contours of phase angle. The analytic and numerical solutions coincide in the figure. The dashes lines distinguish the inner fluid region and the boundary-layer region.

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Figure 3

The analytic and numerical solutions of primary flow for α=0.05 and δ=5. (a) The contours of velocity amplitude. (b) The contours of phase angle. The analytic and numerical solutions coincide in the figure.

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Figure 4

The analytic (dashed curves) and numerical (solid curves) solutions of primary flow for α=0.3 and δ=0.1. (a) The contours of velocity amplitude, and (b) the contours of phase angle.

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Figure 5

The primary azimuthal shear stress on the plate surface as a function of the radial coordinate r for α=0.05 and four different values of δ. (a) The stress amplitude. (b) The phase angle of stress.

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Figure 6

The coefficients of azimuthal velocity as functions of the vertical coordinate z. Since the z-coordinate has been scaled by the local radial length rl, the coefficients are representative of the interior flow not too close to the periphery wall. Note the value of V01 has been magnified 15 times, and V02 and V03 100 and 500 times, respectively.

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Figure 7

The coefficients of radial velocity as functions of the vertical coordinate z. The coefficients are representative of the interior flow. The higher order coefficients have been magnified.

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Figure 8

The coefficients of vertical velocity as functions of the vertical coordinate z. The coefficients are representative of the interior flow. The higher order coefficients have been magnified.

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Figure 9

Dimensional stresses on the plate surface for the rotation speed ω=150 and 300rpm, respectively (solid lines: primary stresses, dashed lines: secondary stresses).

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