The Periodical Shear Environment of a Cone-and-Plate Bioreactor

[+] Author and Article Information
C. A. Chung1

Department of Mechanical Engineering, National Central University, Jhongli 320, Taiwan, R.O.C.

C. S. Weng, M. Z. Tu

Department of Mechanical Engineering, National Central University, Jhongli 320, Taiwan, R.O.C.


Corresponding author.

J. Fluids Eng 128(2), 388-393 (Aug 17, 2005) (6 pages) doi:10.1115/1.2170127 History: Received June 06, 2005; Revised August 17, 2005

We investigate theoretically the periodic shear environment of a cone-and-plate bioreactor. The imposed frequency is designated to reflect the periodic nature of mammalian cardiac cycles. The working formula obtained for the distribution of shear stresses shall be of substantial interest for applying periodic shear stresses to cell cultures in vitro.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Schematic diagram of the cone-and-plate bioreactor. The cone rotates in a periodic way with an angular speed defined as ω0+Δωcos(Ωt*).

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Figure 2

The contours of velocity amplitude of primary flow for α=0.05, δ=5, and ω=ω0∕Δω=0.5. Two temporal points are presented: (a) t=π∕2 and (b) t=3π∕2. The analytical (Eq. 17) and numerical solutions coincide in the figure.

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Figure 3

The primary shear stresses on the plate surface for ω=0.5, α=0.05, and δ=1, 5 respectively, at four sequential instants t=0, π∕2, π, and 3π∕2, show that the shear stress is not uniformly distributed in the radial direction when δ becomes large

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Figure 4

The coefficients of secondary flow for (a) the radial velocity, and (b) the vertical velocity. Only the first two largest coefficients are shown. The other coefficients in Eqs. 19,21 are virtually one order smaller in value.

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Figure 5

Dimensionless stresses on the plate surface for ε=1 (solid lines) and ε=3 (dashed lines), and ω=0.5, δ=1. (a) The primary stress in the azimuthal direction, and (b) the secondary stress in the radial direction.




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