Biomedical Engineering Reference
In-Depth Information
Moreover, although some studies have been made of oxytaxis and gyro-
taxis behaviors (Kuznetsov and Avramenko, 2003a,b, 2005; Kuznetsov 2003,
2008; Nield et al. 2004; Kuznetsov et al. 2004), more exhaustive works on the
development of convection regimes beyond critical thresholds (laminar, turbu-
lent, or chaotic...)should be done for microorganisms with various directional
motions (e.g., phototaxis, galvanotaxis, chemotaxis, magnetotaxis...).
Another subject of interest is bioconvection in porous media with the
double-diffusion effects, which is found in numerous applications in environ-
mental sciences and engineering. Some works on this problem by Kuznetsov
and coworkers (Nield and Kuznetsov, 2006; Kuznetsov, 2008) and Nguyen-
Quang et al. (2008) have shown that the bioconvection in porous media with
double-diffusion still remains an open field of research.
Finally, we should also consider the possibility of controlling bioconvec-
tion by/within porous media. In fact, the control of bioconvection by porous
medium was first reported by Kessler (1986b) as mentioned in the previous
part of literature review. Kuznetsov (2008) has realized a numerical inves-
tigation and indicated that vibration is an effective way of controlling the
stability of bioconvection while Nguyen-Quang et al. (2008) have found that
heating from above could strongly weaken the bioconvection flow. Further
studies should be accomplished for this subject.
14.5 Appendix: Boussinesq Approximation for
the Microorganism Suspension
Let us recall that from the Nomenclature below:
ρ w is the specific mass of the fluid (N / m 3 ) .
ρ is the total specific mass of the suspension (N / m 3 ) .
ρ c is the specific mass of the microorganism cells (N / m 3 ) .
ϑ is the volume of 1 microorganism cell.
we have the following:
N ϑ is the total volume of cells in a unit volume of the suspension.
1
N ϑ is the volume of fluid.
ρ c N ϑ is the specific mass of cells.
ρ w (1
N ϑ ) is the specific mass of fluid.
ρ = ρ w (1
N ϑ )+ ρ c N ϑ is the specific mass of the suspension.
or
ρ w ) N ϑ = ρ w +∆ ρϑN
ρ = ρ w +( ρ c
(14.34)
 
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