Application of Porous Media Theories in Marine Biological Modeling - Porous Media: Applications in Biological Systems and Biotechnology - page 372

where τ g is the relaxation time and g i the distribution function for concentra-
tion. The equilibrium distribution function was modified as

= ω i C φ + e

u
c s

·

g ( eq )
i

(10.25)

Accordingly, the concentration and velocity are given by
φC =
i

g i (10.26)

u C =
i

g i c i

(10.27)

By a similar procedure described above, from equation (10.14) one can
obtain the concentration equation for a porous medium

φ ∂C
∂t

+( u ·∇ ) C = ∇· [ D m ∇ C ]

(10.28)

with the effective diffusion coecient
D m = φc s τ g −

2 δ t .

1

(10.29)

10.3 Application of Porous Media in Marine
Microbiology
As mentioned earlier, in marine microbiology there exists a great deal of sit-
uations in which porous media theories apply. From different examples given
above, in this section following problems will be discussed: (1) shear-stress
control at seabed bottom, (2) tortuosity of marine sediments, (3) oscillatory
flows over permeable seabed ripples, (4) nutrient release from sinking marine
aggregates, and (5) enhanced nutrient exchange by burrowing macrozooben-
thos species.

10.3.1 Shear-Stress Control at Bottom Sediment
In a variety of marine microbiological or environmental issues, generating uni-
form shear stress planes are desired. An example is given by sampling devices
applied in marine sciences—known as microcosms—in which a controlled flow
is generated to minimize the erosion threshold by producing a uniform shear
stress on the sediment surface.
Recently, shear stress control devices have been considered in technolo-
gies for integration of cell separation and protein isolation from mammalian