Application of Porous Media Theories in Marine Biological Modeling - Porous Media: Applications in Biological Systems and Biotechnology - page 385

FIGURE 10.15
Streamlines (solid black lines) through and around a complex rectangular cell
containing four different porous geometries (square, rectangle, ellipse, and
circle). The gray contours represent the pressure distribution (high pressure
below the circle and ellipse, low pressure at upper sides of the all geometries).

where g and ρ 0 denote acceleration due to gravity and a reference density,
respectively. Naturally occurring stratifications range from N

0 . 01s − 1 in the

≈

0 . 2s − 1 in estuaries or fjords (Farmer and Ami 1999).
Stratification can have a significant impact on an important aspect of the
marine carbon cycle, since the sedimentation of particulate organic matter is
the main vector of carbon export from surface waters to the deep sea. Particles
also affect marine ecology by providing an important resource for planktonic
microorganisms. Marine particles of size a

ocean to N ≈

0 . 5 mm are commonly referred
to as marine snow. Marine snow typically consist of vestiges of phyto- and
zooplankton, together with gel-like transparent exopolymer particles (TEP).
Marine snow has high porosity,

≥

0 . 99, and small excess density with respect
to the ambient seawater, ∆ ρ p = ρ p −

≥

ρ = O (10kg / m3) (Turner 2002). Because
of the latter, the sinking of marine snow is characterized by low Reynolds
numbers, Re = aU/ν = O (0 . 1

− 1), where U is the settling velocity and ν is the

kinematic viscosity.
Marine snow is known to accumulate at pycnoclines in the ocean, form-
ing thin layers that can persist for days and have highly elevated parti-
cle concentrations (McIntyre et al. 1995; Alldredge et al. 2002; McManus
et al. 2003). It has been speculated that the retention of particles at pyc-
noclines is caused by the slow, diffusion-driven exchange between interstitial
and ambient fluid at the pycnocline (Alldredge and Crocker 1995; Alldredge
1999). Diatom aggregates are nearly impermeable to flow (Ploug et al. 2002),
hence the hydrodynamic properties of the aggregates are defined primarily
by TEP. By reference to comparable gels, the permeability of TEP is esti-
mated as k

O (10 − 17 m − 2 ) (Jackson and James 1986). The diffusivity D of

≤