Hydrodynamics in Porous Media with Applications to Tissue Engineering - Porous Media: Applications in Biological Systems and Biotechnology - page 103

TABLE 3.2
Parameters Values (Named Reference Values in the Text) Introduced in the
Simulations

Parameter Value References

10 − 3 m Diameter of polymeric fibers h 0 . 25 × -

10 − 3 m Implant length L 25 × -

10 − 4 m

Length of the representative
elementary volume l Ch

25 × -

10 − 4 m sec − 1

Mean velocity at the inlet u 0 × -

10 3 kg m − 3 Liquid density ρ × Peng and Palson

1996

10 − 3 Pa

Liquid dynamic viscosity η 0 . 7 × × sec Peng and Palson

1996

10 − 6 m 2 sec − 1

Liquid kinematic viscosity ν 0 . 7 × × Peng and Palson

1996

m − 3 Oxygen concentration at

inlet c 0

0 . 2 mol × -

10 − 9 m 2 sec − 1

Oxygen binary diffusivity in
water D O 2

3 × × Williams et al .

2002

10 − 3 mol m − 3 Michaelis constant k M 6 × × Obradovic et al .

2000

×

10 9 cell

×

m − 2

Cell density on fiber surface
σ Cell

2 -

10 − 17 mol Maximal oxygen consumption

rate V Max

4 × × Komarova et al .

2000 sec − 1 cell − 1

×

10 − 2

Damkohler number Da 3 × *

Peclet number Pe 8 *

10 − 2 Reynolds number Re 3 . 5 × *

10 − 2 Dimensionless Michaelis

constant λ M

3 × *

than the characteristic diffusion velocity of oxygen (about 10 − 5 m sec − 1 )at

the length scale a of the pore. Nevertheless, such a secondary flow is capable
of significantly contributing to the increase in the nutrient transport processes
of oxygen molecules from the center of the channel toward its periphery, where
the consumers of the cell's oxygen lie.
Thus, the mixing effects generated by this flow are contributing to the
homogenization of the oxygen distribution in the vicinity of the fiber surface
as shown in Figure 3.11, where a relative variation of less than 10% around
the mean value of the oxygen concentration is noted.

×