Hydrodynamics in Porous Media with Applications to Tissue Engineering - Porous Media: Applications in Biological Systems and Biotechnology - page 77

Parameter Notation Unit

m − 3 Reference concentration of

the nutrient

c 0 mol ×

Diffusion coe cient of the
nutrient solute

D

m 2

×

s − 1

Da = σ cel ×

V Max × a

Damkohler number

D × c 0

s − 1

Perfusion mean velocity u 0 m ×

m − 3

Density of the culture fluid ρ kg ×

Dynamic viscosity of the
culture fluid

η Pa × sec

u 0 / φ

ρ × a ×

Reynolds number Re =

η

u 0 / φ
D

a ×

Peclet number Pe =

u 0
a

Viscous stresses τ = η ×

Pa

L D

Debye length m

m − 3

Ionic force C i mol ×

V − 1 m − 1

Vacuum permittivity ε 0 C × ×

Relative dielectric constant
of the solvent

ε

mol − 1 Faraday constant F C ×

K − 1 mol − 1 Gas constant R J × ×

Absolute temperature T K

Electric double-layer
potential

ϕ V

Donnan osmotic swelling
pressure

π D Pa

m − 3

Oxygen molar
concentration

c O 2 mol ×

m 2 sec − 1

Oxygen binary diffusivity
in water

D O 2 ×

sec − 1 Perfusion velocity u m ×

Typical size of the solid
heterogeneities in the
porous medium

h m

ν = ρ m 2 sec − 1 Fluid kinematic viscosity ×

Dimensionless Michaelis
constant

λ M

N O 2

Dimensionless oxygen flux
at the frontier

( Continued )