Hydrodynamics in Porous Media with Applications to Tissue Engineering - Porous Media: Applications in Biological Systems and Biotechnology - page 78

Parameter Notation Unit

Normal unit vector of a
considered surface

n

t

Tangent unit vector to a
considered surface

Identity tensor I

Streaming potential ψ V

m 2 sec − 1 Ionic binary diffusion

coecient in water

D ± ×

− J ±

m − 2 sec − 1

Ionic flux density mol × ×

m 2 Pa − 1 sec − 1 Poiseuille permeability

tensor

κ P × ×

mol − 1 m 5 sec − 1 Osmotic permeability

tensor

κ C × ×

m 2 sec − 1

Electroosmotic
permeability tensor

κ E ×

I 0 L
D 0 Fc 0

Nondimensional number
comparing electrical
current and diffusion

J d =

m − 2 sec − 1

Reference electric current
density

I 0 C × ×

Length of the
representative
elementary volume

l Ch m

m 2 sec − 1

Reference diffusion
coecient

D 0 ×

Dean number Dn = Re ×

a / r c 2

Curvature radius of the
flow streamlines

r c m

sec − 1

Secondary transverse fluid
velocity

u t m ×

D O 2
a

sec − 1

Characteristic oxygen
diffusion velocity within
a pore

u D ≈ m ×

3.2 Introduction
Interaction between fluid flow and living media is a complex matter, far
from being completely understood: it is clear that not only cell and tissue