Hydrodynamics in Porous Media with Applications to Tissue Engineering - Porous Media: Applications in Biological Systems and Biotechnology - page 86

3.3.4 Other Physicochemical Factors Affecting
Cell Metabolism
In addition to mechanical stimuli , cultivated tissues are known to react to
other physical signals. For instance, electromagnetic phenomena are important
from cell biology to medicinal applications. Indeed, modern molecular biology
tends to correlate the action of ion transporters and ion channels to the “elec-
tric” action of cells and tissues. Also, cell proliferation is improved by applying
adequate electric fields. Thus, the triggers exerted by ion concentrations and
concomitant electric field gradients have been traced along signaling cascades
till gene expression changes in the nucleus (Funk et al . 2009). Moreover, at the
small scale, the living tissues can present a “membrane behaviour.” They are
impermeable to organic solutes with large molecules, such as polysaccharides,
while permeable to water and small, uncharged solutes. Permeability may
depend on solubility properties, charge, or chemistry as well as solute size.
Osmosis provides the primary means by which water is transported into and
out of cells. The turgor pressure of a cell is largely maintained by osmosis,
across the cell membrane, between the cell interior and its relatively hypo-
tonic environment (Maton et al. 1997). Moreover the swelling properties of
connective biological tissues such as cartilage can be explained by the osmotic
disjoining pressure (Huyghe and Janssen 1997).
To take into account these electrochemical effects, it is necessary to com-
bine the transport equations with equations governing the electrolyte move-
ment coupled with local electrodynamical field evolutions.
An important property inherent in many biological charged porous media
is the negative charge of their surface, which is a consequence of the presence of
some chemical negative sites such as hydroxyl complex. This negative charge
is compensated by the adsorption of cations on the surface forming the inner
compact layer commonly referred to as the immobile stern layer. Nevertheless
the majority of the excess of positively charged counterions are located in the
electrolyte aqueous solution externally to the solid phase forming an outer
diffuse layer composed of mobile charges. Together with the fixed charged
groups of the solid matrix these ions form the so-called electrical double layer
(see Figure 3.3).
The thickness of t his double layer is characterized by the Debye length

L D = εε 0 RT/ 2 F 2 C i ,which inversely depends on the ionic concentrations,
that is to say on the ionic force C i (Hunter 2001). Here ε 0 is the vacuum
permittivity, ε is the relative dielectric constant of the solvent, R is the gas
constant, T is the absolute temperature, and F is the Faraday constant.
These electrical phenomena are generally purely microscopical since the Debye
length is classi ca lly of a few nanometers. The dimensionless electric double-
layer potential ϕ = Fϕ / RT obeys the well-known nonlinear Poisson-Boltzmann
equation:

1
L 2 D

∆( ϕ )= sinh ϕ (3.7)