Biomedical Engineering Reference
In-Depth Information
FIGURE 9.3
Aqueous pore-membrane representation of the
SC.
this method that there is not conclusive evidence that this route actually
exists:
“While interpreting the model predictions it should be remem-
bered that no direct physical evidence has been proposed on the
existence of pores within the skin.” (Tezel and Mitragotri 2003)
“While has been no direct evidence for the physical existence
of aqueous pore channels in the skin to date, some researchers have
claimed that the presence of an aqueous pore pathway can be inferred
from evidence of connected lacunar domains within the lipid lamellar
bilayers.” (Kushner et al. 2007b)
The concept has been used to describe pure diffusion through the
SC
(Mitragotri 2003; Kushner et al. 2007b; Tezel et al. 2003), or electrically
enhanced diffusion (nonstructure altering) in which electrophoretic and elec-
troosmotic contributions are considered (Li et al. 2001, 2004).
This class of solute transport description relies on a hindrance factor, which
is based on a spherical solute transported through a fluid-filled cylindrical
pore. In the presence of an applied electric field, the flux can be represented
by the modified Nernst-Plank equation:
H
D
dC
+
W
vC
J
=
ε
τ
CzF
RT
dφ
dx
−
dx
−
(9.12)
Here the passive diffusion component across the membrane is represented
by the term
D
d
dx
. The electrophoretic component is
dφ
dx
, where
z
is the
charge of the ionic permeant (solute),
F
is Faraday's number,
R
is the gas
constant,
T
is the absolute temperature, and
φ
is the electric potential. The
electroosmotic-induced convective flow is
vC
,
where
v
is the average flow veloc-
ity. Here the term
H
is the diffusion hindrance factor, which is associated
with Brownian motion and electrophoretic migration within the resistive mem-
brane, while the term
W
is a convective flow hindrance factor associated with
the bulk electroosmotic convective flow within the membrane. The hindrance
CzF
RT
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