Biomedical Engineering Reference
In-Depth Information
10 -2
Poiseuille effect
Osmosis
Electro-osmosis
10 -4
10 -6
10 -8
10 -10
10 -5
10 -4
10 -3
Ionic Force (mol 1 -3 )
10 -2
10 -1
10 0
FIGURE 3.7
Coupled fluid velocities versus the ionic force considering a model of plane
channel for the water-saturated electrolyte pore with 10 nm thickness and
negative surface charge of 0.2 C/m 2 density: (i) hydraulic (Poiseuille) gradient
of 10 MPa/m; (ii) osmotic gradient of 10 4 mol/m 4 ; (iii) electroosmotic gradient
of 10 V/m.
and electroosmotic driving gradients as exhibited by the generalized Poiseuille
law (Lemaire et al . 2008):
u =
κ P
p
κ C
C i κ E
ψ
(3.24)
κ i are calculated using homogenization
procedures adapted from Moyne and Murad (2002). In Figure 3.7, using the
obtained expressions of these permeability parameters, we present the result-
ing fluid velocity as a function of the ionic force. Here, we consider a model of
plane channel for a representative pore. This channel is filled with water-
saturated electrolyte, has 10 nm thickness and negative surface charge of
0.2 C/m 2 density. Flow is generated by driving gradients corresponding to
a physiological situation (Figure 3.7). If the velocity contribution due to the
hydraulic effect remains constant since it only depends on the geometry of the
pore, the electrochemical velocities do change with the ionic force variations.
In particular, the lower the ionic force is, the higher the double-layer thick-
ness is, and the more ecient the osmotic effect is. Moreover, in this model,
since the surface charge density, which governs electroosmosis eciency, is
not modified by the ionic force changes, electroosmotic effect is only slightly
affected for the largest ionic force values. Thus electroosmosis seems to be
the main fluid transport mechanism through very thin pores for physiological
biochemical conditions.
The coupled permeability tensors
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