Biomedical Engineering Reference
In-Depth Information
(2.168)
where D is the effective diffusion coefficient. According to (2.40) , the diffusion coefficient of the ion
with
V$
i
¼
0
;
j
z
þ j¼j
z
1 is:
2 D
D
þ
D
¼
(2.169)
D þ þ
D
where D
are the diffusion coefficients of the cations and anions, respectively. Since the
convection current is zero ( i C ¼
and D
þ
r e E el ) due to electroneutrality, the electrical current in the electrolyte
is caused by electro-migration and diffusion ( i O >>
i D ):
i ¼ i O þ i D ¼ F 2
ðm þ þ m ÞcE el FðD þ D ÞVc;
(2.170)
where E is the electric field strength. Diffusive current i D is usually much smaller than the electro-
migration current i O ; thus, i
x
i O ¼
s el E el . The conservation of ionic species and currents can be
formulated for the conductivity as:
D s
D t ¼ DV
2 s:
(2.171)
V$ð
s el E el Þ¼
0
:
(2.172)
With Gauss's law
3 E el Þ¼
r el ;
the current continuity equation can be written as:
r el ¼
3 E el $V
s
=
s
:
(2.173)
where 3 is the permittivity of the liquid and is assumed to be uniform.
2.6.2 Electrophoresis
Electrophoresis is the motion of a charged particle relative to the surrounding liquid in an electric field
( Fig. 2.34 ). Because of the small size and low Reynolds number involved, the Stokes model can be
assumed for the motion of the particle:
q surf E el ¼
6 pu ep r p ;
(2.174)
FIGURE 2.34
Electrophoretic motion of a positively charged sphere.
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