Biomedical Engineering Reference
In-Depth Information
Figure 4.8
Electrosensitivity observed in predatory behaviour of the
elasmobranch species. The diagram shows the anatomy of the ampullae of
Lorenzini, including the pores at the edge of the ventral sides of the fin, and
the network of canals leading to the centrally located ampullae.
In conventional viscous models, time-averaged macroscopic
motion is analysed by lumping all collisions together into a very
familiar macroscopic 'friction' term (Papoulis, 1965; Reif, 1965).
Ionic motion is described by the viscous Lorentz equation where
motion isretarded by the drag term,
m
ν
v
(Durney etal., 1988).
m
d
d
t
=
qE
+
q
v
×
B
−
m
ν
v
(4.3)
Relating this equation to the physical world, ionic mobility
(velocity per unit E field,
μ
=
E
) can be measured experimentally
(Pethig, 1988). From Eq. (4.1) it is seen that for the case
E
=
1V
m
−
1
at constant drift velocity (
d
d
t
=
0), a macroscopic viscosity can
bedefined
ν
=
q
m
μ
,ignoringanyeffectsduetotheLGF.Usingcalcium
ionsasourexample,wheretheionicmass
m
is40
×
1.67
×
10
−
27
kg,
the ionic charge
q
is 2
×
1.6
×
10
−
19
C,
μ
Ca
is measured to be 6.2
×
10
−
8
ms
−
1
per V m
−
1
.Hence
ν
=
7.8
×
10
13
s
−
1
.
Figure4.8showsthemotionthatwasanalyticallycalculatedfrom
Eq. (4.1), assuming a range of different viscosities with a 1 V m
−
1
Efieldappliedinthe
x
direction. The particle is assumed to start
from the origin with non-zero initial velocity (
200
√
3m
v
tot
=
