Biomedical Engineering Reference
In-Depth Information
visibly demonstrate effects of these fields upon the thermal motion
using the same random collision sequence, which is also shown
for comparison. The E field in this case increases the cylindrical
diffusion rate; the B field reduces it.
Another comparison was performed between the uninfluenced
thermal motion and static E and B field exposure levels using a
physically realistic collision rate 7.8
10
13
col s
−
1
. No discernible
difference between the uninfluenced thermal agitation and the E
and B field cases is now seen by simple visual inspection. Since the
offsets are known to be orders of magnitude less than the thermal
velocities, the results are no surprise. However, such tiny offsets
have macroscopic effects when the averaging time is long enough.
These results when examined carefully illustrate how in liquids the
offsets induced by E and B fields are orders of magnitude less than
the thermal velocities. Yet in the macroscopic world, these offsets
are clearly visible as ionic currents, while thermal noise may not
be as apparent. We must be careful not to ignore macroscopically
significant offsets because of their apparent insignificance with
thermal motionswhen viewed microscopically.
Numerical examination of the offsets yields insight into the
collision sequences. Figure 4.16a shows the total cylindrical offset
ρ
for the E field case, while Fig. 4.16b shows the distribution of
the phase angle
φ
of the offset directions where the
X
direction
corresponds to zero phase angle (
φ
=
arctan(
y
/
x
)). Similarly for the
B field case, Fig. 4.16g shows the total offset
r
, while Fig. 4.16h
shows a distribution of the offset phase angle
φ
. The angles of the
thermal trajectories for both E and B field cases are not shown
but are randomly distributed similar to the B field offset phase
angle distribution shown in Fig. 4.16h. Distributions of the angular
difference between thermal and offset directions are shown in Figs.
4.16cand4.16iforbothcases.Theseplotsshowthecoherenceofthe
static E field offsets and the stochastic nature of the B field offsets,
whiledemonstratingtherelationshipsbetweenthedirectionsofthe
offsetsandthethermalmotion.Itisseenthatdependingonwhether
the offsets are coherent or stochastic, there is a dramatic effect
uponthetotaloffset.Thepresenceofatimeinvariantionicmobility
(6.2
×
10
−
8
ms
−
1
per V m
−
1
) is seen in Fig. 4.16a, while a similar
drift is lacking from Fig. 4.16g. These results are further discussed
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