Biomedical Engineering Reference
In-Depth Information
(b)
(a)
(c)
Figure 4.11
Random walk thermal agitation only. (a) Positional offsets, (b)
velocity magnitude and (c) velocity parallel and orthogonal to the
z
axis.
a free-flight period. Figure 4.11c shows the velocity components
parallel and orthogonal to the
z
axis of Cartesian (
x
,
y
,
z
)and
cylindrical (
ρ
,
φ
,
z
) coordinates. The random walk model simplifies
the actual physics, ignoring large fluctuations that occur in the
collision process due to electrostatic forces between outer shell
electrons; the single-ionmodelconsiders only short-range effects.
a
When a uniform, static E field is applied to the medium and
ion, the random walk is modified, as illustrated in Fig. 4.12a,b,
which shows the position and velocity offsets. Figure 4.12c shows
a
While the present model treats only the motions of single ions, multi-particle
models must consider long-range ion-ion interactions. In bioeffect models, long-
range effects are best tied in to the ionic concentrations rather than using the more
conventional Ewald sums, etc. (Allan and Tildesley, 1987).
