Information Technology Reference
In-Depth Information
1
2
l
D
¼
DðÞ
is determined by the average diffusion coefficients of the medium components
D
and by the period
of the processes occurring in the environment. The state of the
medium inside such elementary volume corresponds to full intermixing. The
dynamics of the environment in such volumes is relatively simple. At the same
time, their interaction due to diffusion leads to complex spatiotemporal regimes.
˄
4.6.1 Some Details
Various approaches are known to describe the Belousov-Zhabotinsky reaction. The
conventional model of the process (the Field-K¨r¨s-Noyes (FKN) approximation)
is based on 11 stages, whose dynamics is described by two kinetic equations for the
reaction inhibitor
u
(HBrO
2
) and activator
v
(the highest valence of a metal ion—
Fe
3+
):
u
∂
t
¼
ʼ
ð
u
Þ
ʵ
∂
∂
v
∂
½
qv
þ φ
þ
u
1
ð
u
Þþ
D
u
Δ
u
,
t
¼
u
ʻ
v
þ
D
u
Δ
v
:
ð
ʼ þ
u
Þ
are the parameters determining the initial concentrations of the
components of the reaction and the rate constants of the intermediate reactions
occurring in the system. Unfortunately, these constants are not known today with an
accuracy sufficient for practical applications. However, over a number of years, the
composition of the media to suit the specific dynamic regimes has been defined.
Thus empirical connections between the values of the parameters
ʵ
,
q
, and
ʼ
and the
relative content of molecular components in the environment were established. The
value
Here,
ʵ
,
q
, and
ʼ
is introduced into kinetic equations only when photosensitive catalyst of the
reaction is employed. This value takes into account the influence of light radiation
on the dynamics of the environment (see next chapter).
For systems with complete intermixing, the term in the kinetic equations respon-
sible for the diffusion of medium components is discarded. In this case, it is easy to
qualitatively describe the main dynamic regimes of the medium. Suppose that the
initial state of the Belousov-Zhabotinsky medium corresponds to arbitrary concen-
trations of its components. Then the reactions occurring in the medium should lead
it to a steady state or states, which correspond to the point of intersection of the
curves
φ
u
∂
v
∂
∂
∂
t
¼
0,
t
¼
0
:
These curves, called zero isoclines, are a convenient tool for the qualitative
description of dynamic regimes of the Belousov-Zhabotinsky media.
