Chemistry Reference
In-Depth Information
with fractional (fractal) dimension. However, the experimental data about
rates fluctuation moments testify, that small-scale properties of turbulent
current cannot be described with the aid of self-similar fractal [2]. There-
fore, a “heterogeneous fractals” were used for turbulent dissipative struc-
tures description. Such fractals formation rules on each scales hierarchy step
are chosen randomly in correspondence with some probability distribution.
Besides energy transfer is described with the aid of random fragmentation
model in supposition, that between process different stages a correlation is
absent. In this case fractal volume has no global invariance properties in
respect to similarity transformation. Nevertheless, there exists the fractal re-
lationship between active whirls number on nth fragmentation steps <
N
n
>
and turbulent structures characteristic scale
L
n
[2]:
d
NL
,
~
f
n
n
(6.1)
where
d
f
is fractal dimension.
If to consider the cluster network density n
cl
as <
N
n
> and to choose statis-
tical segment length
l
st
as the scale, then the Eq. (6.1) is changed as follows
[7]:
d
n
~
l
.
(6.2)
f
cl
st
The value
d
f
of amorphous polymers cluster structure was determined
according to the mechanical tests results (the Eqs. (1.9) and (2.20)).
d
l
is adduced for PC and
PAr, which turns out to be linear and, hence, corresponds to the Eqs. (6.1)
and (6.2). Thus, the value n
cl
(or j
cl
) can be considered as an analog of active
whirls number on segmental level.
Goldstein and Mosolov [8] offered the general relationship for estima-
tion of fractal liquid viscosity h(l):
l
):
f
st
hh
-
( )~
l
l
2
d
,
(6.3)
f
0
where
l
is a flow characteristic scale, h
o
is constant.
