Chemistry Reference
In-Depth Information
47
1.04
1.035
46.5
1.03
1.025
46
1.02
1.015
45.5
1.01
1.005
45
1
1 10
3
0
200
400
600
800
shear rate /s
-1
Figure 3.11
The axial ratio and orientation angle of a liquid drop 10 mm in diameter
and with Z
i
¼
0.8Z
o
and g
io
¼
40mNm
-1
. Data calculated from the ana-
lysis of Cox.
15
where the drop radius is a and the interfacial tension is g
io
. Now, the axial ratio
of the prolate ellipsoid is
r
a
¼
R
f
þ
1
1
R
f
ð
3
:
45
Þ
and its orientation angle in the shear field relative to the flow direction is
a
¼
p
4
þ
1
19
20
gaZ
i
g
io
2
tan
1
ð
3
:
46
Þ
0.01, hydrodynamic interactions
between particles become important. In a flowing suspension, particles move at
the velocity of the streamline corresponding to the particle centre. Hence,
particles will come close to particles on nearby streamlines and the disturbance
of the fluid around one particle interacts with that around passing particles.
The details of the interactions were analysed by Batchelor
17
and we may write
the viscosity in shear flow as
Z
ð
0
Þ
Z
o
As the concentration is increased above j
B
¼
1
þ
2
:
5j
þ
6
:
2j
2
þ
O
ð
j
3
Þ
ð
3
:
47a
Þ
or in extensional flow:
Z
ð
0
Þ
Z
o
¼
1
þ
2
:
5j
þ
7
:
6j
2
þ
O
ð
j
3
Þ
ð
3
:
47b
Þ
There are three points to be made about eqn (3.47). Firstly, the viscosity is the
low-shear-limiting value, Z(0), indicating that we may expect some thinning as
the deformation rate is increased. The reason is that a ''uniform'' distribution
was used (ensured by significant Brownian motion,
i.e. P
e
o
1) and this
