Biomedical Engineering Reference
In-Depth Information
FIGURE 6.36
Dimensionless temperature distribution between the two heaters as a function of dimensionless time t*.
with
8
v
R
i
A ¼
(6.38)
rR
i
L
plug
s
lg
x þ L
plug
cos
f
a
s
lg
ðxÞ
cos
f
r
:
At the relatively slow velocity observed later in the experiment, we can assume the same contact angle
at the receding and advancing sides
ðf
r
¼ f
a
¼ fÞ
. Applying this assumption and
(6.34)
into
(6.38)
results in
2
B ¼
rR
i
L
plug
g
q
x þ L
plug
qðxÞ
cos
f:
2
B ¼
(6.39)
From
(6.37)
, the position of the left side of the plug can be determined as
Z
t
B
A
t þ
B
A
2
exp
ðAtÞ:
x ¼
u
d
t ¼ x
0
þ
(6.40)
0
Figure 6.37
depicts the typical positions and velocity of a liquid plug driven by thermocapillary effect
according to the above model.
Search WWH ::
Custom Search