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Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 329
/
2
/
e
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2023
iii
Paper 329
2
e
2026-09-28
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Insert the
velocity
from part
d
into the uniform-
film
equation
:
d
t
d
h
0
=
−
8
μL
3
γ
(
a
2
)
1/2
h
0
3/2
.
(1)
If
h
i
=
h
0
(
0
)
, integration gives
h
0
(
t
)
=
[
h
i
−
1/2
+
16
μL
a
3
γ
2
,
t
]
−
2
.
(2)
Thus
h
0
(
t
)
∼
9
γ
2
t
2
128
μ
2
L
2
a
(
t
→
∞
)
.
(3)
The
film
thins algebraically and does not reach zero thickness in finite
time
within this continuum
model
; rupture would require
physics
omitted here, such
as
intermolecular forces
.
Ancestors
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e
2
Paper 329
iii
2023
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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