Problem Set 3
Rheology and Polymer Processing
Due Friday 4/23/10
1. A polymer blend is being prepared by mixing 80 kg of one polymer sample A (number
average molecular weight
M
n,A
=10,000 g/mol and weight average molecular weight
M
w,A
=15,000 g/mol) with 20kg of another sample B (
M
n,B
=20,000 g/mol and
M
w,B
=50,000
g/mol).
Calculate the number average and weight average molecular weights of the mixture,
M
n,mix
and
M
w,mix
, respectively.
What is the heterogeneity index?
2.
a)
From the definitions of
M
n
and
M
w
,
M
n
=
N
i
M
i
i
∑
N
i
i
∑
and
M
w
=
N
i
M
i
2
i
∑
N
i
M
i
i
∑
,
show that
M
w
M
n
−
1
=
N
i
N
j
M
i
−
M
j
(
)
2
j
∑
i
∑
2
N
i
M
i
i
∑
2
.
b)
What does this result imply about the relative magnitudes of
M
n
and
M
w
?
3.
The characteristics of two fluids, A and B, have been investigated by (1) measuring the
terminal velocity of a sphere falling in a large bath of each fluid, and (2) measuring the volume
flow rate of each at a specified pressure gradient.
In (1) a 0.5 cm diameter sphere weighing
0.104 g fell with a terminal velocity of 0.75 cm/s in both fluids.
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 Spring '10
 gohan
 Fluid Dynamics, average molecular weight, volumetric flow rates, Stokes drag law

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