Transcribed Text
Problem 1 True or False (you can provide justification if you want, but not required)
(a) The viscosity of a Newtonian fluid is constant at all shear rates and all temperatures.
(b) A material with tan 8> 1 behaves as a viscous liquid.
(c) A purely clastic material has a relaxation time of 0 seconds.
(d) Above the yield stress, a Bingham plastic behaves like a Newtonian fluid.
(c) The Bagley correction is required to correct for nonhomogeneous flow in a circular parallel
plate geometry.
(f) All components of the total stress tensor are zero when no flow is present.
Problem 2
Ketchup at 30°C may be described by the following constitutive equation: TAS 10+2705  whereas an
unknown sample from Home Depot at 30°C obeys the following model T>x 8y's where Txx is the shear
stress in Pa, and j is the shear rate in
(a) Evaluate the viscosities for ketchup and unknown at shear rates of 0.01, and 100 sec".
(b) Name the constitutive models that describe the two substances and state the general
differences (as many as possible) between them.
Problem 3
Consider the vector/tensor operation given by: a bec d:y P [Note there is no operator between vectors a
and b, cand d. and y and pl There is also a double dot product between d and y
(a) Does this yield a tensor, vector or scalar?
(b) Write down the end product of this operation in terms of index notation. NOTE: Do not
expand!! Show your work! Keep your final answer in terms of i,j,k (e.g., a,be gor whatever)
Problem 4
The velocity field for a material has the general form: y= [vx, Vy, O]; i.e, has components.
Here v, U(I +by²), Vy U (12bxy), V2 = 0 with U and b being constants
(a) Given that the fluid is Newtonian, what type of a flow is it?
(b) If the fluid were NonNewtonian, what type of flow(s) could this be describing?
(c) Is the flow homogeneous?
Please validate your answers with reasoning, explanations, or calculations/analysis to get credit.
Problem 5
A chemist wants to measure certain properties about various formulations she has put together. Please
help her out by explaining for each case (ac) what type of geometry to use and what type of
experiment(s) to perform so she can calculate the desired property. If desired, you may sketch example
experimental results to aid in your explanations.
(a) Relaxation time of a dilute, monodisperse polymer solution in a volatile, lowviscosity organic
solvent.
(b) Yield stress of a concentrated suspension of 50 um diameter particles.
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(c) How much the viscosity of a concentrated polymer solution ay=] s1 changes upon heating
from 25°C to 300°C.
Problem 6
Consider the viscosity versus shear rate plot of a material, as shown below on loglog scale plot. [Note
that the slopes of the lines are 1 and 0.5]. Your advisor, unfortunately, wants you to have it plotted as:
(a) Shear stress versus shear rate on a loglog scale graph (like below). Please sketch such a plot and
provide as much details as possible (e.g., values at transition points, slopes, etc.)
(b) Viscosity versus shear stress on loglog scale graph (like below). Please sketch such a plot with
as much details as possible (e.g., slope, numbers wherever possible, etc).
100
1
0.5
10
0.1
1.0
Shear rate
Problem 7
Mr. Formulation Chemist (FC) has been trying
un
to design novel colloidal formulations. For one
of his samples, Mr. FC finds the following G'
in
versus oscillatory strain data. These data were
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taken at constant frequency. In one case the
data was obtained using a vane geometry; in
another case, the data was obtained using a
to'
parallel plate geometry with smooth plates.
Explain what you think is (are) the reason(s)
is
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for the discrepancy in the data. Also explain
which data correspond to which geometry.

y
Strain amplitude Yo
2
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