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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 non-homogeneous 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 (1-2bxy), 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 Non-Newtonian, 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 (a-c) 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, low-viscosity organic solvent. (b) Yield stress of a concentrated suspension of 50 um diameter particles. 1 (c) How much the viscosity of a concentrated polymer solution ay=] s-1 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 log-log 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 log-log 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 log-log 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 102 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 10 for the discrepancy in the data. Also explain which data correspond to which geometry. - y Strain amplitude Yo 2

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