Errata forSolution Manual to Understanding Rheology

Oxford University Press, 2001. Available from Amazon.comIncludes also solutions to extra problems from the web.

by Dr. Faith A. Morrison, Associate Professor of Chemical Engineering

Michigan Technological University

Chem-Sci-Eng 202 C

1400 Townsend Drive

Houghton, MI 49931-1295

email fmorriso@mtu.edu

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Appendix C

Chapter 22.39) The correct answer for III is 71.

Solutions to Extra Problems:

2.48

2.49

2.50

Chapter 3p.94 - Problem 3.12 The "+" signs are missing between the terms of v.del v on the top of page 94. The corrected page 94 is here.

p.99 - Problem 3.7 - Two problems were run together during typesetting. The first problem ends with the period after viscosity. The second problem begins "The equivalent pressure . . . " and goes to the end of the problem. The solution to this second problem is not in the instructor's manual.

p.100 Problem 3.15 There is no solution for the flow rate in the solution manual. The solution is given here.

Problem 3.18 In the solution for the pressure profile in this problem, the square on the zeta in the equation at the bottom of page 131 is dropped. This square should be carried through to the final solution.

p.103 - Problem 3.21. There are errors in the solution. A better solution from Morrison An Introduction to Fluid Mechanics (Cambridge 2013) is given here.

Problem 3.24 Helical Flow. The wrong boundary condition was used on velocity; it should be r=kappa R, v_z=V; a better solution from Morrison An Introduction to Fluid Mechanics (Cambridge 2013) is given here. See also Middleman, Funamentals of Polymer Processing, page 109.

Solutions to Extra Problems:

3.26

Chapter 4

Solutions to Extra Problems:

4.19

4.20

4.21

Chapter 55.7 The solution for problem 5.7 (Page 264) has a typo in the final solution. It should be 3*mu.

Solutions to Extra Problems:

5.19

5.20

5.21

Chapter 6

Solutions to Extra Problems:

6.9

Chapter 77.14 The sketch of the elongation startup function predicted for a PL-GNF is correct, but it could be better. It should show several start-up curves for different elongation rates. These curves would each look like instantaneous steup-ups at t=0, but the level of the step would decrease as a function of increasing el ongation rate (for a deformation-thinning material).

7.29 Axial Annular Flow. There is an error in the application of l'Hopital's rule for part c. The modifications may be found in this PDF file.

7.30 Tangential Annular Flow. There is a minor integration error in the solution for the pressure profile. Pages 12-14 of the solution are modified; the modifcation may be found in this PDF file.

Solutions to Extra Problems:

7.36

Chapter 8In many problem solutions for this chapter (8.9, 8.10, 8.11, 8.15, 8.16, 8.20) I have written the shear velocity profile in terms of gamma dot or gamma_dot_21 instead of in terms of sigma_dot. Although these are not wrong (since the magnitude of the rate-of-deformation tensor, gamma dot, equals sigma_dot and gamma dot_21 for shear), they do not match the text, and they do not reinforce the meaning that sigma_dot is a proscribed function. The preferred notation is followed in the solution to problem 8.6.

8.15 This solution is incomplete. The rest of the solution is here.

8.18 Some pages of the solution are missing and out of order. Page one is page 525 on the CD. The rest of the solution is here (to appear).

8.19 Some pages of the solution are mixed up. For this problem the solution is pages 524, 526, 527.

8.23 The solution on the CD ROM is wrong; it seems to be for some other data. The correct plot is in this PDF file.

8.26 The data are in this file. The solution on the CD is technically a good fit, but it does not correctly identify the longest relaxation time. A revised solution is here.

8.27 The data are in this file.

8.28 The data are in this file.

8.31 The final answer for lambda (longest relaxation time) is given as 0.04, but that is the value of 1/lambda. The correct value for lambda is 25s.

Solutions to Extra Problems:

8.36

8.37 The GNF models are good for situations where the behavior of the viscosity (shear thinning, shear thickening, yield stress) are the most important factor, such as in pressure-drop/flow rate calculations. They capture:

- shear thinning
- pressure drop/flow rate
- zero-shear viscosity (Carreau Yassuda)
- yield stress (Bingham)
- Trouton’s law (elongational viscosity)

They fail to capture:

- shear normal stresses
- memory
- startup, cessation (all time-dependent effects)
- molecular effects (relaxation time, dependence on MW)

The GLVE models are good for small strain and slow experiments where viscoelasticity is important. They capture:

- small-amplitude oscillatory shear
- step strain (especially the generalized Maxwell model)
- time effects (startup, cessation)
- memory (relaxation time)

They fail to capture:

- shear thinning
- nonlinear effects such as in step strain (damping function)
- shear normal stresses

Chapter 9In many problem solutions for this chapter (9.15, 9.16) I have written the shear velocity profile in terms of gamma dot or gamma_dot_21 instead of in terms of sigma_dot. Although these are not wrong (since the magnitude of the rate-of-deformation tensor, gamma dot, equals sigma_dot and gamma dot_21 for shear), they do not match the text, and they do not reinforce the meaning that sigma_dot is a proscribed function. The preferred notation is followed in the solution to problem 9.17.

Solutions to Extra Problems:

9.59 All parameters of the Oldroyd 8 are zero except lambda2=-Psi10/2eta0 and mu2=-1/eta0*(Psi10/2+Psi20). This gives the form of the second order fluid on page 456.

9.60 These two different approaches predict different probability distribution funcions Psi(R), but since the stress tensor just depends on the second moment of the probability distribution function <RR>, two models that predict different Psi(R) can predict the same stress tensor if the second moments of the two predictions are the same. This is what happened in this case.

9.61 The total force on combination is the same as the force on the lone dashpot (1) and is also the same as on the force on the combination dashpot+spring in parallel. The forces (F2) on the individual elements in the parallel unit are the same. The displacments overall are additive. With this information, you can follow the same procedure as in Chapter 8 to obtain the result. The relaxation time lambda1 of the Jeffrey's model equals (mu1+mu2)/G; the zero shear viscosity eta0 of the Jeffrey's model is equal to mu1 (the viscosity of the lone dashpot). The retardation time lambda2 is equal to mu2/G), the ration of the viscosity in the parallel unit to the spring constant in the parallel unit. Note that if mu2=0 the model reverts to the Maxwell model.

9.62 In affine motion the motion at all length scales is the same as the motion at macroscopic lengthscales.

9.63

9.64

9.65

9.66

Chapter 10

10.9 There is an algebra mistake at the bottom of the solution to the second part (R2/R1 should be R1/R2. The method is correct, but the answer should be 606 psi (not 66). The discussion should be replaced with the following: "For both Newtonian and PL-GNF a doubling of the length of the capillary doubles the pressure. The effect of radius, however, is much more pronounced for the Newtonian fluid. Halving the radius for a Newtonian fluid increases the pressure drop by a factor of 16 (2^4) while the same change causes the pressure drop developed by the PL-GNF to increase by a factor of 6 only."

10.14 The viscosity in the plot of the solution to this problem is labeled in Pa s, but the correct units are poise.

Appendix C

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