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Design of viscometers corresponding to a universal molecular simulation method

Published online by Cambridge University Press:  05 December 2011

Kaushik Dayal  and
Richard D. James
Kaushik Dayal
Affiliation:
Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Richard D. James*
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present conceptual designs of viscometers corresponding to our new exact molecular simulation method (Dayal & James, J. Mech. Phys. Solids, vol. 58 (2), 2010, pp. 145–163). The molecular simulation method is a generalization of the method of Lees & Edwards (J. Phys. C: Solid State Phys., vol. 5, 1972, p. 1921), and includes a three-parameter family of incompressible flows, as well as compressible flows and unsteady flows exhibiting vortex stretching. All fluids are allowed. The method gives a way to simulate these flows using relatively few molecules, in the absence of a constitutive relation describing the fluid. This paper presents conceptual designs for viscometers that produce large families of these flows. The basic theme of this paper is that the flows discussed here are a better way to characterize the properties of complex fluids than the currently available methods, such as those based on viscometric flows.

JFM classification

Complex Fluids: Complex Fluids Mathematical Foundations: Computational methods Micro-/Nano-fluid dynamics: Non-continuum effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 691 , 25 January 2012 , pp. 461 - 486
Copyright
Copyright © Cambridge University Press 2011

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References

1. Bentley, B. J. & Leal, L. G. 1986 A computer-controlled four-roll mill for investigations of particle and drop dynamics in two-dimensional linear shear flows. J. Fluid Mech. 167 (1), 219–240.CrossRefGoogle Scholar
2. Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535 (1), 189–214.CrossRefGoogle Scholar
3. Chan, N. Y., Chen, M. & Dunstan, D. E. 2009 Elasticity of polymer solutions in Couette flow measured by fluorescence resonance energy transfer (FRET). Eur. Phys. J. E: Soft Matter Biol. Phys. 30 (1), 37–41.CrossRefGoogle ScholarPubMed
4. Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids 2 (5), 765–777.CrossRefGoogle Scholar
5. Coleman, B. D., Markovitz, H. & Noll, W. 1966 Viscometric Flows of Non-Newtonian Fluids: Theory and Experiment. Springer.CrossRefGoogle Scholar
6. Crowley, D. G., Frank, F. C., Mackley, M. R. & Stephenson, R. G. 1976 Localized flow birefringence of polyethylene oxide solutions in a four roll mill. J. Polym. Sci. 14 (6), 1111–1119.Google Scholar
7. Dayal, K. & James, R. D. 2010 Nonequilibrium molecular dynamics for bulk materials and nanostructures. J. Mech. Phys. Solids 58 (2), 145–163.CrossRefGoogle Scholar
8. Dumitrica, T. & James, R. D. 2007 Objective molecular dynamics. J. Mech. Phys. Solids 55 (10), 2206–2236.CrossRefGoogle Scholar
9. Dunn, J. E. & Fosdick, R. L. 1974 Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Ration. Mech. Anal. 56 (3), 191–252.CrossRefGoogle Scholar
10. Ericksen, J. L. & Rivlin, R. S. 1955 Stress–deformation relations for isotropic materials. Arch. Ration. Mech. Anal. 4, 323–425.Google Scholar
11. Evans, D. J. & Morriss, G. P. 2008 Statistical Mechanics of Nonequilibrium Liquids. Cambridge University Press.CrossRefGoogle Scholar
12. Giesekus, H. 1962 Stromungen mit konstantem Geschwindigkeitsgradienten und die Bewegung von darin suspendierten Teilchen. Rheol. Acta 2 (2), 101–112 and 112–122.CrossRefGoogle Scholar
13. Giesekus, H. 1982 A unified approach to a variety of constitutive models for polymer fluids based on the concept of configuration-dependent molecular mobility. Rheol. Acta 21 (4), 366–375.CrossRefGoogle Scholar
14. Haller, G. 2005 An objective definition of a vortex. J. Fluid Mech. 525, 1–26.CrossRefGoogle Scholar
15. Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Report CTR-S88. Center for Turbulence Research.Google Scholar
16. Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285 (1), 69–94.CrossRefGoogle Scholar
17. Kim, K. S., Clifton, R. J. & Kumar, P. 1977 A combined normal- and transverse-displacement interferometer with an application to impact of y-cut quartz. J. Appl. Phys. 48 (10), 4132–4139.CrossRefGoogle Scholar
18. Kraynik, A. M. & Reinelt, D. A. 1992 Extensional motions of spatially periodic lattices. Intl J. Multiphase Flow 18 (6), 1045–1059.CrossRefGoogle Scholar
19. Lagnado, R. R. & Leal, L. G. 1990 Visualization of three-dimensional flow in a four-roll mill. Exp. Fluids 9 (1), 25–32.CrossRefGoogle Scholar
20. Lees, A. W. & Edwards, S. F. 1972 The computer study of transport processes under extreme conditions. J. Phys. C: Solid State Phys. 5, 1921.CrossRefGoogle Scholar
21. Oldroyd, J. G. 1950 On the formulation of rheological equations of state. Proc. R. Soc. Lond. Ser. A. Math. Phys. Sci. 200 (1063), 523.Google Scholar
22. Parlato, P. 1969 Non-viscometric flows of viscoelastic liquids. Master’s thesis, Department of Chemical Engineering, University of Delaware.Google Scholar
23. Pipkin, A. C. & Tanner, R. I. 1972 A survey of theory and experiment in viscometric flows of viscoelastic liquids. Mech. Today 1, 262–321.Google Scholar
24. Rivlin, R. S. 1956 Solution of some problems in the exact theory of visco-elasticity. J. Ration. Mech. Anal. 5, 179.Google Scholar
25. Taylor, G. I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. Ser. A 146 (858), 501.Google Scholar
26. Thien, N. P. & Tanner, R. I. 1977 A new constitutive equation derived from network theory. J. Non-Newtonian Fluid Mech. 2 (4), 353–365.CrossRefGoogle Scholar
27. Ting, T. W. 1963 Certain non-steady flows of second-order fluids. Arch. Ration. Mech. Anal. 14 (1), 1–26.CrossRefGoogle Scholar
28. Todd, B. D. & Daivis, P. 2007 Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: techniques and applications. Mol. Simul. 33 (3), 189–229.CrossRefGoogle Scholar
29. Torza, S. 1975 Shear-induced crystallization of polymers. I. The four-roller apparatus. J. Polym. Sci. 13 (1), 43–57.Google Scholar
30. Yin, W. L. & Pipkin, A. C. 1970 Kinematics of viscometric flow. Arch. Ration. Mech. Anal. 37 (2), 111–135.CrossRefGoogle Scholar