0
Technical Briefs

Bridging the Gap Between Continuum Mechanical Microrotation Viscosity and Lagrangian Point-Particles

[+] Author and Article Information
Lihao Zhao

e-mail: lihao.zhao@ntnu.no
Department of Energy and
Process Engineering,
The Norwegian University of Science and Technology,
Trondheim, NO-7491 Norway

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 12, 2013; final manuscript received August 2, 2013; published online September 19, 2013. Assoc. Editor: Prashanta Dutta.

J. Fluids Eng 135(12), 124502 (Sep 19, 2013) (4 pages) Paper No: FE-13-1082; doi: 10.1115/1.4025201 History: Received February 12, 2013; Revised August 02, 2013

The microrotation viscosity is an essential fluid property in micropolar fluid dynamics. By considering a dilute suspension of inertial spherical point-particles in an otherwise Newtonian fluid, an explicit analytical expression for the microrotation viscosity is derived. This non-Newtonian continuum mechanical fluid property is seen to be proportional with the viscosity of the carrier fluid and the local particle loading. A number of assumptions were made in order to arrive at this simple relation, which implies that the microrotation viscosity should be considered as a flow variable rather than as a constant fluid property.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Eringen, A. C., 1964, “Simple Microfluids,” Int. J. Eng. Sci., 2, pp. 205–217. [CrossRef]
Eringen, A. C., 1966, “Theory of Micropolar Fluids,” J. Math. Mech., 16, pp. 1–18. [CrossRef]
Ariman, T., Turk, M. A., and Sylvester, N. D., 1973, “Microcontinuum Fluid mechanics—a Review,” Int. J. Eng. Sci., 11, pp. 905–930. [CrossRef]
Ariman, T., Turk, M. A., and Sylvester, N. D., 1974, “Applications of Microcontinuum Fluid Mechanics,” Int. J. Eng. Sci., 12, pp. 273–293. [CrossRef]
Łukaszewicz, G., 1999, Micropolar Fluids—Theory and Applications, Birkhäuser Verlag, Boston, MA.
Gad-El-Hak, M., 1999, “The Fluid Mechanics of Micro-Devices,” ASME J. Fluids Eng., 121, 1215–1233. [CrossRef]
Papautsky, I., Brazzle, J., Ameel, T., and Frazier, A. B., 1999, “Laminar Fluid Behavior in Microchannels Using Micropolar Fluid Theory,” Sensors Actuators, 73, pp. 101–108. [CrossRef]
Chen, J., Liang, C., and Lee, J. D., 2010, “Theory and Simulation of Micropolar Fluid Dynamics,” Proc. IMechE N: J. Nanoeng. Nanosyst., 224, pp. 31–39. [CrossRef]
Frish, M. B., and Webb, W. W., 1981, “Direct Measurement of Vorticity by Optical Probe,” J. Fluid Mech.107, pp. 173–200. [CrossRef]
Ye, J., and Roco, M. C., 1992, “Particle Rotation in a Couette Flow,” Phys. Fluids A, 4, pp. 220–224. [CrossRef]
Mortensen, P. H., Andersson, H. I., Gillissen, J. J. J., and Boersma, B. J., 2007, “Particle Spin in a Turbulent Shear Flow,” Phys. Fluids19, p. 078109. [CrossRef]
Zhao, L., and Andersson, H. I., 2011, “On Particle Spin in Two-Way Coupled Turbulent Channel Flow Simulations,” Phys. Fluids, 23, p. 093302. [CrossRef]
Bellani, G., Byron, M. L., Collignon, A. G., Meyer, C. R., and Variano, E. A., 2012, “Shape Effects on Turbulent Modulation by Large Nearly Neutrally Buoyant Particles,” J. Fluid Mech., 712, pp. 41–60. [CrossRef]
Balachandar, S., and Eaton, J. K., 2010, “Turbulent Dispersed Multiphase Flow,” Annu. Rev. Fluid Mech., 42, pp. 111–133. [CrossRef]
Irgens, F., 2008, Continuum Mechanics, Springer Verlag, Berlin.
Marchioli, C., and Soldati, A., 2002, “Mechanisms for Particle Transfer and Segregation in a Turbulent Boundary Layer,” J. Fluid Mech., 468, pp. 283–315. [CrossRef]
Zhao, L. H., and Andersson, H. I., 2012, “Statistics of Particle Suspensions in Turbulent Channel Flow,” Comm. Comp. Phys., 11, pp. 1311–1322. [CrossRef]
Andersson, H. I., Zhao, L., and Barri, M., 2012, “Torque-Coupling and Particle-Turbulence Interactions,” J. Fluid Mech., 696, pp. 319–329. [CrossRef]
Elghobashi, S., 2006, “An Updated Classification Map of Particle-Laden Turbulent Flows,” Proceedings of the IUTAM Symposium on Computational Multiphase Flow, S.Balachandar and A.Prosperetti, eds., Springer, Houten, The Netherlands, pp. 3–10.
Snijkers, F., D'Avino, G., Maffettone, P. L., Greco, F., Hulsen, M., and Vermant, J., 2009, “Rotation of a Sphere in a Viscoelastic Liquid Subjected to Shear Flow. Part II. Experimental Results,” J. Rheol., 53, pp. 459–480. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Microrotation viscosity μr in particle-laden turbulent channel flow at Re = 180. Variation of the viscosity ratio μr/μ for some different Stokes numbers St from the channel wall at z+ = 0 to the channel center at z+ = 180. Here, z+ is the wall-normal coordinate z normalized with the viscous length scale μ/(ρ uτ).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In