Abstract
Viscosity is the resistance of fluids to motion. The dynamic viscosity at a point of a homogeneous fluid, μ, is defined as the ratio of the local shear stress, τ, and the local velocity gradient, also called the rate of shear, γ. The kinematic viscosity of a fluid, ν, is equal to the ratio μ/ρ f.
There is a category of fluids, called Newtonian fluids , for which the dynamic viscosity, μ, does not depend on the rate of shear and is solely a property of the fluid. In non-Newtonian fluids the viscosity depends on the rate of shear. Simple fluids that are used as base fluids in nanofluid systems, such as water, most refrigerants, engine oil, and ethyl glycol, are Newtonian fluids. The addition of the nanoparticles in a base fluid may render the heterogeneous mixture non-Newtonian.
Firstly, this chapter examines the analytical models of the viscosity of simple fluids and suspensions. The analytical treatment delineates the differences between suspensions of spheres and ellipsoidal particles. The concepts of effective viscosity and intrinsic viscosity are introduced with the methodology of their application to nanofluid systems. Secondly, the experimental results that pertain to Newtonian nanofluid suspensions are presented. This section includes sections on the types of viscometers used; how the measurements with heterogeneous Newtonian suspensions are different; and correlations stemming from experimental data for nanofluids. Thirdly, the rheology of solid–liquid suspensions is examined with special emphasis on the rheological characteristics of nanofluids and especially of CNT nanofluids that seem to exhibit non-Newtonian behavior. Fundamental results on the drag coefficient and heat transfer of particles in non-Newtonian fluids are also presented. Fourthly, because the pressure drop of a thermal system depends on the friction factor, this parameter is examined for channels of nanofluids. Analytical and experimental results are presented in this section on the friction factors with and without velocity slip on the walls of the channels.
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Notes
- 1.
The coefficient of the exponent in the Nguyen et al. (2007) publication is 0.148. However, it appears that the authors have used the value of the volumetric fraction as percentages rather than a pure number with decimal points (that is 2 % was used as the number 2 in the original correlation, not as 0.02).
- 2.
As with the Newtonian fluids, η is a weak function of the pressure, P.
- 3.
At the time of these publications the terms “nanofluid” and “nanoparticles” had not yet been adopted. The experimental data and the conclusions pertain to what are now called “aqueous nanofluids.”
References
Abdullhasan, A. K., Al-Jabair S., & Sultan, K. (2012). Experimental investigation of heat transfer and flow of nanofluids in horizontal circular tube. World Academy of Science, Engineering and Technology, 61, 484–491.
Acharya, A., Mashelkar, R. A., & Ulbrecht, J. (1976). Flow of inelastic and viscoelastic fluids past spheres. Rheologica Acta, 15, 454–468.
Anoop, K. B., Kabelac, S., Sundarajan, T., & Das, S. (2009). Rheological and flow characteristics of nanofluids. Journal of Applied Physics, 106, 034909.
Batchelor, G. (1977). The effect of Brownian motion on the bulk stress in a suspension of spherical particles. Journal of Fluid Mechanics, 83, 97–117.
Bejan, A. (2006). Advanced engineering thermodynamics (3rd ed.). New York, NY: Wiley.
Brinkman, H. (1952). The viscosity of concentrated suspensions in solutions. The Journal of Chemical Physics, 20, 571–582.
Buongiorno, J. (2006). Convective transport in nanofluids. Journal of Heat Transfer, 128, 240–250.
Chandrasekar, M., Suresh, S., & Chandra-Bose, A. (2011). Experimental studies on heat transfer and friction factor characteristics of Al2O3-water nanofluids in a circular pipe under transition flow with wire coil inserts. Heat Transfer Engineering, 32, 485–496.
Chen, H., Ding, Y., He, Y., & Tan, C. (2007). Rheological behavior of ethylene glycol based titania nanofluids. Chemical Physics Letters, 444, 333–337.
Chhabra, R. P. (2007). Bubbles, drops and particles in non-Newtonian fluids (2nd ed.). Boca Raton, FL: CRC.
Choi, C. H., Ulmanella, U., Kim, J., Ho, C. M., & Kim, C. J. (2006). Effective slip and friction reduction in nanograted superhydrophobic microchannels. Physics of Fluids, 18, 087105.
Chopkar, M., Sudarshan, S., Das, P. K., & Manna, I. (2008). Effect of particle size on thermal conductivity of nanofluids. Metallurgical and Materials Transactions A, 39(7), 1535–1542.
Das, S. K., Putra, S. K., & Roetzel, W. (2003). Pool boiling characteristics of nanofluids. International Journal of Heat and Mass Transfer, 46, 851–862.
DeGennes, P. G. (1990). Introduction to polymer dynamics. Cambridge: Cambridge University Press.
Din, X. Z., & Michaelides, E. E. (1998). Transport processes of water and protons through micro-pores. AIChE Journal, 44, 35–42.
Ding, Y., Alias, H., Wen, D., & Williams, R. A. (2006). Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids). International Journal of Heat and Mass Transfer, 49, 240–250.
Einstein, A. (1906). Eine neue bestimung der molekuldimensionen. Annalen der Physik, 19, 289–306.
Einstein, A. (1911). Berichtigung zu meiner Arbeit: “Eine neue bestimung der molekuldimensionen”. Annalen der Physik, 34, 591–592.
El-Genk, M. S., & Yang, I. H. (2008). Friction numbers and viscous dissipation heating for laminar flows of water in microtubes. Journal of Heat Transfer, 130, 082405-1–082405-13.
Farmer, L. K., & Michaelides, E. E. (1984). A model for slurry flows based on the equations of turbulence. Journal of Pipelines, 4, 185.
Feng, Z. G., & Michaelides, E. E. (2002). Hydrodynamic force on spheres in cylindrical and prismatic enclosures. International Journal of Multiphase Flow, 28, 479–496.
Fogelson, A. L., & Peskin, C. S. (1988). A fast numerical method for solving the three-dimensional Stokes equation in the presence of suspended particles. Journal of Computational Physics, 79, 50–69.
Frenkel, N., & Acrivos, A. (1967). On the viscosity of a concentrated suspension of solid spheres. Chemical Engineering Science, 6, 847–853.
Ghosh, U. K., Kumar, S., & Upadhyay, S. N. (1992). Mass transfer from spherical and non-spherical particles to non-Newtonian fluids. Polymer-Plastics Technology and Engineering, 31, 271–278.
Gibbs, J. W. (1878). On the equilibrium of heterogeneous substances. In J. W. Gibbs (Ed.), The collective works of J. Willard Gibbs. New York, NY: Longmans. 1928.
Happel, J. (1957). Viscosity of suspensions of uniform spheres. Journal of Applied Physics, 28, 1288–1292.
Happel, J., & Brenner, H. (1986). Low Reynolds number hydrodynamics. Washington, DC: Martinus Nijhoff (reprint, original work published 1963).
Hrenya, C. M., & Sinclair, J. L. (1997). Effects of particle-phase turbulence in gas-solid flows. AIChE Journal, 43(4), 853–869.
Hwang, K. S., Jang, P. S., & Choi, S. U. S. (2009). Flow and heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime. International Journal of Heat and Mass Transfer, 52, 193–199.
Jeans, J. J., Sir. (1925). The dynamical theory of gases (4th ed., reprint). New York, NY: Dover Publications, 1954.
Jeffery, G. B. (1922). The motion of ellipsoidal particles immersed in a viscous fluid. Proceedings of the Royal Society, A102, 161–179.
Kartushinski, A., Michaelides, E. E., Rudi, U. A., Shcheglov, I. N., & Tisler, S. V. (2011). Numerical simulation of three-dimensional gas-solid particle flow in a horizontal pipe. AIChE Journal, 11, 2977–2988.
Kawase, Y., & Ulbrecht, J. (1981). Drag and mass transfer in non-Newtonian flows through multi-particle systems at low Reynolds numbers. Chemical Engineering Science, 36, 1193.
Kestin, J. (1978). A course in thermodynamics (Vol. 1 and 2). Washington, DC: Hemisphere.
Kestin, J., Paul, R., Shankland, I. R., & Khalifa, H. E. (1980). A high-temperature, high-pressure oscillating-disk viscometer for concentrated ionic solutions. Berichte der Bunsengesellschaft für Physikalische Chemie, 84, 1255–1260.
Khanafer, K., & Vafai, K. (2011). A critical synthesis of thermophysical characteristics of nanofluids. International Journal of Heat and Mass Transfer, 54, 4410–4428.
Kim, S., Kim, C., Lee, W. H., & Park, S. R. (2011). Rheological properties of alumina nanofluids and their implication to the heat transfer enhancement mechanism. Journal of Applied Physics, 110, 034316-1–034316-6.
Ko, G. H., Heo, K., Lee, K., Kim, D. S., Kim, C., Sohn, Y., et al. (2007). An experimental study of the pressure drop of nanofluids containing carbon nanotubes in a horizontal tube. International Journal of Heat and Mass Transfer, 50, 4749–4753.
Krieger, I. M. (1972). Rheology of polydisperse lattices. Advances in Colloid and Interface Science, 3, 111–136.
Krieger, I. M., & Dougherty, T. J. (1959). A mechanism for non‐Newtonian flow in suspensions of rigid spheres. Transactions. Society of Rheology, 3, 137–152.
Krieger, I. M., & Eguiluz, M. (1976). The second electroviscous effect in polymer lattices. Transactions of the Society of Rheology , 20, 29–45.
Kuhn, W., & Kuhn, H. (1945). Bedeutung beschränkt freier Drehbarkeit für die Viskosität und Strömungsdoppelbrechung von Fadenmolekellösungen. Helvetica Chimica Acta, 28, 1533–1579.
Lauga, E., Brenner, M. P., & Stone, H. A. (2007). Microfluidics: The no-slip boundary condition, chapter 9. In C. Tropea, A. Yarin, & J. F. Foss (Eds.), Experimental fluid mechanics. Berlin: Springer.
Lee, S. W., Park, S. D., Kang, S., Bang, I. C., & Kim, J. H. (2011). Investigation of viscosity and thermal conductivity of SiC nanofluids for heat transfer applications. International Journal of Heat and Mass Transfer, 54, 433–438.
Lee, J. F., Sears, F. W., & Turcotte, D. L. (1963). Statistical thermodynamics. Reading, MA: Addison Wesley.
Liu, Z. H., & Liao, L. (2009). Forced convective flow drag and heat transfer characteristics of carbon nanotube suspensions in a horizontal small tube. Heat and Mass Transfer, 45(8), 1129–1136.
Lundgren, T. S. (1972). Slow flow through stationary random beds and suspensions of spheres. Journal of Fluid Mechanics, 51, 273–299.
Maiga, E. S., Palm, J., Nguyen, C. T., Roy, G., & Galanis, N. (2005). Heat transfer enhancement by using nanofluids in forced convection flows. International Journal of Heat and Fluid Flow, 26, 530–546.
Masoud-Hosseini, S., Moghadassi, A., & Henneke, D. (2010). A new dimensionless group model for determining the viscosity of nanofluids. Journal of Thermal Analysis and Calorimetry, 100, 873–877.
Masoumi, N., Sohrabi, N., & Behzadmehr, A. (2009). A new model for calculating the effective viscosity of nanofluids. Journal of Applied Physics, 42, 055501.
Masuda, H., Ebata, A., Teramae, K., & Hishinuma, N. (1993). Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (dispersion of c-Al2O3, SiO2 and TiO2 ultra-fine particles). Netsu Bussei, 4, 227–233.
Maxey, M. R. (1987). The motion of small spherical particles in a cellular flow field. Physics of Fluids, 30, 1915–1928.
Michaelides, E. E. (1984). A model for the flow of solid particles in gases. International Journal of Multiphase Flow, 10, 61–75.
Michaelides, E. E. (1987). Motion of particles in gases: Average velocity and pressure loss. Journal of Fluids Engineering, 109, 172.
Michaelides, E. E. (2006). Particles, bubbles and drops—Their motion, heat and mass transfer. Hackensack, NJ: World Scientific Publishing.
Michaelides, E. E. (2013). Heat and mass transfer in particulate suspensions. New York, NY: Springer.
Mooney, M. (1951). The viscosity of a concentrated suspension of spherical particles. Journal of Colloid Science, 6, 162–170.
Mostafa, A. A., & Elghobashi, S. E. (1985). A two-equation turbulence model for jet flows laden with vaporizing droplets. International Journal of Multiphase Flow, 11, 515–533.
Munson, B. R., Young, D. F., Okiishi, T. H., & Huwbsch, W. W. (2009). Fundamentals of fluid mechanics. Hoboken, NJ: Wiley.
Nguyen, C. T., Desgranges, F., Roy, G., Galanis, N., Marie, T., Boucher, S., et al. (2007). Temperature and particle-size dependent viscosity data for water based nanofluids—Hysteresis phenomenon. International Journal of Heat and Fluid Flow, 28, 1492–1506.
Pak, B. C., & Cho, Y. (1998). Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Experimental Heat Transfer, 11, 151–170.
Probstein, R. F. (1994). Physicochemical hydrodynamics (2nd ed.). New York, NY: Elsevier.
Ruan, B., & Jacobi, A. M. (2012). Ultrasonication effects on thermal and rheological properties of carbon nanotube suspensions. Nanoscale Research Letters. doi:10.1186/1556-276X-7-127.
Russel, W. R., Saville, D. A., & Schowalter, W. R. (1989). Colloidal dispersions. New York, NY: Cambridge University Press.
Schlichting, H. (1979). Boundary layer theory (7th ed.). New York, NY: McGraw-Hill.
Showalter, W.R. (1978). Mechanics of non-Newtonian fluids . Oxford: Pergamon Press.
Squires, K. D., & Eaton, J. K. (1991). Preferential concentration of particles by turbulence. Physics of Fluids, 3, 1169–1178.
Syam-Sundar, L., & Sharma, K. V. (2010). Turbulent heat transfer and friction factor of Al2O3 nanofluid in circular tubes with twisted tape inserts. International Journal of Heat and Mass Transfer, 53, 1409–1416.
Tien, C. L., & Lienhard, J. H. (1979). Statistical thermodynamics. New York, NY: Hemisphere. Revised Printing.
Tseng, W. J., & Chen, C. N. (2003). Effect of polymeric dispersant on rheological behavior of nickel–terpinol suspensions. Materials Science and Engineering, A347, 145–153.
Tseng, W. J., & Lin, K. C. (2003). Rheology and colloidal structure of aqueous TiO2 nanoparticle suspensions. Materials Science and Engineering, A355, 186–192.
Vand, V. (1948). Viscosity of solutions and suspensions. I Theory. Journal of Physical and Colloid Chemistry, 52, 277–299.
Wang, X., Xu, X., & Choi, S. U. S. (1999). Thermal conductivity of nanoparticle fluid mixture. Journal of Thermophysics and Heat Transfer, 13, 474–480.
Yang, Y., Grulke, E. A., Zhang, Z. G., & Wu, G. (2006). Thermal and rheological properties of carbon-nanotube-in-oil dispersions. Journal of Applied Physics, 99, 114307.
Yu, W., France, D. M., Smith, D. S., Singh, D., Timofeeva, E. V., & Routbort, J. L. (2009). Heat transfer to a silicon carbide/water nanofluid. International Journal of Heat and Mass Transfer, 52, 3606–3612.
Zhou, S. Q., Ni, R., & Funfschilling, D. (2010). Effects of shear rate and temperature on viscosity of alumina polyalphaolefins nanofluids. Journal of Applied Physics, 107, 054317.
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Michaelides, E.E.(. (2014). Viscosity. In: Nanofluidics. Springer, Cham. https://doi.org/10.1007/978-3-319-05621-0_4
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