Viscosity of Nanofluids. Why It Is Not Described by the Classical Theories

Author(s)
Valery Ya. Rudyak

ABSTRACT

Transport properties of nanofluids are extensively studied last decade. This has been motivated by the use of nanosized systems in various applications. The viscosity of nanofluids is of great significance as the application of nanofluids is always associated with their flow. However, despite the fairly large amount of available experimental information, there is a lack of systematic data on this issue and experimental results are often contradictory. The purpose of this review is to identify the typical parameters determining the viscosity of nanofluids. The dependence of the nanofluid viscosity on the particles concentration, their size and temperature is analyzed. It is explained why the viscosity of nanofluid does not described by the classical theories. It was shown that size of nanoparticles is the key characteristics of nanofluids. In addition the nanofluid is more structural liquid than the base one.

Cite this paper

Rudyak, V. (2013) Viscosity of Nanofluids. Why It Is Not Described by the Classical Theories.*Advances in Nanoparticles*, **2**, 266-279. doi: 10.4236/anp.2013.23037.

Rudyak, V. (2013) Viscosity of Nanofluids. Why It Is Not Described by the Classical Theories.

References

[1] S. Choi, “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” In: D. A. Siginer and H. P. Wang, Eds., Developments Applications of Non-Newtonian Flows, Vol. 231, ASME, New York, 1995, pp. 99-105.

[2] V. Ya. Rudyak and S. L. Krasnolutskii, “On Kinetic Theory of Diffusion of Nanoparticles in a Rarefied Gas,” Atmospheric and Oceanic Optics, Vol. 16, No. 5-6, 2003, pp. 468-471.

[3] V. Ya. Rudyak and A. A. Belkin, “Mechanisms of Collective Nanoparticles Interaction with Condensed Solvent,” Thermophysics & Aeromechanics, Vol. 11, No. 2, 2004, pp. 54-63.

[4] V. Ya. Rudyak, “Kinetic Theory and Modern Aerohydromechanics,” Journal of Applied and Industrial Mathe matics, Vol. 8, No. 3, 2005, pp. 120-148.

[5] V. Ya. Rudyak, A. A. Belkin and S. L. Krasnolutskii, “Statistical Theory of Nanoparticle Transport Processes in Gases and Liquids,” Thermophysics & Aeromechanics, Vol. 12, No. 4, 2005, pp. 506-516.

[6] S. Sh. Hosseini, A. Shahrjerdi and Y. Vazifeshenas, “A Review of Relations for Physical Properties of Nanofluids,” Australian Journal of Basic and Applied Sciences, Vol. 5, No. 10, 2011, pp. 417-435.

[7] I. M. Mahbubul, R. Saidur and M. A. Amalina, “Latest Developments on the Viscosity of Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 55, No. 4, 2012, pp. 874-885. doi:10.1016/j.ijheatmasstransfer.2011.10.021

[8] D. C. Venerus, et al., “Viscosity Measurements on Colloidal Dispersions (Nanofluids) for Heat Transfer Applications,” Applied Rheology, Vol. 20, No. 4, 2010, Article ID: 44582.

[9] G. Paul, J. Philip, B. Raj, P. K. Das and I. Manna, “Synthesis Characterization and Thermal Property Measurement of Nano-Al95Zn05 Dispersed Nanofluid Prepared by a Two-Step Process,” International Journal of Heat and Mass Transfer, Vol. 54, No. 15-16, 2011, pp. 3783-3788. doi:10.1016/j.ijheatmasstransfer.2011.02.044

[10] W. Yu, H. Xie, Y. Li and L. Chen, “Experimental Investigation on Thermal Conductivity and Viscosity of Aluminum Nitride Nanofluid,” Particuology, Vol. 9, No. 2, 2011, pp. 187-191. doi:10.1016/j.partic.2010.05.014

[11] F. Perrin, “Etude Mathématique du Mouvement Brow nien de Rotation,” Annales Scientifiques de L’Ecole Nor male Superieure, Vol. 3, No. 45, 1928, pp. 1-51.

[12] A. Einstein, “Eine Neue Bestimmung der Molekiildi mensionen,” Annalen der Physik, Vol. 19, Ser. 4, 1906, pp. 289-306. doi:10.1002/andp.19063240204

[13] J. C. Maxwell, “A Treatise on Electricity and Magnet ism,” Clarendon Press, Oxford, 1873.

[14] J. O. Hirschfelder, Ch. F. Curtiss and R. B. Bird, “Mo lecular Theory of Gases and Liquids,” Wiley, New York, 1954.

[15] R. C. Reid, J. M. Prausnitz and T. K. Sherwood, “The Properties of Gases and Liquids,” McGraw-Hill Book Comp., New York, 1977.

[16] V. Ya. Rudyak, “Kinetics of Finely Dispersed Gas Suspension,” Soviet Technical Physics Letters, Vol. 18, No. 10, 1992, pp. 681-682.

[17] V. Ya. Rudyak, “The Kinetic Equations of Rarefied Gas Suspensions,” Proceedings of the 21st International Sym posium on Rarefied Gas Dynamics, 1999, pp. 271-278.

[18] V. Ya. Rudyak and S. L. Krasnolutskii, “Kinetic Description of Nanoparticle Diffusion in Rarefied Gas,” Doklady Physics, Vol. 46, No. 12, 2001, pp. 897-899. doi:10.1134/1.1433539

[19] V. Ya. Rudyak and S. L. Krasnolutskii, “Diffusion of Nanoparticles in a Rarefied Gas,” Technical Physics, Vol. 47, No. 7, 2002, pp. 807-812. doi:10.1134/1.1495039

[20] V. Ya. Rudyak and S. L. Krasnolutsky, “Effective Viscidity Coefficient for Rarefied Nano Gas Suspensions,” Atmosphere and Ocean Optics, Vol. 17, No. 5, 2004, pp. 468-475.

[21] V. Ya. Rudyak, S. L. Krasnolutskii and E. N. Ivaschenko, “Influence of the Physical Properties of the Material of Nanoparticles on Their Diffusion in Rarefied Gases,” Journal of Engineering Physics and Thermophysics, Vol. 81, No. 3, 2008, pp. 520-524. doi:10.1007/s10891-008-0063-y

[22] V. Ya. Rudyak and S. L. Krasnolutskii, “The Interaction Potential of Dispersed Particles with Carrier Gas Molecules,” Proceedings of the 21st International Symposium on Rarefied Gas Dynamics, Vol. 1, 1999, pp. 264-270.

[23] V. Ya. Rudyak, S. L. Krasnolutskii, “About Viscosity of Rarefied Gas Suspensions with Nanoparticles,” Doklady Physics, Vol. 48, No. 10, 2003, pp. 583-586. doi:10.1134/1.1623543

[24] V. Ya. Rudyak, S. L. Krasnolutskii, A. G. Nasibulin and E. I. Kauppinen, “Methods of Measuring the Diffusion Coefficient and Sizes of Nanoparticles in Rarefied Gas,” Doklady Physics, Vol. 47, No. 10, 2002, pp. 758-761. doi:10.1134/1.1519325

[25] V. Ya. Rudyak and S. L. Krasnolutskii, “The Calculation and Measurement of Nanoparticles Diffusion Coefficient in Rarefied Gases,” Journal of Aerosol Science, Vol. 35, No. 1, 2003, pp. 579S-580S.

[26] V. Ya. Rudyak, S. N. Dubtsov and A. M. Baklanov, “Temperature Dependence of the Diffusion Coefficient of Nanoparticles,” Technical Physics Letters, Vol. 34, No. 6, 2008, pp. 519-521. doi:10.1134/S1063785008060217

[27] V. Ya. Rudyak, S. N. Dubtsov and A. M. Baklanov, “Measurements of the Temperature Dependent Diffusion Coefficient of Nanoparticles in the Range of 295 600K at Atmospheric Pressure,” Journal of Aerosol Science, Vol. 40, No. 10, 2009, pp. 833-843. doi:10.1016/j.jaerosci.2009.06.006

[28] W. B. Russel, D. A. Saville and W. R. Schowalter, “Colloidal Dispersions,” Cambridge University Press, Cambridge, 1989.

[29] G. R. Batchelor, “Brownian Diffusion of Particles with Hydrodynamic Interaction,” Journal of Fluid Mechanics, Vol. 74, Pt. 1, 1976, pp. 1-29. doi:10.1017/S0022112076001663

[30] G. R. Batchelor, “The Effect of Brownian Motion on the Bulk Stress in a Suspension of Spherical Particles,” Journal of Fluid Mechanics, Vol. 83, Pt. 1, 1977, pp. 97-127. doi:10.1017/S0022112077001062

[31] A. Acrivos and E. Y. Chang, “A Model for Estimating Transport Quantities in Two-Phase Materials,” Physics of Fluids, Vol. 29, No. 3-4, 1986, pp. 459-464.

[32] M. Mooney, “The Viscosity of a Concentrated Suspension of Spherical Particles,” Journal of Colloid Science, Vol. 6, No. 1, 1951, pp. 162-170.

[33] I. M. Krieger and T. J. Dougherty, “A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres,” Journal of Rheology, Vol. 3, No. 1, 1959, pp. 137-145. doi:10.1122/1.548848

[34] N. A. Frankel and A. Acrivos, “On the Viscosity of a Concentrated Suspension of Solid Spheres,” Chemical Engineering Science, Vol. 22, No. 6, 1967, pp. 847-853. doi:10.1016/0009-2509(67)80149-0

[35] I. M. Krieger, “Rheology of Monodisperse Lattices,” Advances in Colloid and Interface Science, Vol. 3, No. 1, 1972, pp. 111-132. doi:10.1016/0001-8686(72)80001-0

[36] E. N. da C. Andrade, “Viscosity of Liquids,” Nature, Vol. 125, 1930, pp. 309-324. doi:10.1038/125309b0

[37] E. N. da C. Andrade, “A Theory of the Viscosity of Liq uids,” Philosophical Magazine, Vol. 17, No. 112, 1934, pp. 497-514.

[38] A. Ya. Malkin and A. I. Isaev, “Rheology, Concepts, Methods, & Applications,” Chemical Publishing, Toronto, 2006.

[39] A. Graham, “On the Viscosity of Suspensions of Solid Spheres,” Applied Scientific Research, Vol. 37, No. 3-4, 1981, pp. 275-286. doi:10.1007/BF00951252

[40] D. C. Venerus, et al., “Viscosity Measurements on Col loidal Dispersions (Nanofluids) for Heat Transfer Appli cations,” Applied Rheology, Vol. 20, No. 4, 2010, Article ID: 44582.

[41] H. Chen, Y. Ding, Y. He and C. Tan, “Rheological Be havior of Ethylene Glycol Based Titania Nanofluids,” Chemical Physics Letters, Vol. 444, No. 4-6, 2007, pp. 333-337. doi:10.1016/j.cplett.2007.07.046

[42] H. Chen, Y. Ding and C. Tan, “Rheological Behavior of Nanofluids,” New Journal of Physics, Vol. 9, No. 10, 2007, p. 367.

[43] L. Colla, L. Fedele, M. Scattolini and S. Bobbo, “Wa ter-Based Fe2O3 Nanofluid Characterization: Thermal Conductivity and Viscosity Measurements and Correla tion,” Advances in Mechanical Engineering, Vol. 2012, No. 1, 2012, Article ID: 674947. doi:10.1155/2012/674947

[44] J. Garg, et al., “Enchanced Thermal Conductivity and Viscosity of Copper Nanoparticles in Ethylene Glycol Nanofluid,” Applied Physics Letters, Vol. 103, No. 7, 2008, Article ID: 074301. doi:10.1063/1.2902483

[45] F. S. Oueslati and R. Bennace, “Heterogeneous Nanoflu ids: Natural Convection Heat Transfer Enhancement,” Nanoscale Research Letters, Vol. 6, No. 3, 2011, p. 222. doi:10.1186/1556-276X-6-222

[46] P. K. Namburu, D. P. Kulkarni, A. Dandekar and D. K. Das, “Experimental Investigation of Viscosity and Spe cific Heat and Silicon Dioxide Nanofluids,” Micro & Nano Letters, Vol. 2, No. 3, 2007, pp. 67-71. doi:10.1049/mnl:20070037

[47] P. K. Namburu, D. P. Kulkarni, D. Misra and D. K. Das, “Viscosity of Copper Oxide Nanoparticles Dispersed in Ethylene Glycol and Water Mixture,” Experimental Ther mal and Fluid Science, Vol. 32, No. 2, 2007, pp. 397-402. doi:10.1016/j.expthermflusci.2007.05.001

[48] C. T. Nguyen, et al., “Viscosity Data for Al2O3-Water Nanofluid-Hysteresis: Is Heat Transfer Enhancement Us ing Nanofluids Reliable?” International Journal of Thermal Sciences, Vol. 47, No. 2, 2008, pp. 103-111. doi:10.1016/j.ijthermalsci.2007.01.033

[49] B.C. Pak and Y. I. Cho, “Hydrodynamic and Heat Trans fer Study of Dispersed Fluids with Submicron Metallic Oxide Particles,” Experimental Heat Transfer, Vol. 11, No. 2, 1998, pp. 151-170. doi:10.1080/08916159808946559

[50] X. Wang, X. Xu and S. U. S. Choi, “Thermal Conductiv ity of Nanoparticle-Fluid Mixture,” Journal of Thermo physics and Heat Transfer, Vol. 13, No. 4, 1999, pp. 474-480. doi:10.2514/2.6486

[51] Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang and H. Lu, “Heat Transfer and Flow Behaviour of Aqueous Suspen sions of TiO2 Nanoparticles (Nanofluids) Flowing Up ward through a Vertical Pipe,” International Journal of Heat and Mass Transfer, Vol. 50, No. 11-12, 2007, pp. 2272-2281. doi:10.1016/j.ijheatmasstransfer.2006.10.024

[52] C. T. Nguyen, F. Desgranges, G. Roy, N. Galanis, T. Marei, S. Boucher and H. Mintsa, “Temperature and Par ticle-Size Dependent Viscosity Data for Water-Based Nanofluids—Hysteresis Phenomenon,” International Jour nal of Heat and Fluid Flow, Vol. 28, No. 6, 2007, pp. 1492-1506. doi:10.1016/j.ijheatfluidflow.2007.02.004

[53] P. Prasher, D. Song and J. Wang, “Measurements of Na nofluid Viscosity and Its Implications for Thermal Ap plications,” Applied Physics Letters, Vol. 89, No. 13, 2006, Article ID: 133108. doi:10.1063/1.2356113

[54] J. Chevalier, O. Tillement and F. Ayela, “Rheological Properties of Nanofluids Flowing Through Microchan nels,” Applied Physics Letters, Vol. 91, No. 23, Article ID: 233103.

[55] E. V. Timofeeva, D. S. Smith, W. Yu, D. M. France, D. Singh and J. L. Routbo, “Particle Size and Interfacial Ef fects on Thermo-Physical and Heat Transfer Characteris tics of Water-Based α-SiC Nanofluids,” Nanotechnology, Vol. 21, No. 21, 2010, Article ID: 215703. doi:10.1088/0957-4484/21/21/215703

[56] V. Y. Rudyak, A. A. Belkin, E. A. Tomilina and V. V. Egorov, “Nanoparticle Friction Force and Effective Vis cosity of Nanofluids,” Defect and Diffusion Forum, Vol. 273-276, No. 6, 2008, pp. 566-571.

[57] V. Y. Rudyak, A. A. Belkin and V. V. Egorov, “On the Effective Viscosity of Nanosuspensions,” Technical Phy sics, Vol. 54, No. 8, 2009, pp. 1102-1109. doi:10.1134/S1063784209080039

[58] G. Balasubramanian, S. Sen and I. K. Puri, “Shear Visco sity Enhancement in Water—Nanoparticle Suspensions,” Physics Letters, Vol. A 376, No. 6-7, 2012, pp. 860-863.

[59] V. Y. Rudyak, S. V. Dimov, V. V. Kuznetsov and S. P. Bardakhanov, “Measurement of the Viscosity Coefficient of an Ethylene Glycol-Based Nanofluid with Silicon Dioxide Particles,” Doklady Physics, Vol. 58, No. 5, 2013, pp. 173-176. doi:10.1134/S1028335813050042

[60] V. Y. Rudyak, V. Dimov and V. V. Kuznetsov, “About Dependence of the Nanofluid Viscosity Coefficient on the Temperature and Size of the Particles,” Technical Physics Letters, Vol. 39, No. 17, 2013, pp. 53-59.

[61] T. X. Phuoc and M. Massoudi, “Experimental Obser vations of the Effects of Shear Rates and Particle Con centration on the Viscosity of Fe2O3-Deionized Water Nanofluids,” International Journal of Thermal Sciences, Vol. 48, No. 7, 2009, pp. 1294-1301. doi:10.1016/j.ijthermalsci.2008.11.015

[62] A. D. Sommers, K. L. Yerkes and A. R. Runion, “A Stu dy of the Thermal-Hydraulic Performance and System Level Effects of Aluminum Oxide-Propanol Nanofluid,” Proceedings of the 14th International Heat Transfer Conference, Washington DC, 2010, Article ID: 22931.

[63] V. Y. Rudyak and A. A. Belkin, “Simulation of the Trans port Coefficients of Nanofluids,” Nanosystems: Physics, Chemistry, Mathematics, Vol. 1, No. 1, 2010, pp. 156-177.

[64] V. Y. Rudyak, “Nonlocal Solution of the Boltzmann Equation,” Zhurnal Tekhnicheskoi Fiziki, Vol. 65, No. 11, 1995, pp. 29-40.

[65] V. Y. Rudyak, S. L. Krasnolutskii and D. A. Ivanov, “The Interaction Potential of Nanoparticles,” Doklady Physics, Vol. 57, No. 1, 2012, pp. 33-35. doi:10.1134/S1028335812010053

[66] V. Y. Rudyak, S. L. Krasnolutskii and D. A. Ivanov, “Molecular Dynamics Simulation of the Nanofluid Vis cosity Coefficient,” Proceedings Russian Conference Mo dern Problems of the Rarefied Gas Dynamics, Novosi birsk, 26-30 July 2013, pp. 98-101

[1] S. Choi, “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” In: D. A. Siginer and H. P. Wang, Eds., Developments Applications of Non-Newtonian Flows, Vol. 231, ASME, New York, 1995, pp. 99-105.

[2] V. Ya. Rudyak and S. L. Krasnolutskii, “On Kinetic Theory of Diffusion of Nanoparticles in a Rarefied Gas,” Atmospheric and Oceanic Optics, Vol. 16, No. 5-6, 2003, pp. 468-471.

[3] V. Ya. Rudyak and A. A. Belkin, “Mechanisms of Collective Nanoparticles Interaction with Condensed Solvent,” Thermophysics & Aeromechanics, Vol. 11, No. 2, 2004, pp. 54-63.

[4] V. Ya. Rudyak, “Kinetic Theory and Modern Aerohydromechanics,” Journal of Applied and Industrial Mathe matics, Vol. 8, No. 3, 2005, pp. 120-148.

[5] V. Ya. Rudyak, A. A. Belkin and S. L. Krasnolutskii, “Statistical Theory of Nanoparticle Transport Processes in Gases and Liquids,” Thermophysics & Aeromechanics, Vol. 12, No. 4, 2005, pp. 506-516.

[6] S. Sh. Hosseini, A. Shahrjerdi and Y. Vazifeshenas, “A Review of Relations for Physical Properties of Nanofluids,” Australian Journal of Basic and Applied Sciences, Vol. 5, No. 10, 2011, pp. 417-435.

[7] I. M. Mahbubul, R. Saidur and M. A. Amalina, “Latest Developments on the Viscosity of Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 55, No. 4, 2012, pp. 874-885. doi:10.1016/j.ijheatmasstransfer.2011.10.021

[8] D. C. Venerus, et al., “Viscosity Measurements on Colloidal Dispersions (Nanofluids) for Heat Transfer Applications,” Applied Rheology, Vol. 20, No. 4, 2010, Article ID: 44582.

[9] G. Paul, J. Philip, B. Raj, P. K. Das and I. Manna, “Synthesis Characterization and Thermal Property Measurement of Nano-Al95Zn05 Dispersed Nanofluid Prepared by a Two-Step Process,” International Journal of Heat and Mass Transfer, Vol. 54, No. 15-16, 2011, pp. 3783-3788. doi:10.1016/j.ijheatmasstransfer.2011.02.044

[10] W. Yu, H. Xie, Y. Li and L. Chen, “Experimental Investigation on Thermal Conductivity and Viscosity of Aluminum Nitride Nanofluid,” Particuology, Vol. 9, No. 2, 2011, pp. 187-191. doi:10.1016/j.partic.2010.05.014

[11] F. Perrin, “Etude Mathématique du Mouvement Brow nien de Rotation,” Annales Scientifiques de L’Ecole Nor male Superieure, Vol. 3, No. 45, 1928, pp. 1-51.

[12] A. Einstein, “Eine Neue Bestimmung der Molekiildi mensionen,” Annalen der Physik, Vol. 19, Ser. 4, 1906, pp. 289-306. doi:10.1002/andp.19063240204

[13] J. C. Maxwell, “A Treatise on Electricity and Magnet ism,” Clarendon Press, Oxford, 1873.

[14] J. O. Hirschfelder, Ch. F. Curtiss and R. B. Bird, “Mo lecular Theory of Gases and Liquids,” Wiley, New York, 1954.

[15] R. C. Reid, J. M. Prausnitz and T. K. Sherwood, “The Properties of Gases and Liquids,” McGraw-Hill Book Comp., New York, 1977.

[16] V. Ya. Rudyak, “Kinetics of Finely Dispersed Gas Suspension,” Soviet Technical Physics Letters, Vol. 18, No. 10, 1992, pp. 681-682.

[17] V. Ya. Rudyak, “The Kinetic Equations of Rarefied Gas Suspensions,” Proceedings of the 21st International Sym posium on Rarefied Gas Dynamics, 1999, pp. 271-278.

[18] V. Ya. Rudyak and S. L. Krasnolutskii, “Kinetic Description of Nanoparticle Diffusion in Rarefied Gas,” Doklady Physics, Vol. 46, No. 12, 2001, pp. 897-899. doi:10.1134/1.1433539

[19] V. Ya. Rudyak and S. L. Krasnolutskii, “Diffusion of Nanoparticles in a Rarefied Gas,” Technical Physics, Vol. 47, No. 7, 2002, pp. 807-812. doi:10.1134/1.1495039

[20] V. Ya. Rudyak and S. L. Krasnolutsky, “Effective Viscidity Coefficient for Rarefied Nano Gas Suspensions,” Atmosphere and Ocean Optics, Vol. 17, No. 5, 2004, pp. 468-475.

[21] V. Ya. Rudyak, S. L. Krasnolutskii and E. N. Ivaschenko, “Influence of the Physical Properties of the Material of Nanoparticles on Their Diffusion in Rarefied Gases,” Journal of Engineering Physics and Thermophysics, Vol. 81, No. 3, 2008, pp. 520-524. doi:10.1007/s10891-008-0063-y

[22] V. Ya. Rudyak and S. L. Krasnolutskii, “The Interaction Potential of Dispersed Particles with Carrier Gas Molecules,” Proceedings of the 21st International Symposium on Rarefied Gas Dynamics, Vol. 1, 1999, pp. 264-270.

[23] V. Ya. Rudyak, S. L. Krasnolutskii, “About Viscosity of Rarefied Gas Suspensions with Nanoparticles,” Doklady Physics, Vol. 48, No. 10, 2003, pp. 583-586. doi:10.1134/1.1623543

[24] V. Ya. Rudyak, S. L. Krasnolutskii, A. G. Nasibulin and E. I. Kauppinen, “Methods of Measuring the Diffusion Coefficient and Sizes of Nanoparticles in Rarefied Gas,” Doklady Physics, Vol. 47, No. 10, 2002, pp. 758-761. doi:10.1134/1.1519325

[25] V. Ya. Rudyak and S. L. Krasnolutskii, “The Calculation and Measurement of Nanoparticles Diffusion Coefficient in Rarefied Gases,” Journal of Aerosol Science, Vol. 35, No. 1, 2003, pp. 579S-580S.

[26] V. Ya. Rudyak, S. N. Dubtsov and A. M. Baklanov, “Temperature Dependence of the Diffusion Coefficient of Nanoparticles,” Technical Physics Letters, Vol. 34, No. 6, 2008, pp. 519-521. doi:10.1134/S1063785008060217

[27] V. Ya. Rudyak, S. N. Dubtsov and A. M. Baklanov, “Measurements of the Temperature Dependent Diffusion Coefficient of Nanoparticles in the Range of 295 600K at Atmospheric Pressure,” Journal of Aerosol Science, Vol. 40, No. 10, 2009, pp. 833-843. doi:10.1016/j.jaerosci.2009.06.006

[28] W. B. Russel, D. A. Saville and W. R. Schowalter, “Colloidal Dispersions,” Cambridge University Press, Cambridge, 1989.

[29] G. R. Batchelor, “Brownian Diffusion of Particles with Hydrodynamic Interaction,” Journal of Fluid Mechanics, Vol. 74, Pt. 1, 1976, pp. 1-29. doi:10.1017/S0022112076001663

[30] G. R. Batchelor, “The Effect of Brownian Motion on the Bulk Stress in a Suspension of Spherical Particles,” Journal of Fluid Mechanics, Vol. 83, Pt. 1, 1977, pp. 97-127. doi:10.1017/S0022112077001062

[31] A. Acrivos and E. Y. Chang, “A Model for Estimating Transport Quantities in Two-Phase Materials,” Physics of Fluids, Vol. 29, No. 3-4, 1986, pp. 459-464.

[32] M. Mooney, “The Viscosity of a Concentrated Suspension of Spherical Particles,” Journal of Colloid Science, Vol. 6, No. 1, 1951, pp. 162-170.

[33] I. M. Krieger and T. J. Dougherty, “A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres,” Journal of Rheology, Vol. 3, No. 1, 1959, pp. 137-145. doi:10.1122/1.548848

[34] N. A. Frankel and A. Acrivos, “On the Viscosity of a Concentrated Suspension of Solid Spheres,” Chemical Engineering Science, Vol. 22, No. 6, 1967, pp. 847-853. doi:10.1016/0009-2509(67)80149-0

[35] I. M. Krieger, “Rheology of Monodisperse Lattices,” Advances in Colloid and Interface Science, Vol. 3, No. 1, 1972, pp. 111-132. doi:10.1016/0001-8686(72)80001-0

[36] E. N. da C. Andrade, “Viscosity of Liquids,” Nature, Vol. 125, 1930, pp. 309-324. doi:10.1038/125309b0

[37] E. N. da C. Andrade, “A Theory of the Viscosity of Liq uids,” Philosophical Magazine, Vol. 17, No. 112, 1934, pp. 497-514.

[38] A. Ya. Malkin and A. I. Isaev, “Rheology, Concepts, Methods, & Applications,” Chemical Publishing, Toronto, 2006.

[39] A. Graham, “On the Viscosity of Suspensions of Solid Spheres,” Applied Scientific Research, Vol. 37, No. 3-4, 1981, pp. 275-286. doi:10.1007/BF00951252

[40] D. C. Venerus, et al., “Viscosity Measurements on Col loidal Dispersions (Nanofluids) for Heat Transfer Appli cations,” Applied Rheology, Vol. 20, No. 4, 2010, Article ID: 44582.

[41] H. Chen, Y. Ding, Y. He and C. Tan, “Rheological Be havior of Ethylene Glycol Based Titania Nanofluids,” Chemical Physics Letters, Vol. 444, No. 4-6, 2007, pp. 333-337. doi:10.1016/j.cplett.2007.07.046

[42] H. Chen, Y. Ding and C. Tan, “Rheological Behavior of Nanofluids,” New Journal of Physics, Vol. 9, No. 10, 2007, p. 367.

[43] L. Colla, L. Fedele, M. Scattolini and S. Bobbo, “Wa ter-Based Fe2O3 Nanofluid Characterization: Thermal Conductivity and Viscosity Measurements and Correla tion,” Advances in Mechanical Engineering, Vol. 2012, No. 1, 2012, Article ID: 674947. doi:10.1155/2012/674947

[44] J. Garg, et al., “Enchanced Thermal Conductivity and Viscosity of Copper Nanoparticles in Ethylene Glycol Nanofluid,” Applied Physics Letters, Vol. 103, No. 7, 2008, Article ID: 074301. doi:10.1063/1.2902483

[45] F. S. Oueslati and R. Bennace, “Heterogeneous Nanoflu ids: Natural Convection Heat Transfer Enhancement,” Nanoscale Research Letters, Vol. 6, No. 3, 2011, p. 222. doi:10.1186/1556-276X-6-222

[46] P. K. Namburu, D. P. Kulkarni, A. Dandekar and D. K. Das, “Experimental Investigation of Viscosity and Spe cific Heat and Silicon Dioxide Nanofluids,” Micro & Nano Letters, Vol. 2, No. 3, 2007, pp. 67-71. doi:10.1049/mnl:20070037

[47] P. K. Namburu, D. P. Kulkarni, D. Misra and D. K. Das, “Viscosity of Copper Oxide Nanoparticles Dispersed in Ethylene Glycol and Water Mixture,” Experimental Ther mal and Fluid Science, Vol. 32, No. 2, 2007, pp. 397-402. doi:10.1016/j.expthermflusci.2007.05.001

[48] C. T. Nguyen, et al., “Viscosity Data for Al2O3-Water Nanofluid-Hysteresis: Is Heat Transfer Enhancement Us ing Nanofluids Reliable?” International Journal of Thermal Sciences, Vol. 47, No. 2, 2008, pp. 103-111. doi:10.1016/j.ijthermalsci.2007.01.033

[49] B.C. Pak and Y. I. Cho, “Hydrodynamic and Heat Trans fer Study of Dispersed Fluids with Submicron Metallic Oxide Particles,” Experimental Heat Transfer, Vol. 11, No. 2, 1998, pp. 151-170. doi:10.1080/08916159808946559

[50] X. Wang, X. Xu and S. U. S. Choi, “Thermal Conductiv ity of Nanoparticle-Fluid Mixture,” Journal of Thermo physics and Heat Transfer, Vol. 13, No. 4, 1999, pp. 474-480. doi:10.2514/2.6486

[51] Y. He, Y. Jin, H. Chen, Y. Ding, D. Cang and H. Lu, “Heat Transfer and Flow Behaviour of Aqueous Suspen sions of TiO2 Nanoparticles (Nanofluids) Flowing Up ward through a Vertical Pipe,” International Journal of Heat and Mass Transfer, Vol. 50, No. 11-12, 2007, pp. 2272-2281. doi:10.1016/j.ijheatmasstransfer.2006.10.024

[52] C. T. Nguyen, F. Desgranges, G. Roy, N. Galanis, T. Marei, S. Boucher and H. Mintsa, “Temperature and Par ticle-Size Dependent Viscosity Data for Water-Based Nanofluids—Hysteresis Phenomenon,” International Jour nal of Heat and Fluid Flow, Vol. 28, No. 6, 2007, pp. 1492-1506. doi:10.1016/j.ijheatfluidflow.2007.02.004

[53] P. Prasher, D. Song and J. Wang, “Measurements of Na nofluid Viscosity and Its Implications for Thermal Ap plications,” Applied Physics Letters, Vol. 89, No. 13, 2006, Article ID: 133108. doi:10.1063/1.2356113

[54] J. Chevalier, O. Tillement and F. Ayela, “Rheological Properties of Nanofluids Flowing Through Microchan nels,” Applied Physics Letters, Vol. 91, No. 23, Article ID: 233103.

[55] E. V. Timofeeva, D. S. Smith, W. Yu, D. M. France, D. Singh and J. L. Routbo, “Particle Size and Interfacial Ef fects on Thermo-Physical and Heat Transfer Characteris tics of Water-Based α-SiC Nanofluids,” Nanotechnology, Vol. 21, No. 21, 2010, Article ID: 215703. doi:10.1088/0957-4484/21/21/215703

[56] V. Y. Rudyak, A. A. Belkin, E. A. Tomilina and V. V. Egorov, “Nanoparticle Friction Force and Effective Vis cosity of Nanofluids,” Defect and Diffusion Forum, Vol. 273-276, No. 6, 2008, pp. 566-571.

[57] V. Y. Rudyak, A. A. Belkin and V. V. Egorov, “On the Effective Viscosity of Nanosuspensions,” Technical Phy sics, Vol. 54, No. 8, 2009, pp. 1102-1109. doi:10.1134/S1063784209080039

[58] G. Balasubramanian, S. Sen and I. K. Puri, “Shear Visco sity Enhancement in Water—Nanoparticle Suspensions,” Physics Letters, Vol. A 376, No. 6-7, 2012, pp. 860-863.

[59] V. Y. Rudyak, S. V. Dimov, V. V. Kuznetsov and S. P. Bardakhanov, “Measurement of the Viscosity Coefficient of an Ethylene Glycol-Based Nanofluid with Silicon Dioxide Particles,” Doklady Physics, Vol. 58, No. 5, 2013, pp. 173-176. doi:10.1134/S1028335813050042

[60] V. Y. Rudyak, V. Dimov and V. V. Kuznetsov, “About Dependence of the Nanofluid Viscosity Coefficient on the Temperature and Size of the Particles,” Technical Physics Letters, Vol. 39, No. 17, 2013, pp. 53-59.

[61] T. X. Phuoc and M. Massoudi, “Experimental Obser vations of the Effects of Shear Rates and Particle Con centration on the Viscosity of Fe2O3-Deionized Water Nanofluids,” International Journal of Thermal Sciences, Vol. 48, No. 7, 2009, pp. 1294-1301. doi:10.1016/j.ijthermalsci.2008.11.015

[62] A. D. Sommers, K. L. Yerkes and A. R. Runion, “A Stu dy of the Thermal-Hydraulic Performance and System Level Effects of Aluminum Oxide-Propanol Nanofluid,” Proceedings of the 14th International Heat Transfer Conference, Washington DC, 2010, Article ID: 22931.

[63] V. Y. Rudyak and A. A. Belkin, “Simulation of the Trans port Coefficients of Nanofluids,” Nanosystems: Physics, Chemistry, Mathematics, Vol. 1, No. 1, 2010, pp. 156-177.

[64] V. Y. Rudyak, “Nonlocal Solution of the Boltzmann Equation,” Zhurnal Tekhnicheskoi Fiziki, Vol. 65, No. 11, 1995, pp. 29-40.

[65] V. Y. Rudyak, S. L. Krasnolutskii and D. A. Ivanov, “The Interaction Potential of Nanoparticles,” Doklady Physics, Vol. 57, No. 1, 2012, pp. 33-35. doi:10.1134/S1028335812010053

[66] V. Y. Rudyak, S. L. Krasnolutskii and D. A. Ivanov, “Molecular Dynamics Simulation of the Nanofluid Vis cosity Coefficient,” Proceedings Russian Conference Mo dern Problems of the Rarefied Gas Dynamics, Novosi birsk, 26-30 July 2013, pp. 98-101