Abstract
The shear viscosity coefficients of water and water-based nanofluids with copper particles are calculated by the molecular dynamics method. Copper nanoparticles with a diameter of 2, 4 and 10 nm were used in the simulation. The volume fraction of nanoparticles was varied from 1 to 5%. The interaction of water molecules with each other was modeled using the Lennard–Jones potential. The Rudyak–Krasnolutskii and Rudyak–Krasnolutskii–Ivanov potentials were used as nanoparticle–molecule and nanoparticles interaction potentials, respectively. The viscosity coefficient was calculated using the fluctuation–dissipation theorem by the Green–Kubo formula. It is shown that the viscosity of the nanofluid significantly exceeds the viscosity of the coarse-grained suspension and increases with a decrease in the nanoparticles size at their fixed volume fraction. The correlation functions determining the viscosity coefficient of the nanofluid were analyzed in detail. The radial distribution functions of pure water and nanofluids are also presented in the paper. It is shown that the liquid near the nanoparticle is structured much more strongly than in the bulk. This greater ordering of the nanofluid is one of the main factors determining the increase in nanofluids viscosity.
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References
Rudyak VY, Minakov AV. Thermophysical properties of nanofluids. Eur Phys J E. 2018;41:15.
Rudyak VY. Modern understanding of the thermophysical properties of nanofluids and features of their flows. J Nanofluids. 2019;8:1–15.
Hosseini SS, Shahrjerdi A, Vazifeshenas Y. A review of relations for physical properties of nanofluids. Aust J Basic Appl Sci. 2011;10:417.
Mahbubul IM, Saidur R, Amalina MA. Latest developments on the viscosity of nanofluids. Int J Heat Mass Transf. 2012;55:874.
Koca HD, Doganay S, Turgut A, Tavman IH, Saidur R, Mahbubulf IM. Effect of particle size on the viscosity of nanofluids: a review. Renew Sustain Energy Rev. 2018;82:1664.
Wang XQ, Mujumdar AS. Heat transfer characteristics of nanofluids: a review. Int J Therm Sci. 2007;46:1.
Yu W, France DM, Routbort JL, Choi S. Review and comparison of nanofluid thermal conductivity and heat transfer enhancements. Heat Transf Eng. 2008;29:432.
Kleinstreuer K, Yu F. Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review. Nanoscale Res Lett. 2011;6:229.
Kumar PM, Kumar J, Tamilarasan R, Sendhilnathan S, Suresh S. Review on nanofluids theoretical thermal conductivity models. Eng J. 2015;1:67–83.
Eapen DJ, Yip S, Li Y. Mechanism of thermal transport in dilute nanocolloids. Phys Rev Lett. 2007;98:028302.
Rudyak VY, Belkin AA. Modeling of transition coefficients of nanofluids (RU). Nanosyst Phys Chem Math. 2010;1:156.
Rudyak VY, Belkin AA, Tomilina EA. On the thermal conductivity of nanofluids. Tech Phys Lett. 2010;36:660.
Kang H, Zhang Y, Yang M. Molecular dynamics simulation of thermal conductivity of Cu–Ar nanofluid using EAM potential for Cu–Cu interactions. Appl Phys. 2011;4:1001–8.
Rajabpour A, Akizi FY, Heyhat MM, Gordiz K. Molecular dynamics simulation of the specific heat capacity of water–Cu nanofluids. Int Nano Lett. 2013. https://doi.org/10.1186/2228-5326-3-58.
Rudyak VY, Krasnolutskii SL. Dependence of the viscosity of nanofluids on nanoparticle size and material. Phys Lett A. 2014;378:1845.
Rudyak VY, Krasnolutskii SL. Simulation of the nanofluid viscosity coefficient by the molecular dynamics method. Tech Phys. 2015;60(6):798.
Lou Z, Yang M. Molecular dynamics simulations on the shear viscosity of Al2O3 nanofluids. Comput Fluids. 2015;117:17–23.
Bushehri M, Mohebbi A, Rafsanjani H. Prediction of thermal conductivity and viscosity of nanofluids by molecular dynamics simulation. J Eng Thermophys. 2016;25:389–400.
Jabbari F, Rajabpour A, Saedodin S. Thermal conductivity and viscosity of nanofluids: a review of recent molecular dynamics studies. Chem Eng Sci. 2017;17:67–81.
Clementi E, Matsuoka O, Yoshimine M. A study of the water dimer potential surface. J Chem Phys. 1976;64:1351.
Stillinger FH, Rahman A. Improved simulation of liquid water by molecular dynamics. J Chem Phys. 1974;60:1545.
Rahman A, Stillinger FH, Lemberg HL. Study of a central force model for liquid water by molecular dynamics. J Chem Phys. 1975;63:5223.
Berendsen HJC, et al. Interaction models for water in relation to protein hydration. In: Pullman B, editor. Intermolecular forced, vol. 77. Dordrecht: Reidel; 1981. p. 331–42.
Jorgensen WL, Chandrasekhar J, Madura JD. Comparison of simple potential functions for simulating liquid water. J Chem Phys. 1983;79:926.
Jorgensen WL. Revised TIPS for simulations of liquid water and aqueous solutions. J Chem Phys. 1982;77:4156.
Silverstein KAT, Haymet ADJ, Dill KA. A simple model of water and the hydrophobic effect. J Am Chem Soc. 1998;120:3166.
Berendsen HJC, Grigera JR, Straatsma TP. The missing term in effective pair potentials. J Phys Chem. 1987. https://doi.org/10.1021/j100308a038.
Gonzalez MA, Abascal JLF. The shear viscosity of rigid water models. Chem Phys. 2010;132:096101.
Medina JS, et al. Molecular dynamics simulations of rigid and flexible water models: temperature dependence of viscosity. Chem Phys. 2011;388:9–18.
Mao Y, Zhang Y. Thermal conductivity, shear viscosity and specific heat of rigid water models. Chem Phys Lett. 2012;542:37–41.
Tazi S, Boţan A, Salanne M, Marry V, Turq P, Rotenberg B. Diffusion coefficient and shear viscosity of rigid water models. J Phys: Condens Matter. 2012. https://doi.org/10.1088/0953-8984/24/28/284117.
Zhang Y, Otani A, Maginn EJ. Reliable viscosity calculation from equilibrium molecular dynamics simulations: a time decomposition method. J Chem Theory Comput. 2015;11:3537–46.
Rapaport DC. The art of molecular dynamics simulation. Cambridge: Cambridge University Press; 1995.
Rudyak VY, Krasnolutskii SL, Ivanov DA. Molecular dynamics simulation of nanoparticle diffusion in dense fluids. Microfluidics Nanofluidics. 2011;4:501–6.
Rudyak VY, Krasnolutskii SL. The interaction potential of dispersed particles with carrier gas molecules. In: Proceedings of 21st international symposium on rarefied gas dynamics, vol 1. Toulouse: Gépadués-Éditions; 1999. p 263–70.
Rudyak VY, Krasnolutsky SL. Diffusion of nanoparticles in a rarefied gas. Tech Phys. 2002;47:807–13.
Rudyak VY, Krasnolutskii SL, Ivanov DA. The interaction potential of nanoparticles. Dokl Phys. 2012;57:33–5.
Rudyak VY. Statistical aerohydromechanics of homogeneous and heterogeneous media. Hydromechanics, vol. 2. Novosibirsk: NSUACE; 2005.
Norman GE, Stegailov VV. Stochastic theory of the classical molecular dynamics method. Math Models Comput Simul. 2013;5:305.
Zubarev D. Nonequilibrium statistical thermodynamics. New York: Consultants Bureau; 1974.
Allen MP, Tildesley DJ. Computer simulation of liquids. Oxford: University Press; 1987.
Rudyak VY, Belkin AA, Ivanov DA, Egorov VV. The simulation of transport processes using the method of molecular dynamics. Self-diffusion coefficient. High Temp. 2008;46:30–9.
Lide DR, editor. CRC handbook of chemistry and physics. 90th ed. Boca Raton: CRC; 2010.
Batchelor GK. The effect of Brownian motion on the bulk stress in a suspension of spherical particles. J Fluid Mech. 1977;83:97–117.
Rudyak VY. Viscosity of nanofluids. Why it is not described by the classical theories. Adv Nanopart. 2013. https://doi.org/10.4236/anp.2013.23037.
Rudyak VY, Belkin AA. On the effect of nanoparticles on fluid structure. Colloid J. 2019;81:487.
Lou Z, Yang M. Molecular dynamics simulations on the shear viscosity of Al2O3 nanofluids. Comput Fluids. 2015. https://doi.org/10.1016/j.compfluid.2015.05.006.
Loya A, Ren G. Molecular dynamics simulation study of rheological properties of CuO–water nanofluid. J Mater Sci. 2015;50:4075.
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The work was supported partially by the Russian Science Foundation (Projects No. 20-19-00043).
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Rudyak, V., Krasnolutskii, S., Belkin, A. et al. Molecular dynamics simulation of water-based nanofluids viscosity. J Therm Anal Calorim 145, 2983–2990 (2021). https://doi.org/10.1007/s10973-020-09873-8
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DOI: https://doi.org/10.1007/s10973-020-09873-8