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Evaporation of Suspended Nanofluid (SiO\(_{2}\)/Water) Droplets: Experimental Results and Modelling

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Abstract

The results of experimental studies and modelling of the evaporation of suspended water droplets containing silicon dioxide SiO\(_{2}\) nanoparticles at mass fractions 0.02 and 0.07 are presented. The experimental results are analysed using the previously developed model for multicomponent droplet heating and evaporation. In this model droplets are assumed to be spherical and the analytical solutions to the heat transfer and species diffusion equations are incorporated into the numerical code. They are used at each timestep of the calculations. Silicon dioxide nanoparticles are considered to be a non-evaporating component. It is demonstrated that both experimental and predicted values of droplet diameters to the power 1.5 decrease almost linearly with time, except at the beginning and the final stages of the evaporation process, and are only weakly affected by the presence of nanoparticles. At the final point in this process, the effect of nanoparticles becomes dominant when their mass fraction at the droplet surface reaches about 40 % and a cenosphere-like structure is formed. Both predicted and observed droplet surface temperatures rapidly decrease during the initial stage of droplet evaporation. After about \(t=100\) s the predicted surface temperature remains almost constant whilst its experimentally observed values increase with time. This might be related to a decrease in the temperature of ambient air in the vicinity of droplets, not taken into account in the model. Both observed and predicted values of the mass fraction of silicon dioxide at the droplet surfaces are shown to increase with time until they reach about 0.4.

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References

  1. S.K. Das, S.U.S. Choi, W. Yu, T. Pradeep, Nanofluids: Science and Technology (Wiley, Hoboken, 2008)

    Google Scholar 

  2. V.Y. Rudyak, A.V. Minakov, Modern Problems of Micro- and Nanofluidics (Nauka, Novosibirsk, 2016). (in Russian)

    Google Scholar 

  3. M.J. Assael, K.D. Antoniadis, W.A. Wakeham, X. Zhang, Potential applications of nanofluids for heat transfer. Int. J. Heat Mass Transf. 138, 597–607 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.086

    Article  Google Scholar 

  4. G. Liang, I. Mudawar, Review of single-phase and two-phase nanofluid heat transfer in macro-channels and micro-channels. Int. J. Heat Mass Transf. 136, 324–354 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.086

    Article  Google Scholar 

  5. V.I. Terekhov, S.V. Kalinina, V.V. Lemanov, The mechanism of heat transfer in nanofluids: state of the art (review). Part 1. Synthesis and properties of nanofluids. Thermophys. Aeromech. 17, 1–14 (2010). https://doi.org/10.1134/S0869864310010014

    Article  ADS  Google Scholar 

  6. P. Katre, S. Balusamy, S. Banerjee, L.D. Chandrala, K.C. Sahu, Evaporation dynamics of a sessile droplet of binary mixture laden with nanoparticles. Langmuir 37, 6311–6321 (2021). https://doi.org/10.1021/acs.langmuir.1c00806

    Article  Google Scholar 

  7. L. Cheng, G. Xia, Q. Li, J.R. Thome, Fundamental issues, technology development, and challenges of boiling heat transfer, critical heat flux, and two-phase flow phenomena with nanofluids. Heat Transf. Eng. 40, 1301–1336 (2019). https://doi.org/10.1080/01457632.2018.1470285

    Article  ADS  Google Scholar 

  8. S.J. Kim, T. McKrell, J. Buongiorno, L.-W. Hu, Experimental study of flow critical heat flux in alumina-water, zinc-oxide- water, and diamond-water nanofluids. J. Heat Transf. 131, 043204 (2009). https://doi.org/10.1115/1.3072924

    Article  Google Scholar 

  9. P. Chen, Enhancement of drops evaporation using nanoparticles and alcohols. Mechanics [physics.med-ph]. Université de Valenciennes et du Hainaut-Cambresis (2018)

  10. X. Zhong, A. Crivoi, F. Duan, Sessile nanofluid droplet drying. Adv. Colloid Interface Sci. 217, 13–30 (2015). https://doi.org/10.1016/j.cis.2014.12.003

    Article  Google Scholar 

  11. K. Sefiane, R. Bennacer, Nanofluids droplets evaporation kinetics and wetting dynamics on rough heated substrates. Adv. Colloid Interface Sci. 147–148, 263–271 (2009). https://doi.org/10.1016/j.cis.2008.09.011

    Article  Google Scholar 

  12. W.A. Sirignano, Fluid Dynamics and Transport of Droplets and Sprays (Cambridge Univ. Press, Cambridge, 1999)

    Book  Google Scholar 

  13. R.-H. Chen, T.X. Phuoc, D. Martello, Effects of nanoparticles on nanofluid droplet evaporation. Int. J. Heat Mass Transf. 53, 3677–3682 (2010). https://doi.org/10.1016/j.ijheatmasstransfer.2010.04.006

    Article  Google Scholar 

  14. R.-H. Chen, T.X. Phuoc, D. Martello, Surface tension of evaporating nanofluid droplets. Int. J. Heat Mass Transf. 54, 2459–2466 (2011). https://doi.org/10.1016/j.ijheatmasstransfer.2011.02.016

    Article  Google Scholar 

  15. W. Zhang, R. Shen, K. Lu, A. Ji, Z. Cao, Nanoparticle enhanced evaporation of liquids: a case study of silicone oil and water. AIP Adv. 2, 042119 (2012). https://doi.org/10.1063/1.4764294

    Article  ADS  Google Scholar 

  16. A.A. Bochkarev, V.I. Polyakova, Numerical modeling of acceleration of liquid evaporation by adding nanoparticles. Proceedings of the Conference ‘Modern problems of the dynamics of rarefied gases’, Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, July 26–29, 2013, pp. 66–68 (In Russian)

  17. V.A. Kumar, S.P. Sathian, Evaporation of a liquid droplet in the presence of a nanoparticle. J. Heat Transf. 140, 054501 (2018). https://doi.org/10.1115/1.4038477

    Article  Google Scholar 

  18. Y. Wei, W. Deng, R.-H. Chen, Effects of insoluble nano-particles on nanofluid droplet evaporation. Int. J. Heat Mass Transf. 97, 725–734 (2016). https://doi.org/10.1016/j.ijheatmasstransfer.2016.02.052

    Article  Google Scholar 

  19. C.S. Handscomb, M. Kraft, A.E. Bayly, A new model for the drying of droplets containing suspended solids. Chem. Eng. Sci. 64, 628–637 (2009). https://doi.org/10.1016/j.ces.2008.04.051

    Article  Google Scholar 

  20. A.V. Minakov, A.S. Lobasov, M.I. Pryazhnikov, L.S. Tarasova, N.Y. Vasilenko, V.Y. Rudyak, Experimental study of the influence of nanoparticles on evaporation of fluids. Tech. Phys. 65, 29–36 (2020). https://doi.org/10.1134/S1063784220010181

    Article  Google Scholar 

  21. V.I. Terekhov, N.E. Shishkin, Evaporation of water droplets containing carbon nanotubes. Tech. Phys. Lett. 38, 25–28 (2012). https://doi.org/10.1134/S1063785012010142

    Article  ADS  Google Scholar 

  22. M. Moghiman, B. Aslani, Influence of nanoparticles on reducing and enhancing evaporation mass transfer and its efficiency. Int. J. Heat Mass Transf. 61, 114–118 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.057

    Article  Google Scholar 

  23. Y. Gan, L. Qiao, Evaporation characteristics of fuel droplets with the addition of nanoparticles under natural and forced convections. Int. J. Heat Mass Transf. 54, 4913–4922 (2011). https://doi.org/10.1016/j.ijheatmasstransfer.2011.07.003

    Article  MATH  Google Scholar 

  24. I. Javed, S.W. Baek, K. Waheed, G. Ali, S.O. Cho, Evaporation characteristics of kerosene droplets with dilute concentrations of ligand-protected aluminum nanoparticles at elevated temperatures. Combust. Flame 160, 2955–2963 (2013). https://doi.org/10.1016/j.combustflame.2013.07.007

    Article  Google Scholar 

  25. W.J. Gerken, A.V. Thomas, N. Koratkar, M.A. Oehlschlaeger, Nanofluid pendant droplet evaporation: experiments and modeling. Int. J. Heat Mass Transf. 74, 263–268 (2014). https://doi.org/10.1016/j.ijheatmasstransfer.2014.03.031

    Article  Google Scholar 

  26. X. Wang, M. Dai, J. Wang, Y. Xie, G. Ren, G. Jiang, Effect of ceria concentration on the evaporation characteristics of diesel fuel droplets. Fuel 236, 1577–1585 (2019). https://doi.org/10.1016/j.fuel.2018.09.085

    Article  Google Scholar 

  27. M. Dai, J. Wang, N. Wei, X. Wang, C. Xu, Experimental study on evaporation characteristics of diesel/cerium oxide nanofluid fuel droplets. Fuel 254, 115633 (2019). https://doi.org/10.1016/j.fuel.2019.115633

    Article  Google Scholar 

  28. S. Tanvir, S. Biswas, L. Qiao, Evaporation characteristics of ethanol droplets containing graphite nanoparticles under infrared radiation. Int. J. Heat Mass Transf. 114, 541–549 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2017.06.059

    Article  Google Scholar 

  29. Y. Gan, L. Qiao, Radiation-enhanced evaporation of ethanol fuel containing suspended metal nanoparticles. Int. J. Heat Mass Transf. 55, 5777–5782 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2012.05.074

    Article  Google Scholar 

  30. Z. Said, M.H. Sajid, R. Saidur, M. Kamalisarvestani, N.A. Rahim, Radiative properties of nanofluids. Int. Commun. Heat Mass Transf. 46, 74–84 (2013). https://doi.org/10.1016/j.icheatmasstransfer.2013.05.013

    Article  Google Scholar 

  31. D. Jing, D. Song, Optical properties of nanofluids considering particle size distribution: experimental and theoretical investigations. Renew. Sustain. Energy Rev. 78, 452–465 (2017). https://doi.org/10.1016/j.rser.2017.04.084

    Article  Google Scholar 

  32. S.P. Fisenko, Y.A. Khodyko, Brownian diffusion inside a micron-sized droplet and the morphology of ensembles of nanoparticles. J. Eng. Phys. Thermophys. 86, 349–355 (2013). https://doi.org/10.1007/s10891-013-0840-0

    Article  Google Scholar 

  33. F.R. Siddiqui, C.Y. Tso, S.C. Fu, H.H. Qiu, C.Y.H. Chao, Evaporation and wetting behavior of silver-graphene hybrid nanofluid droplet on its porous residue surface for various mixing ratios. Int. J. Heat Mass Transf. 153, 119618 (2020). https://doi.org/10.1016/j.ijheatmasstransfer.2020.119618

    Article  Google Scholar 

  34. H.C. Chan, S. Paik, J.B. Tipton, K.D. Kihm, Effect of nanoparticle sizes and number densities on the evaporation and dryout characteristics for strongly pinned nanofluid droplets. Langmuir 23, 2953–2960 (2007). https://doi.org/10.1021/la061661y

    Article  Google Scholar 

  35. E. Starinskaya, A.D. Nazarov, N. Miskiv, S. Starinskiy, Effect of SiO\(_2\) nanoparticle addition on the evaporation of a suspended water droplet. Heat Transf. Res. 53, 43–56 (2022). https://doi.org/10.1615/heattransres.2022041024

    Article  Google Scholar 

  36. R. Mulka, A. Kujawska, B. Zajaczkowski, S. Mancin, M.H. Buschmann, Drying silica-nanofluid droplets. Colloids Surf. A 623, 126730 (2021). https://doi.org/10.1016/j.colsurfa.2021.126730

    Article  Google Scholar 

  37. N.B. Vagraftik, Handbook of Thermophysical Properties of Fluids (Nauka Publishing House, Moscow, 1972). (in Russian)

    Google Scholar 

  38. K. Han, G. Song, X. Ma, B. Yang, An experimental and theoretical study of the effect of suspended thermocouple on the single droplet evaporation. Appl. Therm. Eng. 101, 568–575 (2016). https://doi.org/10.1016/j.applthermaleng.2015.12.022

    Article  Google Scholar 

  39. J.R. Yang, S.C. Wong, An experimental and theoretical study of the effects of heat conduction through the support fiber on the evaporation of a droplet in a weakly convective flow. Int. J. Heat Mass Transf. 45, 4589–4598 (2002). https://doi.org/10.1016/S0017-9310(02)00164-3

    Article  Google Scholar 

  40. D. Brutin, Influence of relative humidity and nano-particle concentration on pattern formation and evaporation rate of pinned drying drops of nanofluids. Colloids Surf. 429, 112–120 (2013). https://doi.org/10.1016/j.colsurfa.2013.03.012

    Article  Google Scholar 

  41. P. Tartarini, M.A. Corticelli, L. Tarozzi, Dropwise cooling: experimental tests by infrared thermography and numerical simulations. Appl. Therm. Eng. 29, 1391–1397 (2009). https://doi.org/10.1016/j.applthermaleng.2008.06.011

    Article  Google Scholar 

  42. A.A. Fedorets, L.A. Dombrovsky, A.M. Smirnov, The use of infrared self-emission measurements to retrieve surface temperature of levitating water droplets. Infrared Phys. Technol. 69, 238–243 (2015). https://doi.org/10.1016/j.infrared.2015.02.005

    Article  ADS  Google Scholar 

  43. V.Y. Borodulin, V.N. Letushko, M.I. Nizovtsev, A.N. Sterlyagov, Determination of parameters of heat and mass transfer in evaporating drops. Int. J. Heat Mass Transf. 109, 609–618 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2017.02.042

    Article  Google Scholar 

  44. S.S. Sazhin, O. Rybdylova, A.S. Pannala, S. Somavarapu, S.K. Zaripov, A new model for a drying droplet. Int. J. Heat Mass Transf. 122, 451–458 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.094

    Article  Google Scholar 

  45. P.A. Strizhak, R.S. Volkov, G. Castanet, F. Lemoine, O. Rybdylova, S.S. Sazhin, Heating and evaporation of suspended water droplets: experimental studies and modelling. Int. J. Heat Mass Transf. 127, 92–106 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.103

    Article  Google Scholar 

  46. S.S. Sazhin, Droplets and Sprays: Simple Models of Complex Processes (Springer, New York, 2022)

    Book  MATH  Google Scholar 

  47. B. Abramzon, W.A. Sirignano, Droplet vaporization model for spray combustion calculations. Int. J. Heat Mass Transf. 32, 1605–1618 (1989). https://doi.org/10.1016/0017-9310(89)90043-4

    Article  Google Scholar 

  48. D.V. Antonov, R.M. Fedorenko, P.A. Strizhak, Z. Nissar, S.S. Sazhin, Puffing/micro-explosion in composite fuel/water droplets heated in flames. Combust. Flame 233, 111599 (2021). https://doi.org/10.1016/j.combustflame.2021.111599

    Article  Google Scholar 

  49. E.M. Starinskaya, N.B. Miskiv, A.D. Nazarov, V.V. Terekhov, V.I. Terekhov, O.D. Rybdylova, S.S. Sazhin, Evaporation of water/ethanol droplets in an air flow: experimental study and modelling. Int. J. Heat Mass Transf. 177, 121502 (2021). https://doi.org/10.1016/j.ijheatmasstransfer.2021.121502

    Article  Google Scholar 

  50. B.S. Radovskii, Random packing density of spherical solids. Rep. Acad. Sci. USSR 4, 184–190 (1972)

    Google Scholar 

  51. A. Einstein, Eine neue Bestimmung der Moleküldimensionen. Ann. Phys. 324, 289–306 (1906)

    Article  MATH  Google Scholar 

  52. S.S. Sazhin, M. Al Qubeissi, R. Nasiri, V.M. Gunko, A.E. Elwardany, F. Lemoine, F. Grisch, M.R. Heikal, A multi-dimensional quasi-discrete model for the analysis of Diesel fuel droplet heating and evaporation. Fuel 129, 238–266 (2014). https://doi.org/10.1016/j.fuel.2014.03.028

    Article  Google Scholar 

  53. R.B. Bird, E.W. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd edn. (Wiley, New York, 2002)

    Google Scholar 

  54. C.M. Silva, H. Li, E.A. Macedo, Models for self-diffusion coefficients of dense fluids, including hydrogen-bonding substances. Chem. Eng. Sci. 53, 2423–2429 (1998). https://doi.org/10.1016/S0009-2509(98)00037-2

    Article  Google Scholar 

  55. J.C. Maxwell, A Treatise on Electricity and Magnetism, 3rd edn. (Oxford University Press, London, 1892)

    MATH  Google Scholar 

  56. C.L. Yaws (ed.), Thermophysical Properties of Chemicals and Hydrocarbons (William Andrew Inc., Norwich, 2008)

    Google Scholar 

  57. B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, 5th edn. (McGraw-Hill Education, New York, 2001)

    Google Scholar 

  58. V.I. Terekhov, V.V. Terekhov, N.E. Shishkin, KCh. Bi, Heat and mass transfer in disperse and porous media: investigation of non-stationary evaporation of liquid droplets. J. Eng. Phys. Thermophys. 83, 883–890 (2010). https://doi.org/10.1007/s10891-010-0410-7

    Article  Google Scholar 

  59. V.S. Zubkov, G.E. Cossali, S. Tonini, O. Rybdylova, C. Crua, M. Heikal, S.S. Sazhin, Mathematical modelling of heating and evaporation of a spheroidal droplet. Int. J. Heat Mass Transf. 108, 2181–2190 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2016.12.074

    Article  Google Scholar 

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Acknowledgements

Work on this paper was supported by the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2021-575) (experimental studies of droplet evaporation processes by E.M. Starinskaya, N.B. Miskiv, A.D. Nazarov, V.V. Terekhov, and V.I. Terekhov; development of the mathematical model by S.S. Sazhin), the Royal Society (UK) (Grant No. IEC 192007) (development and implementation of the mathematical model by O. Rybdylova), and the UKRI (Grant No. MR/T043326/1) (development and implementation of the mathematical model by O. Rybdylova).

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Starinskaya, E.M., Miskiv, N.B., Nazarov, A.D. et al. Evaporation of Suspended Nanofluid (SiO\(_{2}\)/Water) Droplets: Experimental Results and Modelling. Int J Thermophys 44, 64 (2023). https://doi.org/10.1007/s10765-023-03164-8

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