Vol. 32, issue 06, article # 9

Abstract:

Diffusion of hollow nanoparticles in low-density and rarefied gases and the viscosity of aerosols with such particles are studied with the previously developed kinetic theory and molecular dynamics method. Interaction between molecules of a carrier medium is simulated with Lennard-Jones potential, between these molecules and the nanoparticle, with RK potential, and between the nanoparticles, with RKI potential. Nitrogen-based aerosols with hollow and solid aluminum and uranium nanoparticles are considered at a temperature of 300 K and atmospheric pressure. Diameter of the nanoparticles is varied from 5 to 100 nm; the thickness of walls of hollow nanoparticles is 1 nm. It is shown that the diffusion coefficients of hollow nanoparticles always exceed those of solid particles of the same size and the same material, but this difference does not exceed 1%. The viscosity coefficient of aerosol with hollow nanoparticles is always lower than of aerosol with solid particles. The diffusion of hollow and solid aluminum nanoparticles with diameters of 2 and 4 nm in argon of the density r = 0.707 at a temperature of 300 K is also molecular dynamics (MD) simulated. It is shown that diffusion coefficients of hollow and solid nanoparticles of the same diameter and the same material in rarefied gases and liquids are the equal.

Keywords:

nanoparticles, hollow nanoparticles, aerosol, nanoaerosol, gas nanosuspension, nanofluid, diffusion, viscosity

References:

1. Rudyak V.Ya., Minakov A.V. Sovremennyye problemy mikro- i nanoflyuidiki. Novosibirsk: Nauka, 2016. 298 p.
2. Cunningham E. On the velocity of steady fall of spherical particles through fluid medium // Proc. R. Soc. 1910. V. 83. P. 357–365.
3. Millikan R.A. Brownian movement in cases at low pressures // Phys. Rev. 1913. V. 1, N 3. P. 218–221.
4. Millikan R.A. The general law of fall of a small spherical body through a gas, and it’s bearing upon the nature of molecular reflection from surfaces // Phys. Rev. 1923. V. 22, N 1. P. 1–23.
5. Davies C.N. Definitive equations for the fluid resistance of spheres // Proc. Phys. Soc. Lond. 1945. V. 57, part 4, N 322. P. 259‒270.
6. Friedlander S.K. Smoke, dust, Haze. Fundamentals of aerosol dynamics. New York, Oxford: Oxford University Press, 2000. 407 p.
7. Rudyak V.Ya., Krasnolutskij S.L. Kineticheskoye opisaniye diffuzii nanochastits v razrezhennom gaze // Dokl. RAN. 2001. V. 381, N 5. P. 623–625.
8. Rudyak V.Ya., Krasnolutskij S.L., Nasibulin A.G., Kauppinen Ye.I. O metodah izmereniya koeffitsiyenta diffuzii i razmerov nanochastits v razrezhennom gaze // Dokl. RAN. 2002. V. 386, N 5. P. 595–597.
9. Epstein P.S. On the resistance experienced by spheres in their motion through gases // Phys. Rev. 1924. V. 23. P. 710‒733.
10. Baron P.A., Willeke K. Aerosol measurement: Principles, techniques, and applications. NY: Wiley, 2001.
11. Rudyak V.Ya., Dubtsov S.N., Baklanov A.M. Measurements of the temperature dependent diffusion coefficient of nanoparticles in the range of 295–600 K at atmospheric pressure // J. Aerosol Sci. 2009. V. 40, N 10. P. 833–843.
12. Rudyak V.Ya., Krasnolutskij S.L., Ivashchenko Ye.N. O vliyanii fizicheskih svojstv materiala nanochastits na ih diffuziyu v razrezhennyh gazah // Inzhenerno-fizicheskij zhurn. 2008. V. 81, N 3. P. 496–500.
13. Rudyak V.Ya., Krasnolutskij S.L. O vyazkosti razrezhennyh gazovzvesej s nanochastitsami // Dokl. RAN. 2003. V. 392, N 4. P. 435–440.
14. Rudyak V.Ya., Krasnolutskij S.L. Effektivnyj koeffitsiyent vyazkosti razrezhennyh nanogazovzvesej // Optika atmosf. i okeana. 2004. V. 17, N 5–6. P. 498–503.
15. Einstein A.A. A new determination of molecular sizes // Ann. Phys. 1906. V. 19. P. 289–306.
16. Batchelor G.K. The effect of Brownian motion on the bulk stress in a suspension of spherical particles // J. Fluid Mech. 1977. V. 83, part. 1. P. 97–117.
17. Maxwell J.C. A treatise on electricity and magnetism. Oxford: Clarendon Press, 1881.
18. Rudyak V.Ya., Belkin A.A., Tomilina E.A., Egorov V.V. Nanoparticle friction force and effective viscosity of nanofluids // Defect Diffus. Forum. 2008. V. 273–276. P. 566–571.
19. Rudyak V.Yа., Minakov A.V. Thermophysical properties of nanofluids // Eur. Phys. J. E. 2018. V. 41. 12 p.
20. Rudyak V.Ya., Krasnolutskii S.L. Dependence of the viscosity of nanofluids on nanoparticle size and material // Phys. Lett. A. 2014. V. 378. P. 1845–1849.
21. Rudyak V.Ya., Minakov A.V., Smetanina M.S., Pryazhnikov M.I. Eksperimental'nyye dannyye o zavisimosti vyazkosti nanozhidkostej na osnove vody i etilenglikolya ot razmera i materiala chastits // Dokl. RAN. 2016. V. 467, N 3. P. 289–291.
22. Lohani A., Verma A., Joshi H., Yadav N., Karki N. Nanotechnology-based cosmeceuticals // ISRN Dermatol. 2014. 14 p. DOI: 10.1155/2014/843687.
23. Sharma A., Kumar S., Mahadevan N. Nanotechnology: A promising approach for cosmetics // Int. J. Recent Adv. Pharm. Rec. 2012. V. 2(2). P. 54–61.
24. Rudyak V.Ya., Krasnolutskij S.L. Potentsialy vzaimodejstviya polyh nanochastits mezhdu soboj i s molekulami nesushchej sredy // Dokl. AN. 2017. Iss. N 2(35). P. 32–42.
25. Rudyak V.Ya., Krasnolutskij S.L. Diffuziya nanochastits v razrezhennom gaze // Zhurn. tekhn. fiz. 2002. V. 72, iss. 7. P. 13–20.
26. Rudyak V.Ya., Krasnolutskij S.L., Ivanov D.A. O potentsiale vzaimodejstviya nanochastits // Dokl. RAN. 2012. V. 442, N 1. P. 54–56.
27. Hirschfelder J.O., Curtiss C.F., Bird R.B. Molecular theory of gases and liquids. New York: Wiley, 1954. 1219 p.
28. Chapman S., Cowling T.G., Burnett D. The mathematical theory of non-uniform gases: An account of the kinetic theory of viscosity, thermal conduction and diffusion in gases. Cambridge: Cambridge University Press, 1990. 423 p.
29. Reid R.C., Prausnitz J.M. The properties of gases and liquids Sherwood. NY: McGraw-Hill, 1977. 688 p.
30. Heinz H., Vaia R.A., Farmer B.L., Naik R.R. Accurate simulation of surfaces and interfaces of face-centered cubic metals using 12−6 and 9−6 Lennard–Jones potentials // J. Phys. Chem. C. 2008. V. 112, N 44. P. 17281–17290.
31. Rudyak V.Ya., Krasnolutskii S.L., Ivanov D.A. Molecular dynamics simulation of nanoparticle diffusion in dense fluids // Microfluid. Nanofluid. 2011. V. 11, N 4. P. 501–506.
32. Schofield P. Computer simulation studies of the liquid state // Comput. Phys. Comm. 1973. V. 5, N 1. P. 17–23.
33. Zubarev D.N. Neravnovesnaya statisticheskaya termodinamika. M.: Nauka, 1971. 415 p.
34. Rudyak V.Ya., Belkin A.A., Ivanov D.A., Yegorov V.V. Modelirovaniye protsessov perenosa na osnove metoda molekulyarnoj dinamiki. I. Koeffitsiyent samodiffuzii // Teplofizika vysokih temperatur. 2008. V. 46, N 1. P. 35–45.
35. Normann G.E., Stegajlov V.V. Metod klassicheskoj molekulyarnoj dinamiki: zamysel i real'nost' // Nanostruktury. Matematicheskaya fizika i modelirovaniye. 2011. V. 4, N 1. P. 31–59.
36. Normann G.E., Stegajlov V.V. Stohasticheskaya teoriya metoda klassicheskoj molekulyarnoj dinamiki // Matematicheskoye modelirovaniye. 2012. V. 24, N 6. P. 3–44.