• A.A. Avramenko
Keywords: processes in micro- and nano channels, mathematical modeling


A review is presented and analysis of methods for modeling micro- and nano flows is given. The features of mathematical models and the limits of their application are considered depending on the scale of microsystems.


1. Gad-el-Hak M.(1999) The fluid mechanics of microdevices-the freeman scholar lecture. J. Fluids Eng. vol. 121. P. 5 – 33.

2. Karniadakis GE., Beskok A., Aluru A. 2005. Microflows and nanoflows: fundamentals and simulation. Springer, Berlin.

3. Madhawa Hettiarachchi H.D., Golubovic M., William M. Worek, W.J. Minkowycz. 2008. Three- dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature. Int. J. Heat Mass Transfer. 51. P. 5088–5096.

4. Buongiorno J. 2006. Convective transport in nanofluids, J. Heat Transfer. 128. P. 240–250.

5. Chen S, Gary D. Doolen. 1998. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. № 30. P.329 – 364

6. Broadwell JE. 1964. Study of rarefied shear flow by the discrete velocity method. J. Fluid Mech. №19. P. 401–414.

7. Inamuro T., Sturtevant B. .1990. Numerical study of discrete-velocity gases. Phys. Fluids. №2. Р.2196 – 2203.

8. Sukop, M.C., Thorne D.T., Jr. 2006. Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers. Springer, Heidelberg, Berlin, New York. (second printing 2007). 172 p.

9. Chen S., Doolen G.D. 1998. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30. P. 329–364.

10. Luo L.S. 1998. Unified theory of the lattice Boltzmann models for nonideal gases. Phys. Rev. Lett. 81 (8). – P. 1618–1621.

11. Benzi R, Succi S, Vergassola M. 1992. The lattice Boltzmann equation: theory and applications. Phys. Rep. 222 (3). – P. 145–197.

12. Lallemand P., Luo L.S. 2003. Hybrid finitedierence thermal lattice Boltzmann equation Int. J. Mod. Phys. – B 7 (1&2). –P. 41–47.

13. Alexanders F., Chen S., Sterling J. 1994. Lattice Boltzmann thermo-hydrodynamics. Phys. Rev. E. 47. – R2249–R2252.

14. He X., Chen S., Doolen G.D. 1998. A novel thermal model for the lattice Boltzmann method in incompressible limit. J. Comput. Phys. 146. P. 282–300.

15. Qi L., Young W.L., Sinnott S. (1997) Polymerization via cluster Е solid surface impacts: molecular dynamics simulations. J. Phys. Chem. B. V. 101. P. 6883.

16. Zhurkin V.B., Potlev V.I., Florentev V.L. 1980. Atom- atomnye potentsialnye funktsii dlia konformatsionnyh rastchetov nukeinovyh kislot. Molekul. Biologia. T. 14, V. 5. P. 1116–1130 (Rus).

17. Lewis J.P., Sankey O.F. 1995. Geometry and energetics of DNA basepairs and triplets from first principles quantum molecular relaxations. Biophis. J. –V. 69. – P. 1068–1076.

18. Alfonso D.R., Ulloa S.E., Brenner D.W. 1994. Hydrocarbon adsorption on a diamond (100) stepped surface. Phys. Rev. B. V. 49, No. 7. P. 4948–4953.

19. Brenner D.W. 1990. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B. V. 42, No. 15. P. 9458–9471.

20. Jorgensen W. L. et al. 1983. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. V. 79, No. 2. P. 926–935.

21. Schiller D. 2005. Dissipative Particle Dynamics. A Study of the Methodological Background. Diploma Thesis. 180p.

22. Schlijper A.G., Hoogerbrugge P.J., Manke C.W. 1995. Computer simulations of dilute polymer solutions with the dissipative particle dynamics method. J. Rheol. V.39, №3 P.567–579.

23. Bonet Avalos J., Mackie A.D. 1997. Dissipative particle dynamics with energy conservation. Europhys. Lett. V.40, №2. P.141–146.

24. Espanol P. 1997. Dissipative particle dynamics with energy conservation. Europhys. Lett. V.40, №6. P.631–636.

25. Bonet Avalos J., Mackie A.D. 1999. Dynamic and transport properties of dissipative particle dynamics with energy conservation. J. Chem. Phys. V.111, №11. P.5267– 5276.

26. Willemsen S.M., Vlugt T.J.H., Hoefsloot H.C.J., Smit B. 1998. Combining Dissipative Particle Dynamics and Monte Carlo Techniques. J. Comp. Phys. V.147. P.507–517.

27. Warren P.B. (1998) Dissipative particle dynamics. Curr. Op. Coll. Interf. Sci. V.3, №6. P.620–624.

28. Kong Y., Manke C.W., Madden W.G., Schlijper A.G. 1997. Modeling the rheology of polymer solutions by dissipative particle dynamics. Tribology Lett. V.3. P.133–138.

29. Novik K.E., Coveney P.C. 1997. Using dissipative particle dynamics to model binary immiscible fluids. Int. J. Mod. Phys. C. V.8, №4. P. 909–918.

30. Kranenburg M. 2004. Phase transitions of lipid bilayers: a mesoscopic approach. PhD thesis, Universiteit van Amsterdam.

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How to Cite
Avramenko, A. (2017). MULTISCALE ANALYSIS OF MICRO- AND NANO-FLOWS. Thermophysics and Thermal Power Engineering, 39(2), 31-35.