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Methods of Modeling of Microflows and Nanoflows

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Micro- and Nanoflows

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 118))

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Abstract

The development and application of methods of numerical simulation of micro- and nanoflows are urgent tasks because of the lack and inconsistency of systematic experimental data. However, interpretation of results and determination of the applicability area of particular methods of modeling such flows should also be treated carefully and cautiously. In addition, precise terminology is important, because inadequate usage of terms can lead not only to misunderstanding, but even to erroneous ideas about the physics of the phenomena being considered. The usual flows of liquids and gases are rather difficult in the general case. This is even more so for micro- and nanoflows. Therefore, such flows should be treated with different methods. The situation becomes even more complicated if multiphase fluid flows are studied. In the present chapter, all of these situations were considered consecutively. It begins with a brief classification of these flows. After that, the methods of the modeling flows of the rarefied and dense gases and liquids are described. In the following two sections, the modeling of dispersed fluids, including nanofluids, is analyzed. The last section is devoted to a brief description of the method of molecular dynamics, the application of which is necessary for the modeling of nanoflows.

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Notes

  1. 1.

    Strictly speaking, interaction of gas molecules with the surface is not instantaneous. Moreover, incident gas molecules can be adsorbed on the surface and experience ionization or dissociation. Adsorption, in turn, can lead to the formation of an adsorbed layer on the surface, whose state depends on the ambient gas. In addition, gas/surface interaction depends on the surface state, temperature, roughness, etc.

  2. 2.

    This parameter is proportional to the van der Waals parameter and density; therefore, the corresponding expansion can also be called the expansion in terms of density.

  3. 3.

    At the boundary of applicability of the hydrodynamic description, one can try to study a microflow of a moderately dense or dense gas with particles on the order of one micrometer. However, the boundary conditions here should be imposed carefully, because the usual hydrodynamic boundary conditions are invalid for the pseudo-gas of particles (see below).

  4. 4.

    In experiments performed according to the method of Particle Image Velocimetry (PIV), the characteristic size of tracer particles is usually on the order of one micrometer. The estimates show that the single-fluid flow regime is violated in this case. For the fluctuations of the number of tracer particles \( N_{hp} \) in a physically infinitesimal hydrodynamic volume to be small, their density should satisfy the condition \( 1/\sqrt {N_{hp} } \sim1/\sqrt {r_{ph}^{3} n_{p} } \ll 1 \). It can be easily seen that this condition is valid only if these particles are densely packed, which obviously contradicts the posed problem. In all other cases, the fluctuations of the number of tracer particles are so large that it is impossible to obtain reasonable data on the carrier fluid velocity field. Nanoparticles should be used as tracers in such microchannels, but it should be also done carefully (see the next section).

  5. 5.

    Here, only suspensions are indicated; emulsions and gas-liquid media require a special analysis.

  6. 6.

    Strictly speaking, the disperse component is described by the kinetic equation for the single-particle distribution function only if the particles are not too coarse and the gas suspension is not too dense. Actually, such sufficiently rarefied gas suspensions are of interest for practice. Otherwise, the evolution of the disperse component is described by a system of kinetic equations, which, in addition to the equation for the single-particle distribution function, include equations for multiparticle distribution functions, in particular, the paired distribution function.

  7. 7.

    It should be noted, however, that these velocities can be comparable to or even greater than the gas suspension flow velocity in a microchannel.

  8. 8.

    For simplicity, a flat surface is considered here; otherwise, the friction force also depends on the particle velocity. However, the considered approximation is usually sufficient because the particle size is usually negligibly small as compared to surface curvature.

  9. 9.

    This depends on the surface properties, particle material, energy of interaction, and scattering laws.

  10. 10.

    The term “nanofluid” was first introduced by Choi (1995), who meant a suspension consisting of a carrier liquid and solid nanoparticles. It seems reasonable to extend this term to gas suspensions of nanoparticles for several reasons. First, gas suspensions of nanoparticles have many applications in practice, similar to liquid suspensions of nanoparticles. Second, many properties of nanofluids and nanosuspensions are very close to each other, especially if the carrier gas is sufficiently dense. Finally, the same methods or models can be used for modeling transport processes in gas and liquid suspensions of nanoparticles. For example, implementation of the molecular dynamics method is absolutely identical in both cases.

  11. 11.

    This statement can be made even more severe: beginning from certain particle concentrations, all nanofluids composed on the basis of conventional Newtonian fluids become non-Newtonian.

  12. 12.

    Only the classical systems are considered in that which follows.

  13. 13.

    This assumption appreciably simplifies computations, though is not of principal importance. Moreover, the MD method is actually the only reliable tool for studying the effect of non-additive forces on transport processes.

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Authors and Affiliations

  1. Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, Russian Federation

    Valery Ya. Rudyak

  2. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russian Federation

    Vladimir M. Aniskin, Anatoly A. Maslov & Sergey G. Mironov

  3. Siberian Federal University, Krasnoyarsk, Russian Federation

    Andrey V. Minakov

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  1. Valery Ya. Rudyak
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Rudyak, V.Y., Aniskin, V.M., Maslov, A.A., Minakov, A.V., Mironov, S.G. (2018). Methods of Modeling of Microflows and Nanoflows. In: Micro- and Nanoflows. Fluid Mechanics and Its Applications, vol 118. Springer, Cham. https://doi.org/10.1007/978-3-319-75523-6_1

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