A kinetic theory description of liquid menisci at the microscale. (English) Zbl 1362.82044

Authors’ abstract: A kinetic model for the study of capillary flows in devices with microscale geometry is presented. The model is based on the Enskog-Vlasov kinetic equation and provides a reasonable description of both fluid-fluid and fluid-wall interactions. Numerical solutions are obtained by an extension of the classical direct simulation Monte Carlo (DSMC) to dense fluids. The equilibrium properties of liquid menisci between two hydrophilic walls are investigated, and the validity of the Laplace-Kelvin equation at the microscale is assessed. The dynamical process which leads to the meniscus breakage is clarified.


82C40 Kinetic theory of gases in time-dependent statistical mechanics
82D15 Statistical mechanics of liquids
35Q35 PDEs in connection with fluid mechanics
82D35 Statistical mechanics of metals
65C05 Monte Carlo methods
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
Full Text: DOI


[1] M. Allen, <em>Computer Simulation of Liquids</em>,, Clarendon Press, (1989) · Zbl 0703.68099
[2] R. Ardito, Multiscale finite element models for predicting spontaneous adhesion in MEMS,, Mecanique Industries, 11, 177, (2010)
[3] P. Barbante, A kinetic model for collisional effects in dense adsorbed gas layers,, in Proceedings of the 27th International Symposium on Rarefied Gas Dynamics (eds. I. Wysong and A. Garcia), 458, (1333)
[4] P. Barbante, A kinetic model for capillary flows in MEMS,, in Proceedings of the 28th International Symposium on Rarefied Gas Dynamics (eds. M. Mareschal and A. Santos), 713, (1501)
[5] G. Bird, <em>Molecular Gas Dynamics and the Direct Simulation of Gas Flows</em>,, Clarendon Press, (1995)
[6] N. Carnahan, Equation of state for nonattracting rigid spheres,, J. Chem. Phys., 51, 635, (1969)
[7] C. Cercignani, <em>The Boltzmann Equation and Its Applications</em>,, Springer, (1988) · Zbl 0646.76001
[8] S. Cheng, Capillary adhesion at the nanometer scale,, Phys. Rev. E, 89, (2014)
[9] J. Eggers, Nonlinear dynamics and breakup of free-surface flows,, Reviews of Modern Physics, 69, 865, (1997) · Zbl 1205.37092
[10] D. Enskog, Kinetische theorie der wärmeleitung, reibung und selbstdiffusion in gewissen verdichteten gasen und flüssigkeiten,, K. Svensk. Vet. Akad. Handl., 63, 5, (1922) · JFM 48.0915.02
[11] J. Fischer, Born-Green-Yvon approach to the local densities of a fluid at interfaces,, Phys. Rev. A, 22, 2836, (1980)
[12] A. Frezzotti, A particle scheme for the numerical solution of the Enskog equation,, Phys. Fluids, 9, 1329, (1997) · Zbl 1185.76835
[13] A. Frezzotti, A kinetic model for equilibrium and non-equilibrium structure of the vapor-liquid interface,, in Proceedings of the 23rd International Symposium on Rarefied Gas Dynamics (eds. A. Ketsdever and E. Muntz), 980, (2003) · Zbl 1062.76576
[14] A. Frezzotti, A kinetic model for fluid wall interaction,, Proc. IMechE, 222, 787, (2008)
[15] A. Frezzotti, Mean field kinetic theory description of evaporation of a fluid into vacuum,, Phys. Fluids, 17, (2005) · Zbl 1187.76165
[16] A. Frezzotti, Comparison of molecular dynamics and kinetic modeling of gas-surface interaction,, in Proceedings of the 26th International Symposium on Rarefied Gas Dynamics (ed. T. Abe), 635, (1084)
[17] M. Grmela, Kinetic equation approach to phase transitions,, J. Stat. Phys., 3, 347, (1971)
[18] Z. Guo, Simple kinetic model for fluid flows in the nanometer scale,, Phys. Rev. E, 71, (2005)
[19] J. Hansen, <em>Theory of Simple Liquids</em>,, Academic Press, (2006)
[20] A. Hariri, Modeling of wet stiction in microelectromechanical systems MEMS,, J. Microelectromech. Syst., 16, 1276, (2007)
[21] J. Hirschfelder, <em>The Molecular Theory of Gases and Liquids</em>,, Wiley-Interscience, (1964) · Zbl 0057.23402
[22] W. Kang, Universality crossover of the pinch-off shape profiles of collapsing liquid nanobridges in vacuum and gaseous environments,, Physical Review Letters, 98, (2007)
[23] J. Karkheck, Mean field kinetic theories,, J. Chem. Phys., 75, 1475, (1981)
[24] G. Karniadakis, <em>Microflows and Nanoflows: Fundamentals and Simulation</em>,, Springer, (2005) · Zbl 1115.76003
[25] R. Maboudian, Critical review: Stiction in surface micromechanical structures,, J. Vac. Sci. Technol. B, 15, 1, (1997)
[26] J. Rowlinson, <em>Molecular Theory of Capillarity</em>,, Dover Pubns, (2003)
[27] H. van Beijeren, The modified Enskog equation,, Physica, 68, 437, (1973)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.