Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-18T17:47:25.981Z Has data issue: false hasContentIssue false
  • English
  • Français

Pressure Distribution of the Gaseous Flow in Microchannel: A Lattice Boltzmann Study

Published online by Cambridge University Press:  03 June 2015

Zimian Xu  and
Zhaoli Guo
Get access

Abstract

In this paper the pressure distribution of the gaseous flow in a microchannel is studied via a lattice Boltzmann equation (LBE) method. With effective relaxation times and a generalized second order slip boundary condition, the LBE can be used to simulate rarefied gas flows from slip to transition regimes. The Knudsen minimum phenomena of mass flow rate in the pressure driven flow is also investigated. The effects of Knudsen number (rarefaction effect), pressure ratio and aspect ratio (compression effect) on the pressure distribution are analyzed. It is found the rarefaction effect tends to the curvature of the nonlinear pressure distribution, while the compression effect tends to enhance its nonlinearity. The combined effects lead to a local minimum of the pressure deviation. Furthermore, it is also found that the relationship between the pressure deviation and the aspect ratio follows a pow-law.

Keywords

76P05Lattice Boltzmann methodgaseous flowspressure distributionmicrochannel
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 4 , October 2013 , pp. 1058 - 1072
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]He, X. and Ling, N., Lattice Boltzmann simulation of electrochemical systems, Comput. Phys. Commun., 129 (2000), 158–166.CrossRefGoogle Scholar
[2]Karniadakis, G. E., Beskok, A. and Aluru, N., Microflows and nanoflows: fundamentals and simulation, Int. Appl. Mech., (2005).Google Scholar
[3]Arcidiacono, S., Karlin, I. V., Mantzaras, J. and Frouzakis, C. E., Lattice Boltzmann model for the simulation of multicomponent mixtures, Phys. Rev. E, 76 (2007), 046703.Google Scholar
[4]Arkilic, B., Schmidt, A. and Breuer, S., Gaseous slip flow in long microchannels, J. Microelec-tromech., 6 (1997), 167–178.Google Scholar
[5]Jang, J. and Wereley, S. T., Pressure distributions of gaseous slip flow in straight and uniform rectangular microchannels, Microfluid and Nanofluid, 1 (2004), 41–51.CrossRefGoogle Scholar
[6]Shen, C., Tian, D. B., Xie, C. and Fan, J., Examiation of the LBM in simulation of microchannel flow in transitional regime, Microscale Thermophys. Eng., 8 (2004), 405–410.CrossRefGoogle Scholar
[7]Maurer, J., Tabelin, P., Joseph, P. and Willaime, H., Second-order slip laws in microchannels for helium and nitrogen, Phys. Fluids, 15 (2003), 2613–2621.Google Scholar
[8]Varoutis, S., Naris, S., Hauer, V., Day, C. and Valougeorgis, D., Computational and experimental study of gas flows through long channels of various cross sections in the whole range of the Knudsen number, J. Vac. Sci. Technol. A, 27 (2009), 89–100.CrossRefGoogle Scholar
[9]Ohwada, T., Sone, Y. and Aoki, K., Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules, Phys. Fluids A, 1 (1989), 2042–2049.Google Scholar
[10]Verhaeghe, F., Luo, L. S. and Blanpain, B., Lattice Boltzmann modeling of microchannel flow in slip flow regime, J. Comput. Phys., 228 (2009), 147–157.Google Scholar
[11]Nie, X. B., Doolen, G. D. and Chen, S. Y., Lattice-Boltzmann simulations of fluid flows in MEMS, J. Stat. Phys., 102 (2002), 279–289.Google Scholar
[12]Lim, C. Y., Shu, C., Niu, X. D. and Chew, Y. T., Application of lattice Boltzmann method to simulate microchannel flows, Phys. Fluids, 14 (2002), 2299–2308.Google Scholar
[13]Zhang, Y. H., Qin, R. S. and Emerson, D. R., Lattice Boltzmann simulation of rarefied gas flows in microchannels, Phys. Rev. E, 71 (2005), 047702.Google Scholar
[14]Zhang, J. F., Lattice Boltzmann method for microfluidics: models and applications, Microfluid and Nanofluid, 10 (2005), 1–28.Google Scholar
[15]Guo, Z. L., Zhao, T. S. and Shi, Y., Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows, J. Appl. Phys., 99 (2006), 074903.Google Scholar
[16]Guo, Z. L., Zheng, C. G. and Shi, B. C., Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow, Phys. Rev. E, 77 (2008), 036707.Google Scholar
[17]Cercignani, C., Mathematical Methods in Kinetic Theory, Plenum, New York, 1990.Google Scholar
[18]He, X. Y. and Luo, L. S., A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, 55 (1997), R6333–R6336.CrossRefGoogle Scholar
[19]Shan, X. and He, X., Discretization of the velocity space in the solution of the Boltzmann equation, Phys. Rev. Lett., 80 (1998), 65–68.Google Scholar
[20]Stops, D. W., The mean free path of gas molecules in the transition regime, J. Phys. D, 3 (1970).Google Scholar
[21]Guo, Z. L., Shi, B. C. and Zheng, Ch. G., An extended Navier-Stokes formulation for gas flows in the Knudsen layer near a wall, Euro. Phys. Lett., 80 (2007), 24001.Google Scholar
[22]Niu, X., Hyodo, S. A., Munekata, T. and Suga, K., Kinetic lattice Boltzmann method for microscale gas flows: issues on boundary condition, relaxation time, and regularization, Phys. Rev. E, 76 (2007), 036711.Google Scholar
[23]Zhang, Y. H., Gu, X. J., Barber, R. W. and Emerson, D. R., Capturing Knudsen layer phenomena using a lattice Boltzmann model, Phys. Rev. E, 74 (2006), 046704.Google Scholar
[24]Fichman, M. and Hetsroni, G., Viscosity and slip velocity in gas flow in microchannels, Phys. Fluids, 17 (2005), 123102.Google Scholar
[25]Lockerby, D. A., Reese, J. M. and Gallis, M. A., Capturing the Knudsen layer in continuum-fluid models of non-equilibrium gas flows, AIAA J., 43 (2005), 1391–1393.CrossRefGoogle Scholar
[26]Shan, X., Yuan, X.-F. and Chen, H., Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation, J. Fluid Mech., 550 (2006), 413–441.CrossRefGoogle Scholar
[27]Loyalka, S. K., Petrellis, N. and Strovick, T. S., Some numerical results for the BGK model: Thermal creep and viscous slip problems with arbitrary accomodation at the surface, Phys. Fluids, 18 (1975), 1094–1099.Google Scholar
[28]Nian, X., John, E. and Tim, A., Microtube gas flows with second-order slip flow and temperature jump boundary conditions, Proc. 4th Inter. Conf. on Nanochannels, Microchannnels, and Minichannels, Parts A and B, (2006), 385–393.Google Scholar
[29]Zhou, Y., Zhanga, R., Staroselsky, I., Chen, H., Kim, W. T. and Jhon, M. S., Simulation of microand nano-scale flows via the lattice Boltzmann method, Phys. A, 362 (2006), 68–77.Google Scholar
[30]Darbandi, M. and Daghighi, Y., Computation of rarefied gaseous flows in micro to nano scale channels with slip to transient regimes using general second-order quadratic elements, Proc. 6th Int. Conf. nanochannels, Microchannels and Minichannels, (2008), 55–64.Google Scholar
[31]Kim, S. H., Pitsch, H. and Iain, D. B., Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows, Phys. Rev. E, 77 (2008), 026704.Google Scholar
[32]Duan, Z. P., Second-order gaseous slip flow models in long circular and noncircular microchannels and nanochannels, Microfluid and Nanofluid, 5 (2012), 805–820.Google Scholar
[33]Succi, S., Mesoscopic modelling of slip motion at fluid-solid interfaces with heterogeneus catalysis, Phys. Rev. Lett., 89 (2002), 064502.CrossRefGoogle Scholar
[34]Ansumali, S. and Karlin, I. V., Kinetic boundary conditions in the lattice Boltzmann method, Phys. Rev. E, 66 (2002), 026311.Google Scholar
[35]Shen, C., Faa, J. and Xie, C., Statistical simulation of rarefied gas flows in microchannels, J. Comput. Phys., 189 (2003), 512–526.CrossRefGoogle Scholar
[36]Colin, S., Rarefaction and compressibility effects on steaty and transient gas flow in microchannels, Microfluid and Nanofluid, 1 (2005), 268–279.Google Scholar
[37]Mavriplis, C., Ahn, J. C. and Goulard, R., Heat transfer and flow fields in short microchannels using direct simulation monte carlo, AIAA J. Thermophys., 11 (1997), 489–496.CrossRefGoogle Scholar