Simulation of Micro-Channel and Micro-Orifice Flow Using Lattice Boltzmann Method with Langmuir Slip Model

Document Type: Original Research Paper


Department of Mechanical Engineering, University of Kashan, Kashan, I. R.Iran


Because of its kinetic nature and computational advantages, the Lattice Boltzmann method (LBM) has been well accepted as a useful tool to simulate micro-scale flows. The slip boundary model plays a crucial role in the accuracy of solutions for
micro-channel flow simulations. The most used slip boundary condition is the Maxwell slip model. The results of Maxwell slip model are affected by the accommodation coefficient significantly, but there is not an explicitly relationship between properties at wall and accommodation coefficient. In the present wok, Langmuir slip model is used beside LBM to simulate micro-channel and micro-orifice flows. Slip velocity and nonlinear pressure drop profiles are presented as two major effects in such flows. The results are in good agreement with existing results in the literature.


[1] M. Gad-el Hak: The fluid mechanics of micro devices, ASME journal of fluid engineering 121 (1999) 5-33.

[2] G. Karniadakis, A. Beskok, N. Aluru, (2005), Microflows and nano-flows, Springer, New York.

[3] D.A. Perumal, G.V.S. Kumar, A.K. Daas: Application of Lattice Bpltzmann method to fluid flows in micro-geometries, CFD letters 2-2 (2009) 75-83.

[4] C.M. Ho, Y.C. Tai: Micro-electro-mechanical system (MEMS) and fluid flows, Annual review of fluid mechanics 30 (1998) 579-612.

[5] J. Zhang: Lattice Boltzmann method for microfluidics: models and applications, Micro fluid nanofluid 10 (2011) 1-28.

[6] Z.W. Tian, C. Zho, H.J. Liu, Z.L. Guo: Lattice Boltzmann scheme for simulating thermal microflow, Physica A 385 (2007) 59-68.

[7] C.Y. Lim, X.D. Niu, T.T. Chew: Application of Lattice Boltzmann method to simulate microchannel flows, Physics of fluids 14-7 (2002) 2299-2308.

[8] C. Cercignani, S. Lorenzani: Variational approach to gas flows in micro-channels, Journal of physics of fluids 16 (2004) 3426-3737.

[9] W.M. Zhang, G. Meng, X. Wei: A review on slip models for gas micro-flows, Micro-fluidics and nano-fluidics 13-6 (2012) 845-882.

[10] H.M. Kim, D. Kin, W.T. Kim: Langmuir slip model for air bearing simulation using the Lattice Boltzmann method, IEEE transactions on magnetic 43-6 (2007) 2244-2246.

[11] H.I. Choi, D.H. Lee: Complex micro-scale flow simulations using Langmuir slip condition, Numerical heat transfer A 48 (2005) 407-425.

[12] E. Fathi, I.Y. Akkutlu: Lattice Boltzmann method for simulation of shale gas transport in kerogen, Society of Petroleum Engineers conference (2013), Colorado, USA.

[13] R.S. Myong: Gaseous slip models based on the Langmuir adsorption isotherm, Physics of fluids 16-1 (2004) 104-117.

[14] X. Nie, G.D. Doolen, Sh. Chen: Lattice Boltzmann simulation of fluid flows in MEMS, Journal of statistical physics 107-112 (2001) 279-289.

[15] G.H. Tang, W.Q. Tao, Y.I. He: Lattice Boltzmann method for simulating gas flows in micro-channels, International journal of modern physics C 15-2 (2004) 335-347.

[16] Y. Zhang, R. Qin, D.R. Emerson: Lattice Boltzmann simulation of rarefied gas flows in micro-channels,Physical review E 71 (2005) 1-4.

[17] E. Shirani, S. Jafari: Application of LBM in simulation of flow in simple micro-geometries and micro-porous media, African physical review 1 (2007).

[18] R.S. Myong, J.M. Reese, R.W. Barber, D.R. Emerson: Velocity slip in micro-scale cylindrical qouette flow: the Langmuir model, Physics of fluids 17-8 (2005) 1-11.

[19] Sh. Chen, Zh. Tian: Simulation of micro-channel flow using the lattice Boltzmann method, Physica A388 (2009) 4803-4810.

[20] Sh. Chen, Zh. Tian: Simulation of thermal microchannel flow using the lattice Boltzmann method with Langmuir slip model, International journal of heat and fluid flow 31 (2010) 227-235.

[21] S. Succi, (2001), The Lattice Boltzmann equation: for fluid dynamics and beyond, Oxford university press,New York.

[22] X. Liu, Zh. Guo, A Lattice Boltzmann study of gas flows in a long micro-channel, Computers and mathematics with applications 65 (2013) 186-193.

[23] R.S. Myong, D.A. Lockerby, J.M. Reese, The effect of gaseous slip on micro-scale heat transfer: an extended Gratz problem, International journal of heat and mass transfer 49 (2006) 2502-2513.

[24] A. Beskok, G.E. Karniadakis, W. Trimmer: Rarefaction and compressibility effects in gas microflows,  Journal of fluid engineering 118-3 (1996) 448-456.

[25] E.B. Arkilic, M.A. Schmidt, K.S. Breuer, Gaseous slip flow in long micro-channels, Journal of Microelectro-mechanical systems 6-2 (1997) 167-178.

[26] T. Reis, P.J. Dellar: Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions, Physics of Fluids 24 (2012) 1-18.

[27] M. Wang, Zh. Li: Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method, International Journal of Heat and Fluid Flow 25 (2004) 975–985.