Calculation of Friction Coefficient and Analysis of Fluid Flow in a Stepped Micro-Channel for Wide Range of Knudsen Number Using Lattice Boltzmann (MRT) Method

[1] H. Xue, S. Chen, DSMC Simulation of Microscale Backward-Facing Step Flow, Microscale Thermophysical Engineering 7 (2003) 69-86

[2] S. Ansumali, I. V. Karlin, Kinetic boundary conditions in the lattice Boltzmann method, Physical Review E 66 (2002) 026311.

[3] G. Karniadakis, A. Beskok, N. Aluru, Microflows and Nanoflows Fundamentals and Simulation, Springer, USA, 2005.

[4] R.W. Barber, D.R. Emerson, Challenges in Modeling Gas-Phase Flow in Microchannels: From Slip to Transition, Heat Transfer Engineering 27 (2006) 3-12.

[5] H. Lai, C. Ma, Lattice Boltzmann method for the generalized Kuramoto–Sivashinsky equation, Physica A, Statistical Mechanics and its Applications 388 (2009) 1405-1412.

[6] M. Sbragaglia, S. Succi, Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions, Physics of Fluids (1994-present) 17 (2005).

[7] E.B. Arkilic, M.A. Schmidt, K.S. Breuer, Gaseous slip flow in long microchannels, Microelectromechanical Systems 6 (1997) 167-178.

[8] K. Pong, C. Ho, J. Liu, Y. Tai, Non-linear pressure distribution in uniform microchannels., in:  Application of Microfabrication to Fluid Mechanics, ASME Winter Annual Meeting (1994) 51-56.

[9] G.E.K. Ali Beskok, A Model For Flows In Channels, Pipes, And Ducts At Micro And Nano Scales, Microscale Thermophysical Engineering 3 (1999) 43-77.

[10] J. Suehiro, G. Zhou, H. Imakiire, W. Ding, M. Hara, Controlled fabrication of carbon nanotube NO2 gas sensor using dielectrophoretic impedance measurement, Sensors and Actuators B 108 (2005) 398-403.

[11] A. Agrawal, L. Djenidi, R.A. Antonia, Simulation of gas flow in microchannels with a sudden expansion or contraction, Journal of Fluid Mechanics (2005) 135-144.

[12] Z. Guo, T.S. Zhao, Y. Shi, Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows, Journal of Applied Physics 99 (2006).

[13] Z. Guo, B. Shi, T.S. Zhao, C. Zheng, Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows, Physical Review E 76 (2007) 056704.

[14] Z. Guo, C. Zheng, Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation times, boundary conditions and the Knudsen layer, International Journal of Computational Fluid Dynamics 22 (2008) 465-473.

[15] Z. Guo, C. Zheng, B. Shi, Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow, Physical Review E 77 (2008) 036707.

[16] T. Lee, C.-L. Lin, Rarefaction and compressibility effects of the lattice-Boltzmann-equation method in a gas microchannel, Physical Review E 71 (2005) 046706.

[17] F. Verhaeghe, L.-S. Luo, B. Blanpain, Lattice Boltzmann modeling of microchannel flow in slip flow regime, Journal of Computational Physics 228 (2009) 147-157.

[18] X. Shan, X.-F. Yuan, H. Chen, Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation, Journal of Fluid Mechanics (2006) 413-441.

[19] S. Ansumali, I.V. Karlin, S. Arcidiacono, A. Abbas, N.I. Prasianakis, Hydrodynamics beyond Navier-Stokes: Exact Solution to the Lattice Boltzmann Hierarchy, Physical Review Letters 98 (2007) 124502.

[20] Y.-H. Zhang, X.-J. Gu, R.W. Barber, D.R. Emerson, Capturing Knudsen layer phenomena using a lattice Boltzmann model, Physical Review E 74 (2006) 046704.

[21] G.H. Tang, Y.H. Zhang, X.J. Gu, D.R. Emerson, Lattice Boltzmann modelling Knudsen layer effect in non-equilibrium flows, EPL (Europhysics Letters) 83 (2008) 40008.

[22] A. Homayoon, A.H.M. Isfahani, E. Shirani, M. Ashrafizadeh, A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number, International Communications in Heat and Mass Transfer 38 (2011) 827-832.

[23] H. Shokouhmand, A.H. Meghdadi Isfahani, An improved thermal lattice Boltzmann model for rarefied gas flows in wide range of Knudsen number, International Communications in Heat and Mass Transfer 38 (2011) 1463-1469.

[24] S.S. Chikatamarla, I.V. Karlin, Entropy and Galilean Invariance of Lattice Boltzmann Theories, Physical Review Letters 97 (2006) 190601.

[25] T. Ohwada, Y. Sone, K. Aoki, Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard‐sphere molecules, Physics of Fluids A: Fluid Dynamics 1 (1989) 1588-1599.

[26] P. Lallemand, L.-S. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Physical Review E 61 (2000) 6546-6562.

[27] C.Y. Lim, C. Shu, X.D. Niu, Y.T. Chew, Application of lattice Boltzmann method to simulate microchannel flows, Physics of Fluids (1994-present) 14 (2002) 2299-2308.

[28] V. Michalis, A. Kalarakis, E. Skouras, V. Burganos, Rarefaction effects on gas viscosity in the Knudsen transition regime, Microfluid Nanofluid 9 (2010) 847-853.

[29] S.H. Kim, H. Pitsch, I.D. Boyd, Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows, Physical Review E 77 (2008) 026704.

[30] S.H. Kim, H. Pitsch, I.D. Boyd, Accuracy of higher-order lattice Boltzmann methods for microscale flows with finite Knudsen numbers, Journal of Computational Physics 227 (2008) 8655-8671.

[31] Y. Zhang, R. Qin, D.R. Emerson, Lattice Boltzmann simulation of rarefied gas flows in microchannels, Physical Review E 71 (2005) 047702.

[32] Y.-H. Zhang, X.J. Gu, R.W. Barber, D.R. Emerson, Modelling thermal flow in the transition regime using a lattice Boltzmann approach, EPL (Europhysics Letters) 77 (2007) 30003.

[33] S. Succi, Mesoscopic Modeling of Slip Motion at Fluid-Solid Interfaces with Heterogeneous Catalysis, Physical Review Letters 89 (2002) 064502.

[34]     M.N. Oliveira, L. Rodd, G. McKinley, M. Alves, Simulations of extensional flow in microrheometric devices, Microfluid Nanofluid 5 (2008) 809-826.

[35] T.-M. Liou, C.-T. Lin, Study on microchannel flows with a sudden contraction–expansion at a wide range of Knudsen number using lattice Boltzmann method, Microfluid Nanofluid, 16 (2014) 315-327.

[36] L. Talon, D. Bauer, N. Gland, S. Youssef, H. Auradou, I. Ginzburg, Assessment of the two relaxation time Lattice-Boltzmann scheme to simulate Stokes flow in porous media, Water Resources Research 48 (2012) W04526.

[37] S. Kandlikar, S. Garimella, D. Li, S. Colin, M. King, Heat Transfer and Fluid Flow in Minichannels and Microchannels, Elsevier Amsterdam, Netherlands, San Diego, CA, Oxford, UK, 2005.

[38] H.P. Kavehpour, M. Faghri, Y. Asako, Effects of compressibility and rarefaction on gaseous flows in microchannels, numerical heat transfer, part a: applications 32 (1997) 677-696.