A review on slip models for gas microflows
Tóm tắt
Accurate modeling of gas microflow is crucial for the microfluidic devices in MEMS. Gas microflows through these devices are often in the slip and transition flow regimes, characterized by the Knudsen number of the order of 10−2~100. An increasing number of researchers now dedicate great attention to the developments in the modeling of non-equilibrium boundary conditions in the gas microflows, concentrating on the slip model. In this review, we present various slip models obtained from different theoretical, computational and experimental studies for gas microflows. Correct descriptions of the Knudsen layer effect are of critical importance in modeling and designing of gas microflow systems and in predicting their performances. Theoretical descriptions of the gas-surface interaction and gas-surface molecular interaction models are introduced to describe the boundary conditions. Various methods and techniques for determination of the slip coefficients are reviewed. The review presents the considerable success in the implementation of various slip boundary conditions to extend the Navier–Stokes (N–S) equations into the slip and transition flow regimes. Comparisons of different values and formulations of the first- and second-order slip coefficients and models reveal the discrepancies arising from different definitions in the first-order slip coefficient and various approaches to determine the second-order slip coefficient. In addition, no consensus has been reached on the correct and generalized form of higher-order slip expression. The influences of specific effects, such as effective mean free path of the gas molecules and viscosity, surface roughness, gas composition and tangential momentum accommodation coefficient, on the hybrid slip models for gas microflows are analyzed and discussed. It shows that although the various hybrid slip models are proposed from different viewpoints, they can contribute to N–S equations for capturing the high Knudsen number effects in the slip and transition flow regimes. Future studies are also discussed for improving the understanding of gas microflows and enabling us to exactly predict and actively control gas slip.
Tài liệu tham khảo
citation_journal_title=Exp Therm Fluid Sci; citation_title=Deduction of slip coefficient in slip and transition regimes from existing cylindrical Couette flow data; citation_author=A Agrawal, SV Prabhu; citation_volume=32; citation_publication_date=2008; citation_pages=991-996; citation_doi=10.1016/j.expthermflusci.2007.11.010; citation_id=CR1
citation_journal_title=J Vac Sci Technol A; citation_title=Survey on measurement of tangential momentum accommodation coefficient; citation_author=A Agrawal, SV Prabhu; citation_volume=26; citation_publication_date=2008; citation_pages=634-645; citation_doi=10.1116/1.2943641; citation_id=CR2
citation_journal_title=Annu Rev Fluid Mech; citation_title=Lattice-Boltzmann method for complex flows; citation_author=CK Aidun, JR Clausen; citation_volume=42; citation_publication_date=2010; citation_pages=439-472; citation_doi=10.1146/annurev-fluid-121108-145519; citation_id=CR3
citation_journal_title=Phys Fluid; citation_title=Numerical evaluation of the slip coefficient; citation_author=S Albertoni, C Cercignani, L Gotusso; citation_volume=6; citation_publication_date=1963; citation_pages=993-996; citation_doi=10.1063/1.1706857; citation_id=CR4
citation_journal_title=Phys Fluid; citation_title=Cell size dependence of transport coefficients in stochastic particle algorithms; citation_author=FJ Alexander, AL Garcia, BJ Alder; citation_volume=10; citation_publication_date=1998; citation_pages=1540-1542; citation_doi=10.1063/1.869674; citation_id=CR5
citation_journal_title=Int J Eng Sci; citation_title=New concepts of homogenization applied in rough surface hydrodynamic lubrication; citation_author=A Almqvist, D Lukkassen, A Meidell, P Wall; citation_volume=45; citation_publication_date=2007; citation_pages=139-154; citation_doi=10.1016/j.ijengsci.2006.09.005; citation_id=CR6
citation_journal_title=Phys Rev Lett; citation_title=Hydrodynamics beyond Navier–Stokes: exact solution to the Lattice Boltzmann hierarchy; citation_author=S Ansumali, IV Karlin, S Arcidiacono, A Abbas, N Prasianakis; citation_volume=98; citation_publication_date=2007; citation_pages=124502; citation_doi=10.1103/PhysRevLett.98.124502; citation_id=CR7
citation_journal_title=J Microelectromech Syst; citation_title=Gaseous slip flow in microchannels; citation_author=EB Arkilic, MA Schmidt, KS Breuer; citation_volume=6; citation_publication_date=1997; citation_pages=167-174; citation_doi=10.1109/84.585795; citation_id=CR8
citation_journal_title=J Fluid Mech; citation_title=Mass flow and tangential momentum accommodation in silicon micromachined channels; citation_author=EB Arkilic, KS Breuer, MA Schmidt; citation_volume=437; citation_publication_date=2001; citation_pages=29-43; citation_doi=10.1017/S0022112001004128; citation_id=CR9
citation_journal_title=ASME J Heat Transf; citation_title=An extension to the Navier-Stokes equations to incorporate gas molecular collisions with boundaries; citation_author=EJ Arlemark, SK Dadzie, JM Reese; citation_volume=132; citation_publication_date=2010; citation_pages=041006; citation_doi=10.1115/1.4000877; citation_id=CR10
citation_title=Solid state physics; citation_publication_date=1976; citation_id=CR11; citation_author=NW Ascroft; citation_author=ND Mermin; citation_publisher=Saunders College press
citation_journal_title=J Comput Theoret Nanosci; citation_title=Surface roughness effects in micro and nanofluidic devices; citation_author=N Asproulis, D Drikakis; citation_volume=7; citation_publication_date=2010; citation_pages=1825-1830; citation_doi=10.1166/jctn.2010.1547; citation_id=CR12
citation_journal_title=Microscale Thermophys Eng; citation_title=High-order boundary conditions for gaseous flows in rectangular microducts; citation_author=C Aubert, S Colin; citation_volume=5; citation_publication_date=2001; citation_pages=41-54; citation_doi=10.1080/108939501300005367; citation_id=CR13
citation_journal_title=Microfluid Nanofluid; citation_title=On the mass and momentum transport in the Navier–Stokes slip layer; citation_author=J Badur, M Karcz, M Lemanski; citation_volume=11; citation_publication_date=2011; citation_pages=439-449; citation_doi=10.1007/s10404-011-0809-2; citation_id=CR14
citation_journal_title=ASME J Fluid Eng; citation_title=Pressure drop of fully developed laminar flow in rough microtubes; citation_author=M Bahrami, MM Yovanovich, JR Culham; citation_volume=128; citation_publication_date=2006; citation_pages=632-637; citation_doi=10.1115/1.2175171; citation_id=CR15
citation_journal_title=J Micromech Microeng; citation_title=A phenomenological lubrication model for the entire Knudsen regime; citation_author=P Bahukudumbi, A Beskok; citation_volume=13; citation_publication_date=2003; citation_pages=873-884; citation_doi=10.1088/0960-1317/13/6/310; citation_id=CR16
citation_journal_title=Microscale Thermophys Eng; citation_title=A unified engineering model for steady and quasi-steady shear-driven gas microflows; citation_author=P Bahukudumbi, JH Park, A Beskok; citation_volume=7; citation_publication_date=2003; citation_pages=291-315; citation_doi=10.1080/10893950390243581; citation_id=CR17
citation_journal_title=J Fluid Mech; citation_title=An approach to entropy consistency in second-order hydrodynamic equations; citation_author=R Balakrishnan; citation_volume=503; citation_publication_date=2004; citation_pages=201-245; citation_doi=10.1017/S0022112004007876; citation_id=CR18
Barber RW, Emerson DR (2002) Numerical simulation of low Reynolds number slip flow past a confined sphere. In: 23rd international symposium on rarefied gas dynamics, Whistler, Canada, Daresbury Laboratory, Daresbury, Warrington, England
citation_journal_title=Heat Transf Eng; citation_title=Challenges in modeling gas-phase flow in microchannels: from slip to transition; citation_author=RW Barber, DR Emerson; citation_volume=27; citation_publication_date=2006; citation_pages=3-12; citation_doi=10.1080/01457630500522271; citation_id=CR20
citation_journal_title=Vaccum; citation_title=Isothermal slip flow over curved surfaces; citation_author=RW Barber, Y Sun, XJ Gu, DR Emerson; citation_volume=76; citation_publication_date=2004; citation_pages=73-81; citation_doi=10.1016/j.vacuum.2004.05.012; citation_id=CR21
citation_journal_title=Microfluid Nanofluid; citation_title=Molecular dynamics simulations of shear-driven gas flows in nano-channels; citation_author=M Barisik, A Beskok; citation_volume=11; citation_publication_date=2011; citation_pages=611-622; citation_doi=10.1007/s10404-011-0827-0; citation_id=CR22
citation_journal_title=ASME J Fluids Eng; citation_title=Modelling of laminar flows in rough-wall microchannels; citation_author=R Baviere, G Gamrat, M Favre-Marinet, S Person; citation_volume=128; citation_publication_date=2006; citation_pages=734-741; citation_doi=10.1115/1.2201635; citation_id=CR23
citation_journal_title=Num Heat Transfer Part B; citation_title=Validation of a new velocity-slip model for separated gas microflows; citation_author=A Beskok; citation_volume=40; citation_publication_date=2001; citation_pages=451-471; citation_doi=10.1080/104077901753306593; citation_id=CR24
citation_journal_title=J Thermophys Heat Transf; citation_title=Simulation of heat and momentum transfer in complex microgeometries; citation_author=A Beskok, GE Karniadakis; citation_volume=8; citation_publication_date=1994; citation_pages=647-655; citation_doi=10.2514/3.594; citation_id=CR25
citation_journal_title=J Fluid Eng; citation_title=Rarefaction and compressibility effects in gas microflows; citation_author=A Beskok, GE Karniadakis; citation_volume=118; citation_publication_date=1996; citation_pages=448-456; citation_doi=10.1115/1.2817779; citation_id=CR26
citation_journal_title=Microscale Thermophys Eng; citation_title=A model for flows in channels, pipes, and ducts at micro and nano scales; citation_author=A Beskok, GE Karniadakis; citation_volume=3; citation_publication_date=1999; citation_pages=43-77; citation_doi=10.1080/108939599199864; citation_id=CR27
citation_title=Molecular gas dynamics and the direct simulation of gas flows; citation_publication_date=1994; citation_id=CR28; citation_author=GA Bird; citation_publisher=Clarendon Press
citation_journal_title=Phys Fluid; citation_title=Slip and accommodation coefficients from rarefaction and roughness in rotating microscale disk flows; citation_author=D Blanchard, P Ligrani; citation_volume=19; citation_publication_date=2007; citation_pages=063602; citation_doi=10.1063/1.2739416; citation_id=CR29
citation_journal_title=Tribol Lett; citation_title=Multiscale roughness and modeling of MEMS interfaces; citation_author=CK Bora, EE Flater, MD Street, JM Redmond, MJ Starr, RW Carpick, ME Plesha; citation_volume=19; citation_publication_date=2005; citation_pages=37-48; citation_doi=10.1007/s11249-005-4263-8; citation_id=CR30
citation_journal_title=Phys Rev E; citation_title=Beyond the no-slip boundary condition; citation_author=H Brenner; citation_volume=84; citation_publication_date=2011; citation_pages=046309; citation_doi=10.1103/PhysRevE.84.046309; citation_id=CR31
citation_journal_title=ASME J Tribol; citation_title=Homogenization of the generalized Reynolds equation for ultra-thin gas film and its resolution by FEM; citation_author=GC Buscaglia, M Jai; citation_volume=126; citation_publication_date=2004; citation_pages=547-552; citation_doi=10.1115/1.1739410; citation_id=CR32
citation_journal_title=Appl Phys Lett; citation_title=Temperature dependence of the tangential momentum accommodation coefficient for gases; citation_author=BY Cao, M Chen, ZY Guo; citation_volume=86; citation_publication_date=2005; citation_pages=091905; citation_doi=10.1063/1.1871363; citation_id=CR33
citation_journal_title=Inter J Eng Sci; citation_title=Effect of surface roughness on gas flow in microchannels by molecular dynamics simulation; citation_author=BY Cao, M Chen, ZY Guo; citation_volume=44; citation_publication_date=2006; citation_pages=927-937; citation_doi=10.1016/j.ijengsci.2006.06.005; citation_id=CR34
citation_journal_title=Int J Mol Sci; citation_title=Molecular momentum transport at fluid-solid interfaces in MEMS/NEMS: a review; citation_author=BY Cao, J Sun, M Chen, ZY Guo; citation_volume=10; citation_publication_date=2009; citation_pages=4638-4706; citation_doi=10.3390/ijms10114638; citation_id=CR35
citation_journal_title=J Stat Phys; citation_title=A variational principle for boundary value problems in kinetic theory; citation_author=C Cercignani; citation_volume=1; citation_publication_date=1969; citation_pages=297-311; citation_doi=10.1007/BF01007482; citation_id=CR36
citation_title=Theory and application of the Boltzmann equation; citation_publication_date=1975; citation_id=CR37; citation_author=C Cercignani; citation_publisher=Scottish Academic Press
citation_title=The Boltzmann equation and its applications; citation_publication_date=1988; citation_id=CR38; citation_author=C Cercignani; citation_publisher=Springer-Verlag
citation_title=Mathematical methods in kinetic theory; citation_publication_date=1990; citation_id=CR39; citation_author=C Cercignani; citation_publisher=Plenum
citation_title=Rarefied gas dynamics; citation_publication_date=2000; citation_id=CR40; citation_author=C Cercignani; citation_publisher=Cambridge University Press
citation_journal_title=Transp Theory Stat Phys; citation_title=Kinetic model for gas-surface interaction; citation_author=C Cercignani, M Lampis; citation_volume=1; citation_publication_date=1971; citation_pages=101-114; citation_doi=10.1080/00411457108231440; citation_id=CR41
Cercignani C, Lampis M (1989) Variational calculation of the slip coefficient and the temperature jump for arbitrary gas-surface interactions. In: Rarefied gas dynamics: space related studies, American Institute of Aeronautics and Astronautics, Washington, pp 553–561
citation_journal_title=Phys Fluids; citation_title=Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules; citation_author=C Cercignani, S Lorenzani; citation_volume=22; citation_publication_date=2010; citation_pages=062004; citation_doi=10.1063/1.3435343; citation_id=CR43
citation_journal_title=Microsyst Technol; citation_title=Improvement of sidewall roughness in deep silicon etching; citation_author=M Chabloz, Y Sasaki, T Matsuura, K Tsutsumi; citation_volume=6; citation_publication_date=2000; citation_pages=86-89; citation_doi=10.1007/s005420050003; citation_id=CR44
citation_title=The mathematical theory of nonuniform gases; citation_publication_date=1970; citation_id=CR45; citation_author=S Chapman; citation_author=TG Cowling; citation_publisher=Cambridge University Press
citation_journal_title=Tribol Lett; citation_title=Comparisons of slip-corrected Reynolds lubrication equations for the air bearing film in the head-disk interface of hard disk drives; citation_author=D Chen, DB Bogy; citation_volume=37; citation_publication_date=2010; citation_pages=191-201; citation_doi=10.1007/s11249-009-9506-7; citation_id=CR46
citation_journal_title=Int Commun Heat Mass Transf; citation_title=Fractal characterization of wall roughness on pressure drop in microchannels; citation_author=Y Chen, P Cheng; citation_volume=30; citation_publication_date=2003; citation_pages=1-11; citation_doi=10.1016/S0735-1933(03)00002-2; citation_id=CR47
citation_journal_title=Inter J Heat Fluid Flow; citation_title=Simulation of thermal micro-flow using lattice Boltzmann method with Langmuir slip model; citation_author=S Chen, Z Tian; citation_volume=31; citation_publication_date=2010; citation_pages=227-235; citation_doi=10.1016/j.ijheatfluidflow.2009.12.006; citation_id=CR48
citation_journal_title=Tribol Int; citation_title=Application of modified molecular gas lubrication equation to the analysis of micromotor bushings; citation_author=MD Chen, JW Lin, SC Lee, KM Chang, WL Li; citation_volume=37; citation_publication_date=2004; citation_pages=507-513; citation_doi=10.1016/j.triboint.2004.01.006; citation_id=CR49
citation_journal_title=Phys Rev E; citation_title=Role of surface roughness characterized by fractal geometry on laminar flow in microchannels; citation_author=Y Chen, C Zhang, M Shi, GP Peterson; citation_volume=80; citation_publication_date=2009; citation_pages=026301; citation_doi=10.1103/PhysRevE.80.026301; citation_id=CR50
citation_journal_title=J Vac Sci Technol A; citation_title=Comment on “Survey on measurement of tangential momentum accommodation coefficient” [J Vac Sci Technol A 26, 634 (2008)]; citation_author=AD Chew; citation_volume=27; citation_publication_date=2009; citation_pages=591-592; citation_doi=10.1116/1.3106613; citation_id=CR51
citation_journal_title=Comput Fluid; citation_title=Computations of gas microflows using pressure correction method with Langmuir slip model; citation_author=H Choi, D Lee; citation_volume=37; citation_publication_date=2008; citation_pages=1309-1319; citation_doi=10.1016/j.compfluid.2007.10.016; citation_id=CR52
citation_journal_title=Microfluid Nanofluid; citation_title=Rarefaction and compressibility effects on steady and transient gas flows in microchannels; citation_author=S Colin; citation_volume=1; citation_publication_date=2005; citation_pages=268-279; citation_doi=10.1007/s10404-004-0002-y; citation_id=CR53
citation_journal_title=ASME J Heat Transf; citation_title=Gas microflows in the slip flow regime: a critical review on convective heat transfer; citation_author=S Colin; citation_volume=134; citation_publication_date=2012; citation_pages=020908; citation_doi=10.1115/1.4005063; citation_id=CR54
citation_journal_title=Heat Transf Eng; citation_title=Validation of a second-order slip flow model in rectangular microchannels; citation_author=S Colin, P Lalonde, R Caen; citation_volume=25; citation_publication_date=2004; citation_pages=23-30; citation_doi=10.1080/01457630490280047; citation_id=CR55
citation_journal_title=Physica D; citation_title=A Knudsen layer theory for lattice gases; citation_author=R Cornubert, D d’Humieres, D Levermore; citation_volume=47; citation_publication_date=1991; citation_pages=241-259; citation_doi=10.1016/0167-2789(91)90295-K; citation_id=CR56
citation_journal_title=Superlattices Microstr; citation_title=Numerical analysis of roughness effect on microtube heat transfer; citation_author=G Croce, P Agaro; citation_volume=35; citation_publication_date=2004; citation_pages=601-616; citation_doi=10.1016/j.spmi.2003.09.014; citation_id=CR57
citation_journal_title=J Differ Equ; citation_title=Effective boundary condition at a rough surface starting from a slip condition; citation_author=AL Dalibrard, DG Varet; citation_volume=251; citation_publication_date=2011; citation_pages=3450-3487; citation_doi=10.1016/j.jde.2011.07.017; citation_id=CR58
citation_journal_title=Int J Heat Mass Transf; citation_title=An analysis of second-order slip flow and temperature jump boundary conditions for rarefied gases; citation_author=RG Deissler; citation_volume=7; citation_publication_date=1964; citation_pages=681-694; citation_doi=10.1016/0017-9310(64)90161-9; citation_id=CR59
citation_journal_title=Int J Heat Mass Transf; citation_title=Analytical solution of gaseous slip flow in long microchannels; citation_author=N Dongari, A Agrawal, A Agrawal; citation_volume=50; citation_publication_date=2007; citation_pages=3411-3421; citation_doi=10.1016/j.ijheatmasstransfer.2007.01.048; citation_id=CR60
citation_journal_title=J Fluid Sci Tech; citation_title=Extended Navier–Stokes equations and treatments of micro-channel gas flows; citation_author=N Dongari, R Sambasivam, F Durst; citation_volume=4; citation_publication_date=2009; citation_pages=454-467; citation_doi=10.1299/jfst.4.454; citation_id=CR61
citation_journal_title=Microfluid Nanofluid; citation_title=Predicting microscale gas flows and rarefaction effects through extended Navier–Stokes–Fourier equations from phoretic transport considerations; citation_author=N Dongari, F Durst, S Chakraborty; citation_volume=9; citation_publication_date=2010; citation_pages=831-846; citation_doi=10.1007/s10404-010-0604-5; citation_id=CR62
citation_journal_title=J Phys D Appl Phys; citation_title=Molecular free path distribution in rarefied gases; citation_author=N Dongari, YH Zhang, JM Reese; citation_volume=44; citation_publication_date=2011; citation_pages=125502; citation_doi=10.1088/0022-3727/44/12/125502; citation_id=CR63
citation_journal_title=J Fluid Eng; citation_title=Modeling of Knudsen layer effects in micro/nanoscale gas flows; citation_author=N Dongari, YH Zhang, JM Reese; citation_volume=133; citation_publication_date=2011; citation_pages=071101; citation_doi=10.1115/1.4004364; citation_id=CR64
citation_journal_title=ASME J Fluid Eng; citation_title=Effects of corrugated roughness on developed laminar flow in microtubes; citation_author=Z Duan, YS Muzychka; citation_volume=130; citation_publication_date=2008; citation_pages=031102; citation_doi=10.1115/1.2842148; citation_id=CR65
citation_journal_title=ASME J Heat Transf; citation_title=Effects of axial corrugated roughness on low Reynolds number slip flow and continuum flow in microtubes; citation_author=Z Duan, YS Muzychka; citation_volume=132; citation_publication_date=2010; citation_pages=041001; citation_doi=10.1115/1.3211854; citation_id=CR66
citation_journal_title=Phys Rev Lett; citation_title=Boundary condition for fluid flow: curved or rough surfaces; citation_author=D Einzel, P Panzer, M Liu; citation_volume=64; citation_publication_date=1990; citation_pages=2269; citation_doi=10.1103/PhysRevLett.64.2269; citation_id=CR67
citation_journal_title=Can J Phys; citation_title=Nonlinear transport coefficients and plane Couette flow of a viscous, heat conducting gas between two plates at different temperatures; citation_author=BC Eu, RE Khayat, GD Billing, C Nyeland; citation_volume=65; citation_publication_date=1987; citation_pages=1090-1103; citation_doi=10.1139/p87-180; citation_id=CR68
citation_journal_title=Microfluid Nanofluid; citation_title=Tangential momentum accommodation in microtube; citation_author=T Ewart, P Perrier, IA Graur, JG Meolans; citation_volume=3; citation_publication_date=2007; citation_pages=689-695; citation_doi=10.1007/s10404-007-0158-3; citation_id=CR69
citation_journal_title=J Fluid Mech; citation_title=Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes; citation_author=T Ewart, P Perrier, IA Graur, JG Meolans; citation_volume=584; citation_publication_date=2007; citation_pages=337-356; citation_doi=10.1017/S0022112007006374; citation_id=CR70
citation_journal_title=Phys Fluid; citation_title=Viscosity and slip velocity in gas flow in microchannels; citation_author=M Fichman, G Hetsroni; citation_volume=17; citation_publication_date=2005; citation_pages=123102; citation_doi=10.1063/1.2141960; citation_id=CR71
citation_journal_title=ASME J Fluids Eng; citation_title=Molecular dynamics simulation of adsorbent layer effect on tangential momentum accommodation coefficient; citation_author=GW Finger, JS Kapat, A Bhattacharya; citation_volume=129; citation_publication_date=2007; citation_pages=31-39; citation_doi=10.1115/1.2375128; citation_id=CR72
citation_journal_title=ASME J Tribol; citation_title=Analysis of ultra-thin gas film lubrication based on linearized Boltzmann equation: first report-derivation of a generalized lubrication equation including thermal creep flow; citation_author=S Fukui, R Kaneko; citation_volume=110; citation_publication_date=1988; citation_pages=253-262; citation_doi=10.1115/1.3261594; citation_id=CR73
citation_journal_title=Wear; citation_title=Estimation of gas film lubrication effects beneath sliding bushings of micromotors using a Molecular gas film lubrication equation; citation_author=S Fukui, R Kaneko; citation_volume=168; citation_publication_date=1993; citation_pages=175-179; citation_doi=10.1016/0043-1648(93)90214-7; citation_id=CR74
citation_journal_title=J Vac Sci Technol A; citation_title=Measurements of the tangential momentum accommodation coefficient in the transition flow regime with a spinning rotor gauge; citation_author=DH Gabis, SK Loyalka, TS Storvick; citation_volume=14; citation_publication_date=1996; citation_pages=2592-2598; citation_doi=10.1116/1.579986; citation_id=CR75
citation_journal_title=ASME J Fluid Eng; citation_title=The fluid mechanics of microdevices—the Freeman scholar lecture; citation_author=M Gad-el-Hak; citation_volume=121; citation_publication_date=1999; citation_pages=5-33; citation_doi=10.1115/1.2822013; citation_id=CR76
citation_journal_title=Mec Ind; citation_title=Flow physics in MEMS; citation_author=M Gad-el-Hak; citation_volume=2; citation_publication_date=2001; citation_pages=313-341; citation_id=CR77
citation_journal_title=Int J Heat Mass Transf; citation_title=Comments on “Critical view on new results in micro-fluid mechanics”; citation_author=M Gad-el-Hak; citation_volume=46; citation_publication_date=2003; citation_pages=3941-3945; citation_doi=10.1016/S0017-9310(03)00191-1; citation_id=CR78
citation_journal_title=Heat Transf Eng; citation_title=Gas and liquid transport at the microscale; citation_author=M Gad-el-Hak; citation_volume=27; citation_publication_date=2006; citation_pages=13-29; citation_doi=10.1080/01457630500522305; citation_id=CR79
citation_journal_title=Phys Fluid; citation_title=Direct simulation Monte Carlo-based expressions for the gas mass flow rate and pressure profile in a microscale tube; citation_author=MA Gallis, JR Torczynski; citation_volume=24; citation_publication_date=2011; citation_pages=012005; citation_doi=10.1063/1.3678337; citation_id=CR80
citation_journal_title=Phys Fluids; citation_title=Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow; citation_author=MA Gallis, JR Torczynski, DJ Rader, M Tij, A Santos; citation_volume=18; citation_publication_date=2006; citation_pages=017104; citation_doi=10.1063/1.2166449; citation_id=CR81
citation_journal_title=J Fluid Mech; citation_title=On the role of the Knudsen layer in rapid granular flows; citation_author=JE Galvin, CM Hrenya, RD Wildman; citation_volume=585; citation_publication_date=2007; citation_pages=73-92; citation_doi=10.1017/S0022112007006489; citation_id=CR82
citation_journal_title=Eur J Mech B/Fluid; citation_title=The viscous-slip, diffusion-slip, and thermal-creep problems for a binary mixture of rigid spheres described by the linearized Boltzmann equation; citation_author=RDM Garcia, CE Siewert; citation_volume=26; citation_publication_date=2007; citation_pages=749-778; citation_doi=10.1016/j.euromechflu.2006.12.002; citation_id=CR83
citation_journal_title=Eur J Mech B/Fluid; citation_title=Viscous-slip, thermal-slip, and temperature-jump coefficients based on the linearized Boltzmann equation (and five kinetic models) with the Cercignani_Lampis boundary condition; citation_author=RDM Garcia, CE Siewert; citation_volume=29; citation_publication_date=2010; citation_pages=181-191; citation_doi=10.1016/j.euromechflu.2010.01.005; citation_id=CR84
citation_journal_title=Phys Fluid; citation_title=Velocity slip coefficients based on the hard-sphere Boltzmann equation; citation_author=L Gibelli; citation_volume=24; citation_publication_date=2012; citation_pages=022001; citation_doi=10.1063/1.3680873; citation_id=CR85
citation_journal_title=Microfluid Nanofluid; citation_title=Analytical and numerical description for isothermal gas flows in microchannels; citation_author=IA Graur, JG Meolans, DE Zeitoun; citation_volume=2; citation_publication_date=2006; citation_pages=64-77; citation_doi=10.1007/s10404-005-0055-6; citation_id=CR86
citation_journal_title=Phys Fluid; citation_title=Measurements of tangential momentum accommodation coefficient for various gases in plane microchannel; citation_author=IA Graur, P Perrier, W Ghozlani, JG Meolans; citation_volume=21; citation_publication_date=2009; citation_pages=102004; citation_doi=10.1063/1.3253696; citation_id=CR87
citation_journal_title=J Comp Phys; citation_title=A computational strategy for the regularized 13 moment equations with enhanced wall-boundary conditions; citation_author=XJ Gu, DR Emerson; citation_volume=225; citation_publication_date=2007; citation_pages=263-283; citation_doi=10.1016/j.jcp.2006.11.032; citation_id=CR88
citation_journal_title=Int J Comput Fluid Dyn; citation_title=Analysis of lattice Boltzmann equation for microscale gas flows: relaxation times, boundary conditions and the Knudsen layer; citation_author=Z Guo, C Zheng; citation_volume=22; citation_publication_date=2008; citation_pages=465-473; citation_doi=10.1080/10618560802253100; citation_id=CR89
citation_journal_title=J Appl Phys; citation_title=Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for microgas flows; citation_author=ZL Guo, TS Zhao, Y Shi; citation_volume=99; citation_publication_date=2006; citation_pages=074903; citation_doi=10.1063/1.2185839; citation_id=CR90
citation_journal_title=Phys Rev E; citation_title=Discrete effects on boundary conditions for the lattice Boltzmann equation in simulating microscale gas flows; citation_author=Z Guo, B Shi, T Zhao, C Zheng; citation_volume=76; citation_publication_date=2007; citation_pages=056704; citation_doi=10.1103/PhysRevE.76.056704; citation_id=CR91
citation_journal_title=EPL; citation_title=An extended Navier–Stokes formulation for gas flows in the Knudsen layer near a wall; citation_author=ZL Guo, BC Shi, CG Zheng; citation_volume=80; citation_publication_date=2007; citation_pages=24001; citation_doi=10.1209/0295-5075/80/24001; citation_id=CR92
citation_journal_title=Phys Rev E; citation_title=Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow; citation_author=ZL Guo, CG Zheng, BC Shi; citation_volume=77; citation_publication_date=2008; citation_pages=036707; citation_doi=10.1103/PhysRevE.77.036707; citation_id=CR93
citation_journal_title=Phys Fluids; citation_title=Gas-dynamic boundary conditions of evaporation and condensation: Numerical analysis of the Knudsen layer; citation_author=AV Gusarov, I Smurov; citation_volume=14; citation_publication_date=2002; citation_pages=4242-4255; citation_doi=10.1063/1.1516211; citation_id=CR94
citation_journal_title=Phys Fluid; citation_title=Analysis of discretization in the direct simulation Monte Carlo; citation_author=NG Hadjiconstantinou; citation_volume=12; citation_publication_date=2000; citation_pages=2634-2638; citation_doi=10.1063/1.1289393; citation_id=CR95
citation_journal_title=Phys Fluid; citation_title=Comment on Cercignani’s second-order slip coefficient; citation_author=NG Hadjiconstantinou; citation_volume=15; citation_publication_date=2003; citation_pages=2352-2354; citation_doi=10.1063/1.1587155; citation_id=CR96
citation_journal_title=Phys Fluid; citation_title=The limits of Navier–Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics; citation_author=NG Hadjiconstantinou; citation_volume=18; citation_publication_date=2006; citation_pages=111301; citation_doi=10.1063/1.2393436; citation_id=CR97
citation_journal_title=ASME J Heat Transfer; citation_title=Constant-wall-temperature Nusselt number in micro and nano-channels; citation_author=NG Hadjiconstantinou, O Simek; citation_volume=124; citation_publication_date=2002; citation_pages=356-364; citation_doi=10.1115/1.1447931; citation_id=CR98
citation_journal_title=Inter J Heat Fluid Flow; citation_title=Near-wall effects in rarefied gas micro-flows: some modern hydrodynamic approaches; citation_author=LO Hare, DA Lockerby, JM Reese, DR Emerson; citation_volume=28; citation_publication_date=2007; citation_pages=37-43; citation_doi=10.1016/j.ijheatfluidflow.2006.04.012; citation_id=CR99
citation_journal_title=Annu Rev Fluid Mech; citation_title=Micro-electro-mechanical-systems (MEMS) and fluid flows; citation_author=CM Ho, YC Tai; citation_volume=30; citation_publication_date=1998; citation_pages=579-612; citation_doi=10.1146/annurev.fluid.30.1.579; citation_id=CR100
citation_journal_title=Int Commun Heat Mass Transf; citation_title=A novel modified lattice Boltzmann method for simulation of gas flows in wide range of Knudsen number; citation_author=A Homayoon, AH Meghdadi Isfahani, E Shirani, M Ashrafizadeh; citation_volume=38; citation_publication_date=2011; citation_pages=827-832; citation_doi=10.1016/j.icheatmasstransfer.2011.03.007; citation_id=CR101
citation_journal_title=Nanoscale Microscale Thermophys Eng; citation_title=Investigation of fluid flow and heat transfer characteristics of gases in microchannels with consideration of different roughness shapes at slip flow regime; citation_author=S Hossainpour, MH Khadem; citation_volume=14; citation_publication_date=2010; citation_pages=137-151; citation_doi=10.1080/15567265.2010.500317; citation_id=CR102
citation_journal_title=ASME J Lubr Technol; citation_title=An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances; citation_author=YT Hsia, GA Domoto; citation_volume=105; citation_publication_date=1983; citation_pages=120-130; citation_doi=10.1115/1.3254526; citation_id=CR103
citation_journal_title=ASME J Fluid Eng; citation_title=Influence of three-dimensional roughness on pressure-driven flow through microchannels; citation_author=Y Hu, C Werner, D Li; citation_volume=125; citation_publication_date=2003; citation_pages=871-879; citation_doi=10.1115/1.1598993; citation_id=CR104
citation_journal_title=IEEE Trans Magn; citation_title=A new modified Reynolds equation for ultra-thin film gas lubrication; citation_author=CC Hwang, RF Fung, RF Yang, CI Weng, WL Li; citation_volume=32; citation_publication_date=1995; citation_pages=344-347; citation_doi=10.1109/20.486518; citation_id=CR105
citation_journal_title=J Vac Sci Technol A; citation_title=Slip coefficients for binary gas mixture; citation_author=IN Ivchenko, SK Loyalka, RV Tompson; citation_volume=15; citation_publication_date=1997; citation_pages=2375-2381; citation_doi=10.1116/1.580750; citation_id=CR106
citation_journal_title=J Micromech Microeng; citation_title=Effective heights and tangential momentum accommodation coefficients of gaseous slip flows in deep reactive ion etching rectangular microchannels; citation_author=J Jang, ST Wereley; citation_volume=16; citation_publication_date=2006; citation_pages=493-504; citation_doi=10.1088/0960-1317/16/3/004; citation_id=CR107
citation_journal_title=Int J Heat Mass Transf; citation_title=Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel; citation_author=Y Ji, K Yuan, JN Chung; citation_volume=49; citation_publication_date=2006; citation_pages=1329-1339; citation_doi=10.1016/j.ijheatmasstransfer.2005.10.011; citation_id=CR108
citation_journal_title=J Micromech Microeng; citation_title=Navier–Stokes simulations of gas flow in micro devices; citation_author=D Jie, X Diao, KB Cheong, LK Yong; citation_volume=10; citation_publication_date=2000; citation_pages=372-379; citation_doi=10.1088/0960-1317/10/3/311; citation_id=CR109
citation_journal_title=J Stat Phys; citation_title=Regularization of the Burnett equations via relaxation; citation_author=S Jin, M Slemrod; citation_volume=103; citation_publication_date=2001; citation_pages=1009-1033; citation_doi=10.1023/A:1010365123288; citation_id=CR110
citation_title=Micro flows: fundamentals and simulation; citation_publication_date=2002; citation_id=CR111; citation_author=GE Karniadakis; citation_author=A Beskok; citation_publisher=Springer
citation_title=Microflows and nanoflows: fundamentals and simulation; citation_publication_date=2005; citation_id=CR112; citation_author=GE Karniadakis; citation_author=A Beskok; citation_author=N Aluru; citation_publisher=Springer-Verlag
citation_journal_title=Int Commun Heat Mass Transf; citation_title=Numerical simulation of roughness effects on flow and heat transfer in microchannels at slip flow regime; citation_author=MH Khadem, M Shams, S Hossainpour; citation_volume=36; citation_publication_date=2009; citation_pages=69-77; citation_doi=10.1016/j.icheatmasstransfer.2008.10.009; citation_id=CR113
citation_journal_title=Phys Rev E; citation_title=Analytic solution for a higher-order lattice Boltzmann method: Slip velocity and Knudsen layer; citation_author=SH Kim, H Pitsch; citation_volume=78; citation_publication_date=2008; citation_pages=016702; citation_doi=10.1103/PhysRevE.78.016702; citation_id=CR114
citation_journal_title=IEEE Trans Magnet; citation_title=Langmuir slip model for air bearing simulation using the Lattice Boltzmann method; citation_author=HM Kim, D Kim, WT Kim, PS Chung, MS Jhon; citation_volume=43; citation_publication_date=2007; citation_pages=2244-2246; citation_doi=10.1109/TMAG.2007.893640; citation_id=CR115
citation_journal_title=Phys Rev E; citation_title=Slip velocity and Knudsen layer in the lattice Boltzmann method for microscale flows; citation_author=SH Kim, H Pitsch, ID Boyd; citation_volume=77; citation_publication_date=2008; citation_pages=026704; citation_doi=10.1103/PhysRevE.77.026704; citation_id=CR116
citation_journal_title=ASME J Fluid Eng; citation_title=Computational analysis of wall roughness effects for liquid flow in micro-conduits; citation_author=C Kleinstreuer, J Koo; citation_volume=126; citation_publication_date=2004; citation_pages=1-9; citation_doi=10.1115/1.1637633; citation_id=CR117
citation_journal_title=Phys Fluid; citation_title=Slip coefficients for general gas-surface interaction; citation_author=T Klinc, I Kuscer; citation_volume=15; citation_publication_date=1972; citation_pages=1018; citation_doi=10.1063/1.1694022; citation_id=CR118
citation_journal_title=Phys Fluid A; citation_title=Variable soft sphere molecular model for inverse-power-lawor Lennard–Jones potential; citation_author=K Koura, H Matsumoto; citation_volume=4; citation_publication_date=1992; citation_pages=1083-1085; citation_doi=10.1063/1.858262; citation_id=CR119
citation_journal_title=Acta Astronaut; citation_title=Tangential momentum and thermal accommodation coefficients for hydrogen molecules on graphite surface; citation_author=V Kovalev, A Yakunchikov, F Li; citation_volume=69; citation_publication_date=2011; citation_pages=744-746; citation_doi=10.1016/j.actaastro.2011.05.019; citation_id=CR120
citation_journal_title=J Appl Phys; citation_title=Air friction on rapidly moving surfaces; citation_author=AR Kuhlthau; citation_volume=20; citation_publication_date=1949; citation_pages=217-223; citation_doi=10.1063/1.1698335; citation_id=CR121
citation_journal_title=Phys Rev Lett; citation_title=Roughness induced boundary slip in microchannel flows; citation_author=C Kunert, J Harting; citation_volume=99; citation_publication_date=2007; citation_pages=176001; citation_doi=10.1103/PhysRevLett.99.176001; citation_id=CR122
citation_journal_title=Chem Rev; citation_title=Surface chemistry; citation_author=I Langmuir; citation_volume=13; citation_publication_date=1933; citation_pages=147-191; citation_doi=10.1021/cr60045a001; citation_id=CR123
citation_journal_title=Phys Rev Lett; citation_title=Discrete Boltzmann equation for microfluidics; citation_author=B Li, DY Kwok; citation_volume=90; citation_publication_date=2003; citation_pages=124502; citation_doi=10.1103/PhysRevLett.90.124502; citation_id=CR124
Li ZX, Du DX, Guo ZY (2000) Characteristics of frictional resistance for gas flow in microtubes. In: Proceedings of symposium on energy engineering in the 21st Century, pp 658–664
citation_journal_title=J Micromech Microeng; citation_title=Effects of roughness on rarefied gas flow in long microtubes; citation_author=W-L Li, J-W Lin, S-C Lee, M-D Chen; citation_volume=12; citation_publication_date=2002; citation_pages=149-156; citation_doi=10.1088/0960-1317/12/2/308; citation_id=CR126
citation_journal_title=Microfluid Nanofluid; citation_title=Lattice Boltzmann modeling of microchannel flows in the transition flow regime; citation_author=Q Li, YL He, GH Tang, WQ Tao; citation_volume=10; citation_publication_date=2011; citation_pages=607-618; citation_doi=10.1007/s10404-010-0693-1; citation_id=CR127
citation_journal_title=Phys Rev E; citation_title=Velocity gradient singularity and structure of the velocity profile in the Knudsen layer according to the Boltzmann equation; citation_author=CR Lilley, JE Sader; citation_volume=76; citation_publication_date=2007; citation_pages=1-4; citation_doi=10.1103/PhysRevE.76.026315; citation_id=CR128
citation_journal_title=Proc R Soc A; citation_title=Velocity profile in the Knudsen layer according to the Boltzmann equation; citation_author=CR Lilley, JE Sader; citation_volume=464; citation_publication_date=2008; citation_pages=2015-2035; citation_doi=10.1098/rspa.2008.0071; citation_id=CR129
citation_journal_title=Phys Fluid; citation_title=Numerical and experimental investigation of microchannel flows with rough surfaces; citation_author=TC Lilly, JA Duncan, SL Nothnagel, SF Gimelshein, NE Gimelshein, AD Ketsdever, IJ Wysong; citation_volume=19; citation_publication_date=2007; citation_pages=106101; citation_doi=10.1063/1.2775977; citation_id=CR130
citation_journal_title=Chin Phys B; citation_title=The effect of surface roughness on rarefied gas flows by lattice Boltzmann method; citation_author=CF Liu, YS Ni; citation_volume=17; citation_publication_date=2008; citation_pages=4554-4561; citation_doi=10.1088/1674-1056/17/2/047; citation_id=CR131
citation_journal_title=J Fluid Mech; citation_title=On the modelling of isothermal gas flows at the microscale; citation_author=DA Lockerby, JM Reese; citation_volume=604; citation_publication_date=2008; citation_pages=235-261; citation_doi=10.1017/S0022112008001158; citation_id=CR132
citation_journal_title=Phys Rev E; citation_title=Velocity boundary condition at solid walls in rarefied gas calculations; citation_author=DA Lockerby, JM Reese, DR Emerson, RW Barber; citation_volume=70; citation_publication_date=2004; citation_pages=017303; citation_doi=10.1103/PhysRevE.70.017303; citation_id=CR133
citation_journal_title=AIAA J; citation_title=Capturing the Knudsen layer in continuum-fluid models of nonequilibrium gas flows; citation_author=DA Lockerby, JM Reese, MA Gallis; citation_volume=43; citation_publication_date=2005; citation_pages=1391-1393; citation_doi=10.2514/1.13530; citation_id=CR134
citation_journal_title=Phys Fluids; citation_title=The usefulness of higher-order constitutive relations for describing the Knudsen layer; citation_author=DA Lockerby, JM Reese, MA Gallis; citation_volume=17; citation_publication_date=2005; citation_pages=100609; citation_doi=10.1063/1.1897005; citation_id=CR135
citation_journal_title=Phys Fluid A: Fluid Dyn; citation_title=Some extensions to the Cercignani-Lampis gas-surface scattering kernel; citation_author=RG Lord; citation_volume=3; citation_publication_date=1991; citation_pages=706-710; citation_doi=10.1063/1.858076; citation_id=CR136
citation_journal_title=Phys Fluid; citation_title=Some further extensions of the Cercignani-Lampis gas-surface interaction model; citation_author=RG Lord; citation_volume=7; citation_publication_date=1995; citation_pages=1159-1161; citation_doi=10.1063/1.868557; citation_id=CR137
citation_journal_title=Phil Trans R Soc A; citation_title=Higher order slip according to the linearized Boltzmann equation with general boundary conditions; citation_author=S Lorenzani; citation_volume=369; citation_publication_date=2011; citation_pages=2228-2236; citation_doi=10.1098/rsta.2011.0059; citation_id=CR138
citation_journal_title=Phys Fluids; citation_title=Thermal transpiration in a cylindrical tube; citation_author=SK Loyalka; citation_volume=12; citation_publication_date=1969; citation_pages=2301-2305; citation_doi=10.1063/1.1692346; citation_id=CR139
citation_journal_title=Phys Fluid; citation_title=Approximate method in kinetic theory; citation_author=SK Loyalka; citation_volume=14; citation_publication_date=1971; citation_pages=2291-2294; citation_doi=10.1063/1.1693331; citation_id=CR140
citation_journal_title=Phys A; citation_title=Plane Poiseuille flow: near continuum results for a rigid sphere gas; citation_author=SK Loyalka, KA Hickey; citation_volume=160; citation_publication_date=1989; citation_pages=395-410; citation_doi=10.1016/0378-4371(89)90449-4; citation_id=CR141
citation_journal_title=Phys Fluids A; citation_title=Velocity slip and defect: hard sphere gas; citation_author=SK Loyalka, HA Hickey; citation_volume=1; citation_publication_date=1989; citation_pages=612-614; citation_doi=10.1063/1.857433; citation_id=CR142
citation_journal_title=Phys Fluid; citation_title=Some numerical results for the BGK model: thermal creep and viscous slip problems with arbitrary accommodation of the surface; citation_author=SK Loyalka, N Petrellis, ST Stvorick; citation_volume=18; citation_publication_date=1975; citation_pages=1094; citation_doi=10.1063/1.861293; citation_id=CR143
citation_journal_title=Contin Mech Thermodyn; citation_title=Couette flow with slip and jump boundary conditions; citation_author=W Marques, GM Kremer, FM Sharipov; citation_volume=12; citation_publication_date=2000; citation_pages=379-386; citation_doi=10.1007/s001610050143; citation_id=CR144
citation_journal_title=Phys Fluid; citation_title=Second-order slip laws in microchannels for helium and nitrogen; citation_author=J Maurer, P Tabeling, P Joseph, H Willaime; citation_volume=15; citation_publication_date=2003; citation_pages=2613-2621; citation_doi=10.1063/1.1599355; citation_id=CR145
citation_journal_title=Phil Trans Roy Soc; citation_title=On stresses in rarified gases arising from inequalities of temperature; citation_author=JC Maxwell; citation_volume=170; citation_publication_date=1879; citation_pages=231-256; citation_doi=10.1098/rstl.1879.0067; citation_id=CR146
citation_journal_title=Phys Fluid; citation_title=Gas-surface accommodation coefficients from viscous slip and temperature jump coefficients; citation_author=NG McCormick; citation_volume=17; citation_publication_date=2005; citation_pages=107104; citation_doi=10.1063/1.2111133; citation_id=CR147
citation_journal_title=Int J Numer Meth Fluids; citation_title=Empirical slip and viscosity performance for microscale gas flow; citation_author=MJ Mcnenly, MA Gallis, ID Boyd; citation_volume=49; citation_publication_date=2005; citation_pages=1169-1191; citation_doi=10.1002/fld.1012; citation_id=CR148
citation_journal_title=Microfluid Nanofluid; citation_title=Rarefaction effects on gas viscosity in the Knudsen transition regime; citation_author=VK Michalis, AN Kalarakis, ED Skouras, VN Burganos; citation_volume=9; citation_publication_date=2010; citation_pages=847-853; citation_doi=10.1007/s10404-010-0606-3; citation_id=CR149
citation_journal_title=Phys Rev; citation_title=Coefficients of slip in gases and the law of reflection of molecules from the surfaces of solids and liquids; citation_author=RA Millikan; citation_volume=21; citation_publication_date=1923; citation_pages=217-238; citation_doi=10.1103/PhysRev.21.217; citation_id=CR150
citation_journal_title=J Trib; citation_title=Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip flow model and considering surface accommodation coefficient; citation_author=Y Mitsuya; citation_volume=115; citation_publication_date=1993; citation_pages=289-294; citation_doi=10.1115/1.2921004; citation_id=CR151
citation_journal_title=Superlattices Microstruct; citation_title=The rarefaction effect on the friction factor of gas flow in microchannels; citation_author=GL Morini, M Spiga, P Tartarini; citation_volume=35; citation_publication_date=2004; citation_pages=587-599; citation_doi=10.1016/j.spmi.2003.09.013; citation_id=CR152
citation_journal_title=Microfluid Nanofluid; citation_title=A criterion for experimental validation of slip-flow models for incompressible rarefied gases through microchannels; citation_author=GL Morini, M Lorenzini, M Spiga; citation_volume=1; citation_publication_date=2005; citation_pages=190-196; citation_doi=10.1007/s10404-004-0028-1; citation_id=CR153
citation_journal_title=J Comput Phys; citation_title=A computational method for Eu’s generalized hydrodynamic equations of rarefied and microscale gas dynamics; citation_author=RS Myong; citation_volume=168; citation_publication_date=2001; citation_pages=47-72; citation_doi=10.1006/jcph.2000.6678; citation_id=CR154
citation_journal_title=Phys Fluid; citation_title=Gaseous slip models based on the Langmuir adsorption isotherm; citation_author=RS Myong; citation_volume=16; citation_publication_date=2004; citation_pages=104-117; citation_doi=10.1063/1.1630799; citation_id=CR155
citation_journal_title=J Comput Phys; citation_title=A generalized hydrodynamic computational model for rarefied and microscale diatomic gas flows; citation_author=RS Myong; citation_volume=195; citation_publication_date=2004; citation_pages=655-676; citation_doi=10.1016/j.jcp.2003.10.015; citation_id=CR156
citation_journal_title=Phys Fluid; citation_title=Velocity slip in microscale cylindrical Couette flow: the Langmuir model; citation_author=RS Myong, JM Reese, RW Barber, DR Emerson; citation_volume=17; citation_publication_date=2005; citation_pages=087105; citation_doi=10.1063/1.2003154; citation_id=CR157
citation_journal_title=Superlattices Microstruct; citation_title=Discrete velocity modelling of gaseous mixture flows in MEMS; citation_author=S Naris, D Valougeorgis, F Sharipov, D Kalempa; citation_volume=35; citation_publication_date=2004; citation_pages=629-643; citation_doi=10.1016/j.spmi.2004.02.025; citation_id=CR158
citation_journal_title=Rep Prog Phys; citation_title=Boundary slip in Newtonian liquids: a review of experimental studies; citation_author=C Neto, DR Evans, E Bonaccurso, H-J Butt, VSJ Craig; citation_volume=68; citation_publication_date=2005; citation_pages=2859-2897; citation_doi=10.1088/0034-4885/68/12/R05; citation_id=CR159
citation_journal_title=Phys Fluids; citation_title=Stress-density ratio slip-corrected Reynolds equation for ultra-thin film gas bearing lubrication; citation_author=EY-K Ng, N Liu; citation_volume=14; citation_publication_date=2002; citation_pages=1450-1457; citation_doi=10.1063/1.1456511; citation_id=CR160
citation_journal_title=Int J Rotat Mach; citation_title=A multicoefficient slip-corrected Reynolds equation for micro-thin film gas Lubrication; citation_author=EY-K Ng, N Liu; citation_volume=2; citation_publication_date=2005; citation_pages=105-111; citation_id=CR161
citation_journal_title=Phys Fluids A; citation_title=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; citation_author=T Ohwada, Y Sone, K Aoki; citation_volume=1; citation_publication_date=1989; citation_pages=1588-1599; citation_doi=10.1063/1.857304; citation_id=CR162
citation_journal_title=Annu Rev Fluid Mech; citation_title=Direct Simulation Monte Carlo: recent advances and application; citation_author=ES Oran, CK Oh, BZ Cybyk; citation_volume=30; citation_publication_date=1998; citation_pages=403-441; citation_doi=10.1146/annurev.fluid.30.1.403; citation_id=CR163
citation_journal_title=Heat Mass Transf; citation_title=Roughness induced forced convective laminar-transitional micropipe flow: energy and exergy analysis; citation_author=AA Ozalp; citation_volume=45; citation_publication_date=2008; citation_pages=31-46; citation_doi=10.1007/s00231-008-0407-3; citation_id=CR164
citation_journal_title=Heat Mass Transf; citation_title=Laminar-transitional micropipe flows: energy and exergy mechanisms based on Reynolds number, pipe diameter, surface roughness and wall heat flux; citation_author=AA Ozalp; citation_publication_date=2011; citation_id=CR165
citation_journal_title=J Micromech Microeng; citation_title=Determination of slip coefficient for rarefied gas flows using direct simulation Monte Carlo; citation_author=LS Pan, GR Liu, KY Lam; citation_volume=9; citation_publication_date=1999; citation_pages=89-96; citation_doi=10.1088/0960-1317/9/1/312; citation_id=CR166
citation_journal_title=ASME J Eng Gas Turbines Power; citation_title=Evolutionary optimization of micro-thrust bearings with periodic partial trapezoidal surface texturing; citation_author=CI Papadopoulos, PG Nikolakopoulos, L Kaiktsis; citation_volume=133; citation_publication_date=2011; citation_pages=012301; citation_doi=10.1115/1.4001990; citation_id=CR167
citation_journal_title=Phys Fluid; citation_title=Rarefaction effects on shear driven oscillatory gas flows: a direct simulation Monte Carlo study in the entire Knudsen regime; citation_author=JH Park, P Bahukudumbi, A Beskok; citation_volume=16; citation_publication_date=2004; citation_pages=317-330; citation_doi=10.1063/1.1634563; citation_id=CR168
citation_journal_title=ASME J Tribol; citation_title=Nanoscale effect on ultrathin gas film lubrication in hard disk drive; citation_author=Y Peng, X Lu, J Luo; citation_volume=126; citation_publication_date=2004; citation_pages=347-352; citation_doi=10.1115/1.1614824; citation_id=CR169
citation_journal_title=Microfluid Nanofluid; citation_title=A novel experimental setup for gas microflows; citation_author=J Pitakarnnop, S Varoutis, D Valougeorgis, S Geoffroy, L Baldas, S Colin; citation_volume=8; citation_publication_date=2010; citation_pages=57-72; citation_doi=10.1007/s10404-009-0447-0; citation_id=CR170
citation_journal_title=Phys Rev; citation_title=On gaseous self-diffusion in long capillary tubes; citation_author=WG Pollard, RD Present; citation_volume=73; citation_publication_date=1948; citation_pages=762-774; citation_doi=10.1103/PhysRev.73.762; citation_id=CR171
citation_journal_title=J Fluid Mech; citation_title=Experimental investigation of rarefied gas flow in different channels; citation_author=BT Porodnov, PE Suetin, SF Borisov, VD Akinshin; citation_volume=64; citation_publication_date=1974; citation_pages=417-437; citation_doi=10.1017/S0022112074002485; citation_id=CR172
citation_journal_title=Microfluid Nanofluid; citation_title=Numerical simulation of flow through microchannels with designed roughness; citation_author=AS Rawool, SK Mitra, SG Kandlikar; citation_volume=2; citation_publication_date=2006; citation_pages=215-221; citation_doi=10.1007/s10404-005-0064-5; citation_id=CR173
citation_journal_title=J Comput Theor Nanosci; citation_title=Computing the near-wall region in gas micro and nanofluidics: critical Knudsen layer phenomena; citation_author=JM Reese, Y Zheng, DA Lockerby; citation_volume=4; citation_publication_date=2007; citation_pages=807-813; citation_id=CR174
citation_journal_title=Phys Fluid; citation_title=Extending the Navier–Stokes solutions to transition regime in two-dimensional micro- and nanochannel flows using information preservation scheme; citation_author=E Roohi, M Darbandi; citation_volume=21; citation_publication_date=2009; citation_pages=082001; citation_doi=10.1063/1.3177351; citation_id=CR175
citation_journal_title=J Phys Fluid; citation_title=Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions; citation_author=M Sbragaglia, S Succi; citation_volume=17; citation_publication_date=2005; citation_pages=093602; citation_doi=10.1063/1.2044829; citation_id=CR176
citation_title=Flow of rarefied gases; citation_publication_date=1961; citation_id=CR177; citation_author=SA Schaaf; citation_author=PL Chambre; citation_publisher=Princeton University Press
Schamberg R (1947) The fundamental differential equations and the boundary conditions for high speed slip-flow, and their application to several specific problems. PhD thesis, California Institute of Technology
Seidl M, Steinheil E (1974) Measurement of momentum accommodation coefficients on surfaces characterized by Auger Spectroscopy. In: Rarefied Gas Dynamics, Ninth International Symposium, Germany, pp E 9.1–E 9.12
citation_journal_title=J Fluid Mech; citation_title=Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation; citation_author=X Shan, X Yuan, H Chen; citation_volume=550; citation_publication_date=2006; citation_pages=413-441; citation_doi=10.1017/S0022112005008153; citation_id=CR180
citation_journal_title=Eur J Mech B/Fluid; citation_title=Application of the Cercignani-Lampis scattering kernel to calculations of rarefied gas flows. II. Slip and jump coefficients; citation_author=F Sharipov; citation_volume=22; citation_publication_date=2003; citation_pages=133-143; citation_doi=10.1016/S0997-7546(03)00017-7; citation_id=CR181
Sharipov F (2004) Data on the velocity slip and temperature jump coefficients. In: Proceedings of the 5th international conference on thermal and mechanical simulation and experiments in microelectronics and microsystems-EuroSimE, Shaker, Belgium, pp 243–249
citation_journal_title=J Phys Chem Ref Data; citation_title=Data on the velocity slip and temperature jump on a gas-solid interface; citation_author=F Sharipov; citation_volume=40; citation_issue=2; citation_publication_date=2011; citation_pages=023101; citation_doi=10.1063/1.3580290; citation_id=CR183
citation_journal_title=Phys Fluid; citation_title=Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient; citation_author=F Sharipov, D Kalempa; citation_volume=15; citation_publication_date=2003; citation_pages=1800-1806; citation_doi=10.1063/1.1574815; citation_id=CR184
citation_journal_title=J Phys Chem Ref Data; citation_title=Data on internal rarefied gas flows; citation_author=F Sharipov, V Seleznev; citation_volume=27; citation_issue=3; citation_publication_date=1998; citation_pages=657-706; citation_doi=10.1063/1.556019; citation_id=CR185
citation_journal_title=Phys Fluids; citation_title=A kinetic-theory based first order slip boundary condition for gas flow; citation_author=S Shen, G Chen, RM Crone, MA Dufresne; citation_volume=19; citation_publication_date=2007; citation_pages=086101; citation_doi=10.1063/1.2754373; citation_id=CR186
citation_journal_title=Phys Fluids; citation_title=Viscous-slip, thermal-slip, and temperature-jump coefficients as defined by the linearized Boltzmann equation and the Cercignani-Lampis boundary condition; citation_author=CE Siewert; citation_volume=15; citation_publication_date=2003; citation_pages=1696-1701; citation_doi=10.1063/1.1567284; citation_id=CR187
citation_journal_title=Phys Fluid; citation_title=Model equations in rarefied gas dynamics: Viscous-slip and thermal-slip coefficients; citation_author=CE Siewert, F Sharipov; citation_volume=14; citation_publication_date=2002; citation_pages=4123-4129; citation_doi=10.1063/1.1514973; citation_id=CR188
citation_journal_title=Eur J Mech B/Fluid; citation_title=Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular-diffuse wall conditions; citation_author=CE Siewert, D Valougeorgis; citation_volume=23; citation_publication_date=2004; citation_pages=709-726; citation_doi=10.1016/j.euromechflu.2003.12.002; citation_id=CR189
citation_journal_title=Eur J Mech B/Fluids; citation_title=Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard sphere molecules; citation_author=Y Sone, S Takata, T Ohwada; citation_volume=9; citation_publication_date=1990; citation_pages=273-288; citation_id=CR190
Sreekanth AK (1969) Slip flow through long circular tubes. In: Proceedings of the sixth international symposium on rarefied gas dynamics, Academic, New York, pp 667–676
citation_journal_title=J Phys D Appl Phys; citation_title=The mean free path of gas molecules in the transition regime; citation_author=DW Stops; citation_volume=3; citation_publication_date=1970; citation_pages=685-696; citation_doi=10.1088/0022-3727/3/5/307; citation_id=CR192
citation_journal_title=Phys Fluids; citation_title=Regularization of Grid’s 13 moment equations: derivation and linear analysis; citation_author=H Struchtrup, M Torrilhon; citation_volume=15; citation_publication_date=2003; citation_pages=2668-2680; citation_doi=10.1063/1.1597472; citation_id=CR193
citation_journal_title=Phys Rev E; citation_title=Higher-order effects in rarefied channel flows; citation_author=H Struchtrup, M Torrilhon; citation_volume=78; citation_publication_date=2008; citation_pages=046301; citation_doi=10.1103/PhysRevE.78.046301; citation_id=CR194
citation_journal_title=J Fluid Mech; citation_title=Poiseuille flow at arbitrary Knudsen numbers and tangential momentum accommodation; citation_author=PE Suetin, BT Porodnov, VG Chernjak, SF Borisov; citation_volume=60; citation_publication_date=1973; citation_pages=581-592; citation_doi=10.1017/S0022112073000352; citation_id=CR195
citation_journal_title=J Vac Sci Technol A; citation_title=Analytical modeling of rarefied Poiseuille flow in microchannels; citation_author=Y Sun, WK Chan; citation_volume=22; citation_publication_date=2004; citation_pages=383-395; citation_doi=10.1116/1.1647599; citation_id=CR196
citation_journal_title=Numer Heat Transf A; citation_title=Effects of surface roughness on nitrogen flow in a microchannel using the direct simulation monte carlo method; citation_author=H Sun, M Faghri; citation_volume=43; citation_publication_date=2003; citation_pages=1-8; citation_doi=10.1080/10407780307302; citation_id=CR197
citation_journal_title=Molecular Phys; citation_title=Effect of gas adsorption on momentum accommodation coefficients in microgas flows using molecular dynamic simulations; citation_author=J Sun, ZX Li; citation_volume=106; citation_publication_date=2008; citation_pages=2325-2332; citation_doi=10.1080/00268970802452020; citation_id=CR198
citation_journal_title=J Micromech Microeng; citation_title=A slip model with molecular dynamics; citation_author=Y Sun, WK Chan, N Liu; citation_volume=12; citation_publication_date=2002; citation_pages=316-322; citation_doi=10.1088/0960-1317/12/3/318; citation_id=CR199
citation_journal_title=Int J Mod Phys C; citation_title=Comparison of gas slip models with solutions of linearized Boltzmann equation and direct simulation of Monte Carlo method; citation_author=GH Tang, YL He, WQ Tao; citation_volume=18; citation_publication_date=2007; citation_pages=203-216; citation_doi=10.1142/S0129183107010383; citation_id=CR200
citation_journal_title=Int J Heat Mass Transf; citation_title=Experimental study of compressibility, roughness and rarefaction influences on microchannel flow; citation_author=GH Tang, L Zhuo, YL He, WQ Tao; citation_volume=50; citation_publication_date=2007; citation_pages=2282-2295; citation_doi=10.1016/j.ijheatmasstransfer.2006.10.034; citation_id=CR201
citation_journal_title=Phys Rev E; citation_title=Lattice Boltzmann models for nonequilibrium gas flows; citation_author=GH Tang, YH Zhang, DR Emerson; citation_volume=77; citation_publication_date=2008; citation_pages=046701; citation_doi=10.1103/PhysRevE.77.046701; citation_id=CR202
citation_journal_title=J Vac Sci Technol A; citation_title=The spinning rotor gauge: measurements of viscosity, velocity slip coefficients, and tangential momentum accommodation coefficients; citation_author=P Tekasakul, JA Bentz, RV Tompson, SK Loyalka; citation_volume=14; citation_publication_date=1996; citation_pages=2946-2952; citation_doi=10.1116/1.580249; citation_id=CR203
citation_title=Comparative measurements of tangential momentum and thermal accommodations on polished and on roughened steel spheres; citation_publication_date=1974; citation_id=CR204; citation_author=LB Thomas; citation_author=RG Lord; citation_publisher=Proc Int Symp On Rarefied Gas
citation_journal_title=Microfluid Nanofluid; citation_title=A slip model for micro/nano gas flows induced by body forces; citation_author=QD To, C Bercegeay, G Lauriat, C Leonard, G Bonnet; citation_volume=8; citation_publication_date=2010; citation_pages=417-422; citation_doi=10.1007/s10404-009-0532-4; citation_id=CR205
citation_journal_title=ASME J Heat Transf; citation_title=Experimental investigation of gas flow in microchannels; citation_author=SE Turner, LC Lam, M Faghri, OJ Gregory; citation_volume=126; citation_publication_date=2004; citation_pages=753; citation_doi=10.1115/1.1797036; citation_id=CR206
citation_journal_title=J Microelectromech Syst; citation_title=Compact damping models for laterally moving microstructures with gas-rarefaction effects; citation_author=T Veijola, M Turowski; citation_volume=10; citation_publication_date=2001; citation_pages=263-273; citation_doi=10.1109/84.925777; citation_id=CR207
citation_journal_title=J Fluid Mech; citation_title=An analytically predictive model for moderately rarefied gas flow; citation_author=T Veltzke, J Thoming; citation_volume=698; citation_publication_date=2012; citation_pages=406-422; citation_doi=10.1017/jfm.2012.98; citation_id=CR208
citation_journal_title=Eur J Mech B/Fluids; citation_title=Numerical analysis of the shear and thermal creep flows of a rarefied gas over the plane wall of a Maxwell-type boundary on the basis of the linearized Boltzmann equation for hard-sphere molecules; citation_author=M Wakabayashi, T Ohwada, F Golse; citation_volume=15; citation_publication_date=1996; citation_pages=175-201; citation_id=CR209
citation_journal_title=ASME J Electron Packag; citation_title=Effects of two-dimensional roughness in flow in microchannel; citation_author=XQ Wang, C Yap, AS Mujumdar; citation_volume=127; citation_publication_date=2005; citation_pages=357-361; citation_doi=10.1115/1.1997164; citation_id=CR210
citation_journal_title=Phys Rev E; citation_title=Velocity slip and temperature jump simulations by the three-dimensional thermal finite-difference lattice Boltzmann method; citation_author=M Watari; citation_volume=79; citation_publication_date=2009; citation_pages=066706; citation_doi=10.1103/PhysRevE.79.066706; citation_id=CR211
citation_journal_title=ASME J Fluid Eng; citation_title=Relationship between accuracy and number of velocity particles of the finite-difference lattice Boltzmann method in velocity slip simulations; citation_author=M Watari; citation_volume=132; citation_publication_date=2010; citation_pages=101401; citation_doi=10.1115/1.4002359; citation_id=CR212
citation_journal_title=Phys Fluid; citation_title=A challenge in Navier–Stokes-based continuum modeling: Maxwell-Burnett slip law; citation_author=HC Weng, CK Chen; citation_volume=20; citation_publication_date=2008; citation_pages=106101; citation_doi=10.1063/1.2998451; citation_id=CR213
citation_journal_title=Nanotechnology; citation_title=Gaseous flow in microtubes at arbitrary Knudsen numbers; citation_author=CI Weng, WL Li, CC Hwang; citation_volume=10; citation_publication_date=1999; citation_pages=373-379; citation_doi=10.1088/0957-4484/10/4/302; citation_id=CR214
citation_journal_title=ASME J Tribol; citation_title=A gas lubrication equation for high Knudsen number flows and striated rough surfaces; citation_author=J White; citation_volume=132; citation_publication_date=2010; citation_pages=021701; citation_doi=10.1115/1.4001023; citation_id=CR215
citation_journal_title=Appl Phys Lett; citation_title=slip model for rarefied gas flows at arbitrary Knudsen number; citation_author=L Wu; citation_volume=93; citation_publication_date=2008; citation_pages=253103; citation_doi=10.1063/1.3052923; citation_id=CR216
citation_journal_title=Phys Fluid; citation_title=A generalized compressible Reynolds lubrication equation with bounded contact pressure; citation_author=L Wu, DB Bogy; citation_volume=13; citation_publication_date=2001; citation_pages=2237-2244; citation_doi=10.1063/1.1384867; citation_id=CR217
citation_journal_title=Trans ASME J Tribol; citation_title=New first and second order slip models for the compressible Reynolds equation; citation_author=L Wu, DB Bogy; citation_volume=125; citation_publication_date=2003; citation_pages=558-561; citation_doi=10.1115/1.1538620; citation_id=CR218
citation_journal_title=Microfluid Nanofluid; citation_title=Investigation of laminar flow in microtubes with random rough surfaces; citation_author=R Xiong, JN Chung; citation_volume=8; citation_publication_date=2010; citation_pages=11-20; citation_doi=10.1007/s10404-009-0445-2; citation_id=CR219
Xue H, Fan Q (2000) A high order modification on the analytic solution of microchannel gaseous flows. In: Proceeding of ASME fluids engineering division summer meeting, Boston, USA, FEDSM2000-11313
citation_journal_title=Microfluid Nanofluid; citation_title=Experimental measurement on tangential momentum accommodation coefficient in a single microtube; citation_author=H Yamaguchi, T Hanawa, O Yamamoto, Y Matsuda, Y Egami, T Niimi; citation_volume=11; citation_publication_date=2011; citation_pages=57-64; citation_doi=10.1007/s10404-011-0773-x; citation_id=CR221
citation_journal_title=Phys Fluid; citation_title=Characteristics of reflected gas molecules at a solid surface; citation_author=K Yamamoto, H Takeuchi, T Hyakutake; citation_volume=18; citation_publication_date=2006; citation_pages=046103; citation_doi=10.1063/1.2191871; citation_id=CR222
citation_journal_title=Int J Heat Mass Transf; citation_title=Calculation of Knudsen layers and jump conditions using the linearised G13 and R13 moment methods; citation_author=JB Young; citation_volume=54; citation_publication_date=2011; citation_pages=2902-2912; citation_doi=10.1016/j.ijheatmasstransfer.2011.03.009; citation_id=CR223
citation_journal_title=Phys Rev E; citation_title=Hydrodynamics beyond Navier–Stokes: the slip flow model; citation_author=WP Yudistiawan, S Ansumali, IV Karlin; citation_volume=78; citation_publication_date=2008; citation_pages=016705; citation_doi=10.1103/PhysRevE.78.016705; citation_id=CR224
citation_journal_title=Mech Res Commun; citation_title=New velocity-slip and temperature-jump boundary conditions for Navier–Stokes computation of gas mixture flows in microgeometries; citation_author=I Zahmatkesh, MM Alishahi, H Emdad; citation_volume=38; citation_publication_date=2011; citation_pages=417-424; citation_doi=10.1016/j.mechrescom.2011.06.001; citation_id=CR225
citation_journal_title=Microfluid Nanofluid; citation_title=Lattice Boltzmann method for microfluidics: models and applications; citation_author=J Zhang; citation_volume=10; citation_publication_date=2011; citation_pages=1-28; citation_doi=10.1007/s10404-010-0624-1; citation_id=CR226
citation_journal_title=IEEE/ASME Trans Mechatron; citation_title=Property analysis of the rough slider bearings in micromotors for MEMS applications; citation_author=WM Zhang, G Meng; citation_volume=14; citation_publication_date=2009; citation_pages=465-473; citation_doi=10.1109/TMECH.2009.2023442; citation_id=CR227
citation_journal_title=Phys Rev E; citation_title=Capturing Knudsen layer phenomena using a lattice Boltzmann model; citation_author=YH Zhang, XJ Gu, RW Barber, DR Emerson; citation_volume=74; citation_publication_date=2006; citation_pages=046704; citation_doi=10.1103/PhysRevE.74.046704; citation_id=CR228
citation_journal_title=Phys Rev E; citation_title=Efficient kinetic method for fluid simulation beyond the Navier–Stokes equation; citation_author=R Zhang, X Shan, H Chen; citation_volume=74; citation_publication_date=2006; citation_pages=046703; citation_doi=10.1103/PhysRevE.74.046703; citation_id=CR229
citation_journal_title=Microsys Technol; citation_title=Slip model for the molecular gas film lubrication of the slider bearing in a micromotor; citation_author=WM Zhang, G Meng, JB Zhou, JY Chen; citation_volume=15; citation_publication_date=2009; citation_pages=953-961; citation_doi=10.1007/s00542-009-0828-z; citation_id=CR230
citation_journal_title=Phys Rev E; citation_title=Corrected second-order slip boundary condition for fluid flows in nanochannels; citation_author=HW Zhang, ZQ Zhang, YG Zheng, HF Ye; citation_volume=81; citation_publication_date=2010; citation_pages=066303; citation_doi=10.1103/PhysRevE.81.066303; citation_id=CR231
citation_journal_title=Micro Nano Lett; citation_title=Random surface roughness effect on slider microbearing lubrication; citation_author=WM Zhang, G Meng, ZK Peng; citation_volume=5; citation_publication_date=2010; citation_pages=347-350; citation_doi=10.1049/mnl.2010.0141; citation_id=CR232
citation_journal_title=Tribol Int; citation_title=Performance and stability analysis of gas-lubricated journal bearings in MEMS; citation_author=WM Zhang, JB Zhou, G Meng; citation_volume=44; citation_publication_date=2011; citation_pages=887-897; citation_doi=10.1016/j.triboint.2011.03.004; citation_id=CR233
citation_journal_title=Microfluid Nanofluid; citation_title=Molecular dynamics-based prediction of boundary slip of fluids in nanochannels; citation_author=HW Zhang, ZQ Zhang, YG Zheng, HF Ye; citation_volume=12; citation_publication_date=2012; citation_pages=107-115; citation_doi=10.1007/s10404-011-0853-y; citation_id=CR234
citation_journal_title=Tribol Trans; citation_title=Numerical prediction of surface roughness effect on slip flow in gas-lubricated journal microbearings; citation_author=WM Zhang, G Meng, KX Wei; citation_volume=55; citation_publication_date=2012; citation_pages=71-76; citation_doi=10.1080/10402004.2011.599510; citation_id=CR235
Zheng Y, Reese JM, Scanlon TJ, Lockerby DA (2006) Scaled Navier-Stokes-Fourier equations for gas flow and heat transfer phenomena in micro- and nanosystems. In: Proceedings of ASME ICNMM2006, June 19–21, Limerick, Ireland 96066
citation_journal_title=AIAA J; citation_title=Stabilization of the Burnett equations and application to hypersonic flows; citation_author=X Zhong, RW MacCormack, DR Chapman; citation_volume=31; citation_publication_date=1993; citation_pages=1036-1043; citation_doi=10.2514/3.11726; citation_id=CR237