Abstract
In this chapter, fundamentals of fluid flow and flow modelling aspects in the slip regime have been presented. This includes a brief introduction to the Navier–Stokes equations and the slip boundary condition. A few analytical solutions for flow in the slip regime are then obtained. Finally, we briefly examine the flow in some complex passages and present some useful empirical correlations. These solutions and insights help appreciate the flow physics in the slip regime better.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Acosta R, Muller R, Tobias C (1985) Transport processes in narrow (capillary) channels. AIChE J 31(3):473–482
Agrawal A, Prabhu SV (2008) Deduction of slip coefficient in slip and transition regimes from existing cylindrical Couette flow data. Exp Thermal Fluid Sci 32(4):991–996
Agrawal A, Prabhu SV (2008) Survey on measurement of tangential momentum accommodation coefficient. J Vac Sci Technol A 26(4):634–645
Agrawal A, Djenidi L, Agrawal A (2009) Simulation of gas flow in microchannels with a single 90∘ bend. Comput Fluids 38(8):1629–1637
Albertoni S, Cercignani C, Gotusso L (1963) Numerical evaluation of the slip coefficient. Phys Fluids 6(7):993–996
Arkilic E, Schmidt M, Breuer K (1997) Gaseous slip flow in long microchannels. J Microelectromech Syst 6(2):167–178
Arkilic EB, Breuer KS, Schmidt MA (2001) Mass flow and tangential momentum accommodation in silicon micromachined channels. J Fluid Mech 437:29–43
Barber RW, Emerson DR (2001) A numerical investigation of low Reynolds number gaseous slip flow at the entrance of circular and parallel plate micro-channels. In: ECCOMAS computational fluid dynamics conference, Swansea, Wales
Bentz JA, Tompson R, Loyalka S (1997) The spinning rotor gauge: measurements of viscosity, velocity slip coefficients, and tangential momentum accommodation coefficients for N2 and CH4. Vacuum 48(10):817–824
Cercignani C, Daneri A (1963) Flow of a rarefied gas between two parallel plates. J Appl Phys 34(12):3509–3513
Cercignani C, Lampis M, Lorenzani S (2004) Variational approach to gas flows in microchannels. Phys Fluids 16:3426–3437
Chapman S, Cowling TG (1970) The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction and diffusion in gases. Cambridge University Press, Cambridge
Chen RY (1973) Flow in the entrance region at low Reynolds numbers. J Fluids Eng 95(1):153–158
Chen S, Tian Z (2009) Simulation of microchannel flow using the lattice Boltzmann method. Phys A Stat Mech Appl 388(23):4803–4810
Choi S (1991) Fluid flow and heat transfer in microtubes. Micromechanical sensors, actuators, and systems. ASME, New York, pp 123–134
Colin S, Lalonde P, Caen R (2004) Validation of a second-order slip flow model in rectangular microchannels. Heat Transf Eng 25(3):23–30
Deissler R (1964) An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases. Int J Heat Mass Transf 7(6):681–694
Demsis A, Prabhu SV, Agrawal A (2010) Influence of wall conditions on friction factor for flow of gases under slip condition. Exp Thermal Fluid Sci 34(8):1448–1455
Dombrowski N, Foumeny E, Ookawara S, Riza A (1993) The influence of Reynolds number on the entry length and pressure drop for laminar pipe flow. Can J Chem Eng 71(3):472–476
Dongari N, Agrawal A, Agrawal A (2007) Analytical solution of gaseous slip flow in long microchannels. Int J Heat Mass Transf 50(17):3411–3421
Duan Z (2012) Second-order gaseous slip flow models in long circular and noncircular microchannels and nanochannels. Microfluid Nanofluid 12(5):805–820
Duan Z, Muzychka Y (2010) Slip flow in the hydrodynamic entrance region of circular and noncircular microchannels. J Fluids Eng 132(1):011201
Durst F, Ray S, Ünsal B, Bayoumi O (2005) The development lengths of laminar pipe and channel flows. J Fluids Eng 127(6):1154–1160
Duryodhan VS, Singh SG, Agrawal A (2013) Liquid flow through a diverging microchannel. Microfluid Nanofluid 14(1–2):53–67
Duryodhan VS, Singh SG, Agrawal A (2017) Effect of cross aspect ratio on flow in diverging and converging microchannels. J Fluids Eng 139(6):061203
Ewart T, Perrier P, Graur IA, Méolans JG (2007) Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes. J Fluid Mech 584:337–356
Ewart T, Perrier P, Graur IA, Méolans JG (2007) Tangential momentum accommodation in microtube. Microfluid Nanofluid 3(6):689–695
Fan H, Xue Q (2000) A new analytic solution of the Navier–Stokes equations for microchannel flows. Microscale Thermophys Eng 4(2):125–143
Gad-el Hak M (1999) The fluid mechanics of microdevices—the Freeman scholar lecture. J Fluids Eng 121(1):5–33
Gavasane A, Sachdev SS, Mittal BK, Bhandarkar UV, Agrawal A (2011) A critical assessment of the Maxwell slip boundary condition for rarefied wall bounded flows. Int J Micro-Nano Scale Transp 2:109–116
Graur I, Veltzke T, Méolans J, Ho M, Thöming J (2015) The gas flow diode effect: theoretical and experimental analysis of moderately rarefied gas flows through a microchannel with varying cross section. Microfluid Nanofluid 18(3):391–402
Gu XJ, Emerson DR, Tang GH (2009) Kramer’s problem and the Knudsen minimum: a theoretical analysis using a linearized 26-moment approach. Contin Mech Thermodyn 21(5):345
Hemadri V, Varade VV, Agrawal A, Bhandarkar UV (2016) Investigation of rarefied gas flow in microchannels of non-uniform cross section. Phys Fluids 28(2):022007
Hemadri V, Varade VV, Agrawal A, Bhandarkar UV (2017) Rarefied gas flow in converging microchannel in slip and early transition regimes. Phys Fluids 29:032002.
Hemadri V, Agrawal A, Bhandarkar UV (2018) Determination of tangential momentum accommodation coefficient and slip coefficients for rarefied gas flow in a microchannel. Sādhanā 43(10):164
Hsia YT, Domoto G (1983) An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances. J Lubr Technol 105(1):120–129
Jang J, Wereley ST (2006) Gaseous slip flow analysis of a micromachined flow sensor for ultra small flow applications. J Micromech Microeng 17(2):229
Jie D, Diao X, Cheong KB, Yong LK (2000) Navier–Stokes simulations of gas flow in micro devices. J Micromech Microeng 10(3):372
Karniadakis GE, Beskok A, Aluru N (2006) Microflows and nanoflows: fundamentals and simulation, vol 29. Springer, Berlin
Kennard EH (1938) Kinetic theory of gases with an introduction to statistical mechanics. McGraw-Hill, New York
Lihnaropoulos J, Valougeorgis D (2011) Unsteady vacuum gas flow in cylindrical tubes. Fusion Eng Des 86(9–11):2139–2142
Lockerby DA, Reese JM, Emerson DR, Barber RW (2004) Velocity boundary condition at solid walls in rarefied gas calculations. Phys Rev E 70(1):017303
Loyalka S (1996) Theory of the spinning rotor gauge in the slip regime. J Vac Sci Technol A 14(5):2940–2945
Maurer J, Tabeling P, Joseph P, Willaime H (2003) Second-order slip laws in microchannels for helium and nitrogen. Phys Fluids 15(9):2613–2621
Maxwell JC (1879) On stresses in rarified gases arising from inequalities of temperature. Philos Trans R Soc Lond A 170:231–256
Mitsuya Y (1993) Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient. J Tribol 115:289–289
Morini GL, Spiga M, Tartarini P (2004) The rarefaction effect on the friction factor of gas flow in microchannels. Superlattices Microstruct 35(3):587–599
Muralidhar K, Biswas G (2005) Advanced engineering fluid mechanics. Narosa Publishing House, New Delhi
Niazmand H, Renksizbulut M, Saeedi E (2008) Developing slip-flow and heat transfer in trapezoidal microchannels. Int J Heat Mass Transf 51(25–26):6126–6135
Panigrahi PK (2016) Transport phenomena in microfluidic systems. Wiley, New York
Pfahler J, Harley J, Bau H, Zemel JN (1991) Gas and liquid flow in small channels. Am Soc Mech Eng Dyn Syst Control Div 32:49–60
Pollard W, Present RD (1948) On gaseous self-diffusion in long capillary tubes. Phys Rev 73(7):762
Pong K, Ho CM, Liu J, Tai YC (1994) Non-linear pressure distribution in uniform microchannels. In: Proceedings of application of microfabrication to fluid mechanics, ASME Winter annual meeting, Chicago, pp 51–56
Porodnov B, Suetin P, Borisov S, Akinshin V (1974) Experimental investigation of rarefied gas flow in different channels. J Fluid Mech 64(3):417–438
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
Schlichting H (1960) Boundary layer theory. McGraw-Hill, New York
Sharipov F, Graur I (2014) General approach to transient flows of rarefied gases through long capillaries. Vacuum 100:22–25
Sreekanth A (1969) Slip flow through long circular tubes. In: Trilling L, Wachman HY (eds) Proceedings of the sixth international symposium on rarefied gas dynamics. Academic Press, New York, pp 667–680
Steckelmacher W (1986) Knudsen flow 75 years on: the current state of the art for flow of rarefied gases in tubes and systems. Rep Prog Phys 49(10):1083
Stemme E, Stemme G (1993) A valveless diffuser/nozzle-based fluid pump. Sens. Actuators A 39(2):159–167
Suetin P, Porodnov B, Chernjak V, Borisov S (1973) Poiseuille flow at arbitrary Knudsen numbers and tangential momentum accommodation. J Fluid Mech 60(3):581–592
Tang G, Li Z, He Y, Tao W (2007) Experimental study of compressibility, roughness and rarefaction influences on microchannel flow. Int J Heat Mass Transf 50(11–12):2282–2295
Tekasakul P, Bentz J, Tompson R, Loyalka S (1996) The spinning rotor gauge: measurements of viscosity, velocity slip coefficients, and tangential momentum accommodation coefficients. J Vac Sci Technol A 14(5):2946–2952
Turner SE, Sun H, Faghri M, Gregory OJ (1999) Local pressure measurement of gaseous flow through microchannels. ASME-Publications-HTD 364:71–80
Varade V, Agrawal A, Pradeep AM (2014) Behaviour of rarefied gas flow near the junction of a suddenly expanding tube. J Fluid Mech 739:363–391
Varade V, Agrawal A, Pradeep AM (2014) Experimental study of rarefied gas flow near sudden contraction junction of a tube. Phys Fluids 26(6):062002
Varade V, Agrawal A, Prabhu SV, Pradeep AM (2015) Early onset of flow separation with rarefied gas flowing in a 90∘ bend tube. Exp Thermal Fluid Sci 66:221–234
Veltzke T, Baune M, Thöming J (2012) The contribution of diffusion to gas microflow: an experimental study. Phys Fluids 24(8):082004
Verma B, Demsis A, Agrawal A, Prabhu SV (2009) Semiempirical correlation for the friction factor of gas flowing through smooth microtubes. J Vac Sci Technol A 27(3):584–590
White C, Borg MK, Scanlon TJ, Reese JM (2013) A DSMC investigation of gas flows in micro-channels with bends. Comput Fluids 71:261–271
Wu L (2008) A slip model for rarefied gas flows at arbitrary Knudsen number. Appl Phys Lett 93(25):253103
Wu P, Little W (1984) Measurement of the heat transfer characteristics of gas flow in fine channel heat exchangers used for microminiature refrigerators. Cryogenics 24(8):415–420
Yamaguchi H, Hanawa T, Yamamoto O, Matsuda Y, Egami Y, Niimi T (2011) Experimental measurement on tangential momentum accommodation coefficient in a single microtube. Microfluid Nanofluid 11(1):57–64
Yu D (1995) An experimental and theoretical investigation of fluid flow and heat transfer in microtubes. In: ASME/JSME thermal engineering conference, vol 1
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Agrawal, A., Kushwaha, H.M., Jadhav, R.S. (2020). Microscale Flows. In: Microscale Flow and Heat Transfer. Mechanical Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-030-10662-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-10662-1_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10661-4
Online ISBN: 978-3-030-10662-1
eBook Packages: EngineeringEngineering (R0)