Zusammenfassung
Das Kapitel Mikroströmungen behandelt Strömungen durch sehr kleine Kanäle und um sehr kleine Objekte und ist Teil des Lehrbuches und Nachschlagewerkes H. Oertel jr. Prandtl-Führer durch die Strömungslehre. Nach einigen exemplarischen Anwendungen der Mikroströmungen, werden für Gase und Flüssigkeiten separat die Grenzen der kontinuumsmechanischen Behandlung diskutiert. Molekulare und Kontinuums-Modelle werden zusammen mit den adäquaten Randbedingungen für Mikroströmungen erläutert.
Weitergehend werden aus einer Ähnlichkeitsdiskussion die Konsequenzen der Verkleinerung abgeleitet und spezielle Effekte wie die Elektrokinetik, die (dynamische) Benetzung und dünne Filme abgehandelt. Schließlich wird der Stand der Literatur zum Druckverlust, zur laminar-turbulenten Transition und zum Wärmeübergang in Mikrorohren dargestellt.
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Weiterführende Literatur
Abraham, F.F.: The interfacial density profile of a lennard-jones fluid in contact with a (100) Lennard-Jones wall and its relationship to idealized fluid/wall systems: a Monte Carlo simulation. J. Chem. Phys. 68, 3713 (1978)
Adams, T.M., Abdel-Khalik, S.I., Jeter, S.M., Qureshi, Z.H.: An experimental investigation of single-phase forced convection in microchannels. Int. J. Heat Mass Transf. 41, 851–857 (1998)
Barz, D.P.J.: Ein Beitrag zur Modellierung und Simulation elektrokinetischer Transportprozesse in mikrofluidischen Einheiten. Dissertation, Universität Karlsruhe (2005)
Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (2005)
Bird, G.A.: Molecular Gas Dynamics. Claredon Press, Oxford (1976)
Brutin, D., Topin, F., Tadrist, L.: Transient method for the liquid laminar flow friction factor in microtubes. AIChE J. 49, 2759–2767 (2003)
Burgreen, D., Nakache, F.: Electrokinetic flow in ultrafine capillary slits. J. Phys. Chem. 68, 1084–1091 (1964)
Chan, D.Y.C., Horn, R.G.: The drainage of thin liquid films between solid surfaces. J. Chem. Phys. 83, 5311–5324 (1985)
Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases. Cambridge University Press, Cambridge (1970)
Celata, G.P., Cumo, M., Marconi, V., McPhail, S.J., Zummo, G.: Microtube liquid single-phase heat transfer in laminar flow. Int. J. Heat Mass Transf. 49, 3538–3546 (2006)
Celata, G.P., Cumo, M., McPhail, S.J., Zummo, G.: Single-phase laminar and turbulent heat transfer in smooth and rough microtubes. Microfluid Nanofluid 3, 697–707 (2007)
Choi, S.B., Barron, R.F., Warrington, R.O.: Fluid flow and heat transfer in microtubes. ASME AMD-DSC 32, 123–134 (1991)
Craig, V.S.J., Neto, C., Williams, D.R.M.: Shear-dependent boundary slip in an aqueous Newtonian liquid. Phys. Rev. Lett. 87 (5), 054504 (2001)
de Gennes, P.G.: Wetting: Statistics and dynamics. Rev. Mod. Phys. 57, 827 (1985)
Debye, P., Hückel, E.: Zur Theorie der Elektrolyte. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physikalische Z. 24, 185–206 (1923)
Derzko, N.A.: Review of Monte Carlo methods in kinetic theory. UTIAS Review 35, University of Toronto (1972)
Dongqing, Li: Electrokinetics in Microfluidics. Elsevier, London (2004)
Dussan, E.B.: On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371 (1979)
Dussan, E.B., Davis, S.H.: On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 50, 977 (1974)
Fritz, G.: Über den dynamischen Randwinkel im Fall der vollständigen Benetzung. Z. Angew. Physik 19, 374 (1965)
Gad-el-Hak, M.: The fluid mechanics of microdevices – the Freeman scholar lecture. J. Fluids Engineering 121, 5–33 (1999)
Gad-el-Hak, M.: Flow physics. In: Gad-el-Hak, M. (Hrsg.) The MEMS Handbook: Introduction and Fundamentals, 2. CRC, Boca Raton (2006)
Gee, M.L., McGuiggan, P.M., Israelachvili, J.N., Homola, A.M.: Liquid to solidlike transition of molecularly thin films under shear. J. Chem. Phys. 93, 1895–1906 (1990)
Green, H.: The Structure of Liquids. S. Flügge, (Hrsg.), Handbuch der Physik, Bd. 10. Springer, Berlin (2002)
Herwig, H.: Flow and heat transfer in micro systems: is everything different or just smaller? Z. Angew. Math. Mech. 82, 579–586 (2002)
Hetsroni, G., Mosyak, A., Pogrebnyak, E., Yarin, L.P.: Fluid flow in micro-channels. Int. J. Heat Mass Transf. 48, 1982–1998 (2005a)
Hetsroni, G., Mosyak, A., Pogrebnyak, E., Yarin, L.P.: Heat transfer in micro-channels: comparison of experiments with theory and numerical results. Int. J. Heat Mass Transf. 48, 5580–5601 (2005b)
Hoffman, R.L.: A study of the advancing interface. I. Interface shape in liquid-gas system. J. Colloid Interface Sci. 50, 228 (1975)
Hunter, R.J.: Zeta Potential in Colloid Science: Principles and Applications. Accademic, London (1981)
Ivanov, M.S., Rogasinsky, S.V.: Theoretical analysis of traditional and modern schemes of the DSMC method. In: Proceedings of the 17th RGD Symposium, Bd. 1, Verlag Chemie, Aachen (1991)
Joseph, P., Tabeling, P.: Direct measurement of the apparent slip length. Phys. Rev. E 71, 035303 (2005)
Judy, J., Maynes, D., Webb, B.W.: Characterization of frictional pressure drop for liquid flows through microchannels. Int. J. Heat Mass Transf. 45, 3477–3489 (2002)
Karniadakis, G.E., Beskok, A.: Micro Flows. Fundamentals and Simulation. Springer, New York (2004)
Koplik, P.J., Banavar, J.R.: Continuum deductions from molecular hydrodynamics. Ann. Rev. Fluid Mech. 27, 257–292 (1995)
Lennard-Jones, J.E.: Cohesion. Proc. Phys. Soc. Lond. 43, 461 (1931)
Li, Z.X., Du, D.X., Guo, Z.Y.: Experimental study on flow characteristics of liquid in circular micro-tubes. Microscale Thermophys. Eng. 7 (3), 253–265 (2003)
Li, H., Yoda, M.: An experimental study of slip considering the effects of non-uniform colloidal tracer distributions. J. Fluid Mech. 662, 269–287 (2010)
Lin, T.-Y., Yang, C.-Y.: An experimental investigation on forced convection heat transfer performance in micro tubes by the method of liquid crystal thermography. Int. J. Heat Mass Transf. 50, 4736–4742 (2007)
Löfdahl, L., Gad-el-Hak, M.: Sensors and actuators for turbulent flows. In: Gad-el-Hak, M. (Hrsg.) The MEMS Handbook: Applications, 2. CRC, Boca Raton (2006)
Loose, W., Hess, S.: Rheology of dense model fluids via nonequilibrium molecular dynamics: shear thinning and ordering transition. Rheologica Acta 28, 91–101 (1989)
Maier, C.: Techniken der Hochgeschwindigkeitsmikrokinematographie zur Bewertung von Mikrodosiersystemen und Mikrotropfen. Fortschritts-Bericht 1037, VDI (2004). Dissertation Universität Ulm
Manz, A., Becker, H.: Microsystem Technology in Chemistry and Life Sciences. Springer, Berlin (1999)
Maxwell, J.: On stresses in rarefied gases arising from inequalities of temperature. Philos. Trans. R. Soc. 170 (1), 231–256 (1879)
Meisel, I., Ehrhard, P.: Electrically-excited (electroosmotic) flows in microchannels for mixing applications. Eur. J. Mech. B: Fluids 25, 491–504 (2006)
Moss, J.N., Bird, G.A.: Direct simulation of transitional flow for hypersonic reentry conditions. 84-0223, AIAA (1984)
Nanbu, K.: Numerical simulation of Boltzmann flows of real gases – accuracy of models used in the Monte Carlo method. Rep. Inst. Fluid Science 4, Tohoku University, Sendai (1992)
Oertel, H., jr.: Aerothermodynamik. Springer, Berlin/Heidelberg (1994). Universitätsverlag, Karlsruhe (2005)
Oron, A.: Physics of thin liquid films. In: Gad-el-Hak, M. (Hrsg.) The MEMS Handbook: Introduction and Fundamentals, 2. CRC, Boca Raton (2006)
Oron, A., Davis, S.H., Bankoff, S.G.: Long-scale evolution of thin liquid films. Rev. Modern Phys. 69, 931–980 (1997)
Overbeek, J.T.G.: Electrokinetic phenomena. In: Kruyt, H.R. (Hrsg.) Colloid Science, Bd. 1. Elsevier, Amsterdam (1952)
Probstein, R.F.: Physicochemical Hydrodynamics. Wiley, New York (1994)
Ramos, A., Morgan, H., Green, N.G., Castellanos, A.: AC electrokinetics: a review of forces in microelectrode structures. J. Phys. D: Appl. Phys. 31, 2338–2353 (1998)
Rice, C.L., Whitehead, R.: Electrokinetic flow in a narrow cylindrical capillary. J. Phys. Chem. 69, 4017–4024 (1965)
Rose, W., Heins, R.W.: Moving interfaces and contact angle rate-dependency. J. Colloid Sci. 17, 39 (1962)
Schaaf, S.A., Chambré, P.L.: Flow of Rarefied Gases. Princeton University Press, Princeton (1961)
Schubert, K., Brandner, J.J., Fichtner, M., Linder, G., Schygulla, U., Wenka, A.: Microstructure devices for applications in thermal and chemical process engineering. J. Microscale Thermophys. Eng. 5, 17–39 (2001)
Schwartz, A.M., Tajeda, S.B.: Studies of dynamic contact angles on solids. J. Colloid Interface Sci. 38, 359 (1972)
Sharp, K.V., Adrian, R.J.: Transition from laminar to turbulent flow in liquid filled microtubes. Exp. Fluids 36, 741–747 (2004)
Sharp, K.V., Adrian, R.J., Santiago, J.G., Molho, J.I.: Liquid flows in microchannels. In: Gad-el-Hak, M. (Hrsg.) The MEMS Handbook: Introduction and Fundamentals, 2. CRC, Boca Raton (2006)
Shih, J.C., Ho, C.-M., Liu, J., Tai, Y.-C.: Non-linear pressure distribution in uniform microchannels. ASME AMD-MD, 238 (1995)
Sobhan, C., Garimella, S.V.: A comparative analysis of studies on heat transfer and fluid flow in microchannels. J. Microscale Thermophys. Eng. 5, 293–311 (2001)
Tanner, L.H.: The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12, 1473 (1979)
Thompson, P.A., Troian, S.M.: A general boundary condition for liquid flow at solid surfaces. Nature 389, 360–362 (1997)
Tretheway, D.C., Meinhart, C.D.: Apparent fluid slip at hydrophobic microchannel walls. Phys. Fluids 14, L9–L12 (2002)
Vallet, M., Berge, B., Vovelle, L.: Electrowetting of water and aqueous solutions on Polyethylene Terephthalate insulating films. Polymer 37, 2465–2470 (1996)
Young, T.: An essay on the cohesion of fluids. Philos. Trans. R. Soc. Lond. 95, 65–87 (1805)
Yu, D., Warrington, R., Barron, R., Anieel, T.: An experimental and theoretical investigation of fluid flow and heat transfer in microtubes. In: Proceedings of the ASME/JSME Thermal Engineering Conference, Hawaii, Bd. 1, 523–530 (1995)
Zheng, S., Tai, Y.C.: Streamline based design of a MEMS device for continuous blood cell separation. In: Twelth Hilton Head Workshop on the Science and Technology of Solid-state Sensors, Actuators, and Microsystems, Hilton Head, Bd. 1 (2006)
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Ehrhard, P. (2017). Mikroströmungen. In: Oertel jr., H. (eds) Prandtl - Führer durch die Strömungslehre. Springer Reference Technik . Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-08627-5_12
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