Differences between liquid and gas transport at the microscale

• Autorzy: Gad-el-Hak M.
• Języki publikacji: EN

Abstrakty

EN

Traditional fluid mechanics edifies the indifference between liquid and gag flows as long as certain similarity parameters - most prominently the Reynolds number - are matched. This may or may not be the case for flows in nano- or microdevices. The customary continuum, Navier-Stokes modelling is ordinarily applicable for both air and water flowing in macrodevices. Even for common fluids such as air or water, such modelling bound to fail at sufficiently small scales, but the onset for such failure is different for the two forms of matter. Moreover, when the no-slip, quasi-equilibrium Navier - Stokes system is no longer applicable, the alternative modelling schemes are different for gases and liquids. For dilute gases, statistical methods are applied and the Boltzmann equation is the cornerstone of such approaches. For liquid flows, the dense nature of the matter prec1udes the use of the kinetic theory of gases, and numerically intensive molecular dynamics simulations are the only alternative rooted in first principles. The present artic1e discusses the above issues, emphasizing the differences between liquid and gag transport at the microscale and the physical phenomena unique to liquid flows in minute devices.

Słowa kluczowe

EN

liquid and gas transport; microscale

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2005
• Tom: Vol. 53, nr 4
• Strony: 301--316
• Opis fizyczny: Bibliogr. 82 poz., 7 rys.

Twórcy

autor

Gad-el-Hak M.

• Virginia Commonwealth University, Richmond, Virginia 23284-3015, USA,

Bibliografia

• [1] R.P. Feynman, “There’s plenty of room at the bottom,” in Miniaturization, ed. H.D. Gilbert, pp. 282–296, New York: Reinhold Publishing, 1961.
• [2] T.M. Squires and S.R. Quake, “Microfluidics: fluid physics at the nanoliter scale”, Rev. Mod. Phys. 77 (3), July (2005).
• [3] M. Gad-el-Hak, “The fluid mechanics of microdevices–the Freeman scholar lecture”, J. Fluids Eng. 121, 5–33 (1999).
• [4] H.A. Stone, A.D. Stroock, and A. Ajdari, “Engineering flows in small devices: microfluidics toward a lab-on-a-chip”, Annu. Rev. Fluid Mech. 36, 381–411 (2004).
• [5] M. Gad-el-Hak, ed., The MEMS Handbook, vol. I–III, Boca Raton: CRC Press, 2005.
• [6] G. Em Karniadakis, and A. Beskok, Microflows: Fundamentals and Simulation, New York: Springer-Verlag, 2002.
• [7] G.K. Batchelor, An Introduction to Fluid Dynamics, London: Cambridge University Press, 1967.
• [8] M.J. Lighthill, “Introduction. Real and ideal fluids”, in Laminar Boundary Layers, ed. L. Rosenhead, pp. 1–45. Oxford: Clarendon Press, 1963.
• [9] S. Chapman and T.G. Cowling, The Mathematical Theory of Non-Uniform Gases, third edition, London: Cambridge University Press, 1970.
• [10] G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford: Clarendon Press, 1994.
• [11] M. Knudsen, “Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren”, Annalen der Physik 28, 75–130 (1909).
• [12] S.A. Tison, “Experimental data and theoretical modelling of gas flows through metal capillary leaks”, Vacuum 44, 1171–1175 (1993).
• [13] A. Beskok and G.E. Karniadakis,W. Trimmer, “Rarefaction and compressibility effects in gas microflows”, J. Fluids Eng. 118, 448–456 (1996).
• [14] R.H. Nadolink and W.W. Haigh, “Bibliography on skin friction reduction with polymers and other boundary-layer additives”, Appl. Mech. Rev. 48, 351–459 (1995).
• [15] W. Loose and S. Hess, “Rheology of dense fluids via nonequilibrium molecular hydrodynamics: shear thinning and ordering transition”, Rheologica Acta 28, 91–101 (1989).
• [16] E.B. Dussan and S.H. Davis, “On the motion of fluid-fluid interface along a solid surface”, J. Fluid Mech. 65, 71–95 (1974).
• [17] E.B. Dussan, “The moving contact line: the slip boundary condition”, J. Fluid Mech. 77, 665–684 (1976).
• [18] E.B. Dussan, “On the spreading of liquids on solid surfaces: static and dynamic contact lines”, Annu. Rev. Fluid Mech. 11, 371–400 (1976).
• [19] P.A. Thompson and M.O. Robbins, “Simulations of contact line motion: slip and the dynamic contact angle”, Phys. Rev. Lett. 63, 766–769 (1989).
• [20] H.K. Moffatt, “Viscous and resistive eddies near a sharp corner”, J. Fluid Mech. 18, 1–18 (1964).
• [21] J. Koplik and J.R. Banavar, “Continuum deductions from molecular hydroynamics”, Annu. Rev. Fluid Mech. 27, 257–292 (1995).
• [22] J.R.A. Pearson and C.J.S. Petrie, “On melt flow instability of extruded polymers,” in Polymer Systems: Deformation and Flow, eds. R.E. Wetton, R.W. Whorlow, pp. 163–187, London: Macmillian, 1968.
• [23] S. Richardson, “On the no-slip boundary condition”, J. Fluid Mech. 59, 707–719 (1973).
• [24] M.M. Den, “Issues in viscoelastic fluid mechanics”, Annu. Rev. Fluid Mech. 22, 13–34 (1990).
• [25] M.M. Den, “Extrusion instabilities and wall slip”, Annu. Rev. Fluid Mech. 33, 265–287 (2001).
• [26] E. Lauga, M.P. Brenner, H.A. Stone, “Microfluidics: the no-slip boundary condition”, in Handbook of Experimental Fluid Dynamics, eds. J. Foss, C. Tropea, A. Yarin, New York: Springer, 2005.
• [27] J. Pfahler, J. Harley, H.H. Bau, J.N. Zemel, “Liquid transport in micron and submicron channels”, Sensors & Actuators 21–23, 431–434 (1990).
• [28] J. Pfahler, J. Harley, H.H. Bau and J.N. Zemel, “Gas and liquid flow in small channels,” in Symp. on Micromechanical Systems, Sensors, and Actuators, eds. D. Cho, R. Warrington, A. Pisano, H.H. Bau, C. Friedrich, J. Jara-Almonte, J. Liburdy, ASME DSC- 32, 49–60, 1991. J. Pfahler, “Liquid transport in micron and submicron size channels,” Ph.D. Thesis, University of Pennsylvania, Philadelphia, Pennsylvania, 1992.
• [29] H.H. Bau, “Transport processes associated with microdevices”, Thermal Sci. Eng. 2, 172–178 (1994).
• [30] J.N. Israelachvili, “Measurement of the viscosity of liquids in very thin films”, J. Colloid Interface Sci. 110, 263–271 (1986).
• [31] M.L. Gee, P.M. McGuiggan, J.N. Israelachvili, and A.M. Homola, “Liquid to solidlike transitions of molecularly thin films under shear”, J. Chemical Phys. 93, 1895–1906 (1990).
• [32] D.Y.C. Chan and R.G. Horn, “Drainage of thin liquid films”, J. Chemical Phys. 83, 5311–5324 (1985).
• [33] N.P. Migun and P.P. Prokhorenko, “Measurement of the viscosity of polar liquids in microcapillaries”, Colloid J. of the USSR 49, 894–897 (1987).
• [34] P. Debye and R.L. Cleland, “Flow of liquid hydrocarbons in porous Vycor”, J. Appl. Phys. 30, 843–849 (1959).
• [35] J.L. Anderson and J.A. Quinn, “Ionic mobility in microcapillaries”, J. Chemical Phys. 27, 1208–1209 (1972).
• [36] D.B. Tuckermann and R.F.W. Pease, “High-performance heat sinking for VLSI”, IEEE Electron Device Lett. EDL-2, 126–129 (1981).
• [37] D.B. Tuckermann, and R.F.W. Pease, “Optimized convective cooling using micromachined structures”, J. Electrochemical Soc. 129, C98, March (1982).
• [38] D.B. Tuckermann, “Heat transfer microstructures for integrated circuits,” Ph.D. Thesis, Stanford University, Palo Alto, California, 1984.
• [39] M.G. Guvenc, “V-groove capillary for low flow control and measurement,” in Micromachining and Micropackaging of Transducers, eds. C.D. Fung, P.W. Cheung, W.H. Ko, D.G. Fleming, pp. 215–223, Amsterdam: Elsevier, 1985.
• [40] S. Nakagawa, S. Shoji, and M. Esashi, “A micro-chemical analyzing system integrated on silicon chip,” in Proc. IEEE: Micro Electro Mechanical Systems, Napa Valley, California, IEEE 90CH2832–4, New York: IEEE, 1990.
• [41] K.V. Sharp, “Experimental investigation of liquid and particleladen flows in microtubes,” Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2001.
• [42] K.V. Sharp, R.J. Adrian, J.G. Santiago, and J.I. Molho, “Liquid flow in microchannels,” in The Handbook of MEMS, vol. I, ed. M. Gad-el-Hak, chapter 10, Boca Raton: CRC Press, 2005.
• [43] B.J. Alder and T.E. Wainwright, “Studies in molecular dynamics”, J. Chemical Phys. 27, 1208–1209 (1957).
• [44] B.J.AlderandT.E.Wainwright, “Moleculardynamicsbyelectronic computers”, in Transport Processes in Statistical Mechanics, ed. I. Prigogine, pp. 97–131, New York: Interscience, 1958.
• [45] B.J. Alder and T.E. Wainwright, “Decay of the velocity autocorrelation function”, Phys. Rev. A 1, 18–21 (1970).
• [46] G. Ciccotti,W.G. Hoover, eds, Molecular Dynamics Simulation of Statistical Mechanics Systems, Amsterdam: North Holland, 1986.
• [47] M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, Oxford: Clarendon Press, 1987.
• [48] J.M. Haile, Molecular Dynamics Simulation: Elementary Methods, New York: Wiley, 1993.
• [49] P.A. Thompson and S.M. Troian, “A general boundary condition for liquid flow at solid surfaces”, Nature 389, 360–362 (1997).
• [50] C.L.M.H. Navier, “Mémoire sur les lois du mouvement des fluides”, Mémoires de l’Académie Royale des Sciences de l’Institute de France 6, 389 (1823).
• [51] B.T. Atwood and W.R. Schowalter, “Measurements of slip at the wall during flow of high-density polyethylene through a rectangular conduit”. Rheologica Acta 28, 134–146 (1989).
• [52] F.F. Abraham, J.Q. Broughton, N. Bernstein and E. Kaxiras, “Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture”, Europhys. Lett. 44, 783–787 (1998).
• [53] V.B. Shenoy, R. Miller, E.B. Tadmor, D. Rodney, R. Phillips, and M. Ortiz, “An adaptive finite element approach to atomicscale mechanics – the quasicontinuum method”, J. Mech. Phys. Solids 47, 611–642 (1999).
• [54] R.E. Rudd and J.Q. Broughton, “Concurrent coupling of length scales in solid state systems”, Phys. Status Solidi B 217, 251–291 (2000).
• [55] D.C. Wadsworth and D.A. Erwin, “One-dimensional hybrid continuum/particle simulation approach for rarefied hypersonic flows”, AIAA Paper Number 90–1690, 1990.
• [56] D. Hash and H. Hassan, “A decoupled DSMC/Navier-Stokes analysis of a transitional flow experiment”, AIAA Paper Number 96–353, 1996.
• [57] J. Bourgat, P. Le Tallec, and M. Tidriri, “Coupling Boltzmann and Navier-Stokes equations by friction”, J. Comput. Phys. 127, 227–245 (1996).
• [58] B.J. Alder, “Highly discretized dynamics”, Physica A 240, 193–195 (1997).
• [59] P. Le Tallec and F. Mallinger, “Coupling Boltzmann and Navier- Stokes equations by half fluxes”, J. Comput. Phys. 136, 51–67 (1997).
• [60] S. Tiwari and A. Klar, “Coupling of the Boltzmann and Euler equations with adaptive domain decomposition procedure”, J. Comput. Phys. 144, 710–726 (1998).
• [61] A.L. Garcia, J. Bell,W.Y. Crutchfield, and B.J. Alder, “Adaptive mesh and algorithm refinement using direct simulation Monte Carlo”, J. Comput. Phys. 154, 134–155 (1999).
• [62] O. Aktas and N.R. Aluru, “A combined continuum/DSMC technique for multiscale analysis of microfluidic filters”, J. Comput. Phys. 178, 342–372 (2002).
• [63] R. Roveda, D.B. Goldstein and P.L. Varghese, “Hybrid Euler/ direct simulation Monte Carlo calculation of unsteady slit flow”, J. Spacecr. Rockets 37, 753–760 (2000).
• [64] S.T. O’Connell, and P.A. Thompson, “Molecular dynamicscontinuum hybrid computations: a tool for studying complex fluid flows”, Phys. Rev. E 52, R5792–R5795 (1995).
• [65] J. Li, D. Liao, and S. Yip, “Coupling continuum to moleculardynamics simulation: reflecting particle method and the field estimator”, Phys. Rev. E 57, 7259–7267 (1998).
• [66] N.G. Hadjiconstantinou, “Hybrid atomistic-continuum formulations and the moving contact-line problem”, J. Comput. Phys. 154, 245–265 (1999).
• [67] E.G. Flekkoy, G.Wagner, and J. Feder, “Hybrid model for combined particle and continuum dynamics”, Europhys. Lett. 52, 271–276 (2000).
• [68] H.S. Wijesinghe and N.G. Hadjiconstantinou, “Discussion of hybrid atomistic-continuum methods for multiscale hydrodynamics”, Int. J. Multiscale Comput. Eng. 2, 189–202 (2004).
• [69] H.S. Wijesinghe, R.D. Hornung, A.L. Garcia, and N.G. Hadjiconstantinou, “Three-dimensional hybrid continuum-atomistic simulations for multiscale hydrodynamics”, J. Fluids Eng. 126, 768–777 (2004).
• [70] T. Werder, J.H. Walther, and P. Koumoutsakos, “Hybrid atomistic-continuum method for the simulation of dense fluid flows”, J. Comput. Phys. 205, 373–390 (2005).
• [71] L.L. Baker and N.G. Hadjiconstantinou, “Variance reduction for Monte Carlo solutions of the Boltzmann equation”, Phys. Fluids, (2005), (to be published).
• [72] E. Lauga and H.A. Stone, “Effective slip in pressure-driven Stokes flow”, J. Fluid Mech. 489, 55–77 (2003).
• [73] F.W. Went, “The size of man”, American Scientist 56, 400–413 (1968).
• [74] W.C. Tang, T.-C. Nguyen, and R.T. Howe, “Laterally driven polysilicon resonant microstructures”, Sensors & Actuators 20, 25–32 (1989).
• [75] C. Mastrangelo, and C.H. Hsu, “A simple experimental technique for the measurement of the work of adhesion of microstructures,” Technical Digest IEEE Solid-State Sensors and Actuators Workshop, pp. 208–212, New York: IEEE, 1992.
• [76] L.-S. Fan, Y.-C. Tai, and R.S. Muller, “Integrated movable micromechanical structures for sensors and actuators”, IEEE Transactions on Electronic Devices 35, 724–730 (1988).
• [77] L.-S. Fan, Y.-C. Tai, and R.S. Muller, “IC-processed electrostatic micromotors”, Sensors & Actuators 20, 41–47 (1989).
• 78] Y.-C. Tai, and R.S. Muller, “IC-processed electrostatic synchronous micromotors”, Sensors&Actuators 20, 49–55 (1989).
• [79] S. Brunauer, Physical Adsorption of Gases and Vapours, London: Oxford University Press, 1944.
• [80] A. Majumdar and I. Mezic, “Stability regimes of thin liquid films”, Microscale Thermophys. Eng. 2, 203–213 (1998).
• [81] A. Majumdar and I. Mezic, “Instability of ultra-thin water films and the mechanism of droplet formation on hydrophilic surfaces”, J. Heat Transfer 121, 964–971 (1999).
• [82] J.N. Israelachvili, Intermolecular and Surface Forces, New York: Academic Press, 1991.