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Rise in optimized capillary channels

Published online by Cambridge University Press:  14 August 2013

B. Figliuzzi*
Affiliation:
Department of mechanical Engineering, Massachusetts Institute of Technology, Cambridge, 77 Massachusetts Avenue, MA 02139, USA
C. R. Buie
Affiliation:
Department of mechanical Engineering, Massachusetts Institute of Technology, Cambridge, 77 Massachusetts Avenue, MA 02139, USA
*
Email address for correspondence: crb@mit.edu

Abstract

Many technological applications rely on the phenomenon of wicking flow induced by capillarity. However, despite a continuing interest in the subject, the influence of the capillary geometry on the wicking dynamics remains underexploited. In numerous applications, the ability to promote wicking in a capillary is a key issue. In this article, a model describing the capillary rise of a liquid in a capillary of varying circular cross-section is presented. The wicking dynamics is described by an ordinary differential equation with a term dependent upon the shape of the capillary channel. Using optimal control theory, we were able to design optimized capillaries which promote faster wicking than uniform cylinders. Numerical simulations show that the height of the rising liquid was up to 50 % greater with the optimized shapes than with a uniform cylinder of optimal radius. Experiments on specially designed capillaries with silicone oil show a good agreement with the theory. The methods presented can be useful in the design and optimization of systems employing capillary-driven transport including micro-heat pipes or oil extracting devices.

Type
Papers
Copyright
©2013 Cambridge University Press 

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References

Bell, J. M. & Cameron, F. K. 1906 The flow of liquids through capillary spaces. J. Phys. Chem. 10, 657674.Google Scholar
Bonnans, J., Gilbert, J., Lemaréchal, C. & Sagasetizbal, C. 2003 Numerical Optimization Theoretical and Practical Aspects. Springer.Google Scholar
Bosanquet, C. H. 1923 On the flow of liquids into capillary tubes. Phil. Mag. 45, 525531.CrossRefGoogle Scholar
De Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827863.CrossRefGoogle Scholar
De Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2003 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.Google Scholar
Digilov, R. M. 2008 Capillary rise of a non-Newtonian power law liquid: impact of the fluid rheology and dynamic contact angle. Langmuir 24, 1366313667.Google Scholar
Dussaud, A. D., Adler, P. M. & Lips, A. 2003 Liquid transport in the networked microchannels of the skin surface. Langmuir 19, 73417345.Google Scholar
Erickson, D., Li, D. & Park, C. B. 2002 Numerical simulations of capillary-driven flows in nonuniform cross-sectional capillaries. J. Colloid Interface Sci. 250 (2), 422430.Google Scholar
Fries, N. & Dreyer, M. 2008a An analytic solution of capillary rise restrained by gravity. J. Colloid Interface Sci. 320, 259263.CrossRefGoogle ScholarPubMed
Fries, N. & Dreyer, M. 2008b The transition from inertial to viscous flow in capillary rise. J. Colloid Interface Sci. 327, 125128.Google Scholar
Higuera, F. J., Medina, A. & Linan, A. 2008 Capillary rise of a liquid between two vertical plates making a small angle. Phys. Fluids 20, 102102.Google Scholar
Lewis, F. L., Vrabie, D. & Syrmos, V. L. 2012 Optimal Control. Wiley.Google Scholar
Lorenceau, E., Quéré, D., Ollitrault, J.-Y. & Clanet, C. 2002 Gravitational oscillations of a liquid column. Phys. Fluids 14, 19851992.Google Scholar
Lucas, V. R. 1918 Uber das Zeitgesetz des Kapillaren Aufstiegs von Flssigkeiten. Kolloidn. Z. 23, 1522.Google Scholar
Polzin, K. A. & Choueiri, E. Y. 2003 A similarity parameter for capillary flows. J. Phys. D 36 (24), 3156.Google Scholar
Ponomarenko, A., Quéré, D. & Clanet, C. 2011 A universal law for capillary rise in corners. J. Fluid Mech. 666, 146154.Google Scholar
Princen, H. M. 1969 Capillary phenomena in assemblies of parallel cylinders: I. Capillary rise between two cylinders. J. Colloid Interface Sci. 30 (1), 6975.CrossRefGoogle Scholar
Quéré, D. 1997 Inertial capillary. Europhys. Lett. 39, 533538.Google Scholar
Quéré, D., Raphael, E. & Ollitrault, J.-Y. 1999 Rebounds in a capillary tube. Langmuir 15, 36793682.Google Scholar
Reyssat, M., Courbin, L., Reyssat, E. & Stone, H. A. 2008 Imbibition in geometries with axial variations. J. Fluid Mech. 615, 335344.Google Scholar
Romero, L. A. & Yost, F. G. 1996 Flow in an open channel capillary. J. Fluid Mech. 322, 109129.Google Scholar
Rye, R. R., Mann, J. A. & Yost, F. G. 1996 The flow of liquids in surface grooves. Langmuir 12, 555565.CrossRefGoogle Scholar
Sobhan, C. B., Rag, R. L. & Peterson, G. P. 2007 A review and comparative study of the investigations on micro heat pipes. Intl J. Energy Res. 31 (6–7), 664688.CrossRefGoogle Scholar
Stange, M., Dreyer, M. E. & Rath, H. J. 2003 Capillary driven flow in circular cylindrical tubes. Phys. Fluids 15, 25872601.CrossRefGoogle Scholar
Staples, T. L. & Shaffer, D. G. 2002 Wicking flow in irregular capillaries. Colloids Surf. A 204 (1–3), 239250.Google Scholar
Suman, B. & Kumar, P. 2005 An analytical model for fluid flow and heat transfer in a micro-heat pipe of polygonal shape. Intl J. Heat Mass Transfer 48 (21), 44984509.Google Scholar
Szekely, J., Neumann, A. W. & Chuang, Y. K. 1971 The rate of capillary penetration and the applicability of the Washburn equation. J. Colloid Interface Sci. 35, 273278.CrossRefGoogle Scholar
Warren, P. B. 2004 Late stage kinetics for various wicking and spreading problems. Phys. Rev. E 69, 041601.Google Scholar
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273283.Google Scholar
Weislogel, M. M. & Litcher, S. 1998 Capillary flow in an interior corner. J. Fluid Mech. 373, 349378.Google Scholar
Weislogel, M. M., Thomas, E. A. & Graf, J. C. 2009 A novel device addressing design challenges for passive fluid phase separations aboard spacecraft. Microgravity Sci. Technol. 21 (3), 257268.CrossRefGoogle Scholar
Young, W.-B. 2004 Analysis of capillary flows in non-uniform cross-sectional capillaries. Colloids Surf. A 234, 123128.CrossRefGoogle Scholar
Zhang, J., Watson, S. J. & Wong, H. 2007 Fluid flow and heat transfer in a dual-wet micro heat pipe. J. Fluid Mech. 589, 132.CrossRefGoogle Scholar
Zhmud, B. V., Tiberg, F. & Hallstensson, K. 2000 Dynamics of capillary rise. J. Colloid Interface Sci. 228, 263269.CrossRefGoogle ScholarPubMed