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Quasi-steady capillarity-driven flows in slender containers with interior edges

Published online by Cambridge University Press:  23 September 2011

Mark M. Weislogel ,
J. Alex Baker  and
Ryan M. Jenson
Mark M. Weislogel*
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, PO Box 751, Portland, OR 97207, USA
J. Alex Baker
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, PO Box 751, Portland, OR 97207, USA
Ryan M. Jenson
Affiliation:
Department of Mechanical and Materials Engineering, Portland State University, PO Box 751, Portland, OR 97207, USA
*
†Email address for correspondence: mmw@cecs.pdx.edu
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Abstract

In the absence of significant body forces the passive manipulation of fluid interfacial flows is naturally achieved by control of the specific geometry and wetting properties of the system. Numerous ‘microfluidic’ systems on Earth and ‘macrofluidic’ systems aboard spacecraft routinely exploit such methods and the term ‘capillary fluidics’ is used to describe both length-scale limits. In this work a collection of analytic solutions is offered for passive and weakly forced flows where a bulk capillary liquid is slowly drained or supplied by a faster capillary flow along at least one interior edge of the container. The solutions are enabled by an assumed known pressure (or known height) dynamical boundary condition. Following a series of assumptions this boundary condition can be in part determined a priori from the container dimensions and further quantitative experimental evidence, but not proof, is provided in support of its expanded use herein. In general, a small parameter arises in the scaling of the problems permitting a decoupling of the edge flow from the global bulk meniscus flow. The quasi-steady asymptotic system of equations that results may then be easily solved in closed form for a useful variety of geometries including uniform and tapered sections possessing at least one critically wetted interior edge. Draining, filling, bubble displacement and other imbibing flows are studied. Cursory terrestrial and drop tower experiments agree well with the solutions. The solutions are valued for the facility they provide in computing designs for selected capillary fluidics problems by way of passive transport rates and meniscus displacement. Because geometric permutations of any given design are myriad, such analytic tools are capable of efficiently identifying and comparing critical design criteria (i.e. shape and size) and the impact of various wetting conditions resulting from the fluid properties and surface conditions. Sample optimizations are performed to demonstrate the utility of the method.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Lubrication theory Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 685 , 25 October 2011 , pp. 271 - 305
Copyright
Copyright © Cambridge University Press 2011

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References

1. Akhtara, N., Qureshib, A., Scholtaa, J., Hartniga, C., Messerschmidta, M. & Lehnerta, W. 2009 Investigation of water droplet kinetics and optimization of channel geometry for pem fuel cell cathodes. Intl J. Hydrogen Energy 34 (3), 3104–3111.CrossRefGoogle Scholar
2. Ayyaswamy, P. S., Catton, I. & Edwards, D. K. 1974 Capillary flow in triangular grooves. J. Appl. Mech. 41 (4b), 332.CrossRefGoogle Scholar
3. Bankoff, S. G. 1957 Ebullition from solid surfaces in the absence of a pre-existing gaseous phase. Trans. ASME 79, 735–740.Google Scholar
4. Bico, J. & Quéré, D. 2002 Rise of liquids and bubble in angular capillary tubes. J. Colloid Interface Sci. 247, 162–166.CrossRefGoogle ScholarPubMed
5. Blackmore, W., Weislogel, M. M., Chen, Y., Bunnell, C. T., Kiewidt, L. & Klatte, J. The Capillary Flow Experiments (CFE-2) aboard the ISS: Status. AIAA Paper 2011-1196, pp. 1–10. 49th AIAA Aerospace Sciences Meeting, Jan. 2011.CrossRefGoogle Scholar
6. Bolleddula, D. 2007 Capillary flow analysis and computation of dewetting and wetting resistances in angular geometries. Master’s thesis, Portland State University.Google Scholar
7. Chato, D. J. 2008 Cryogenic fluid transfer for exploration. Tech Rep. TM-215286, Lewis Research Center, Cleveland, OH.Google Scholar
8. Chato, D. J. & Martin, T. A. 2006 Vented tank resupply experiment: flight test results. J. Spacecr. Rockets 3, 5.Google Scholar
9. Chen, Y., Weislogel, M. M. & Nardin, C. 2006 Capillary-driven flows along rounded interior corners. J. Fluid Mech. 566, 235–271.CrossRefGoogle Scholar
10. Chernous’ko, F. L. 1968 Introduction to the Dynamics of a Body Containing a Liquid Under Zero-Gravity Conditions. Computing Center of the Academy of Sciences of the USSR (in Russian). Vychislitel’nyi Tsentr Akad. SSSR. The problem of equilibrium of a fluid subject to forces of gravity and surface tension. [translated for author M.M.W. by Lev A. Slobozhanin].Google Scholar
11. Collicott, S. H. & Weislogel, M. M. 2004 Computation of capillary instabilities using surface evolver. AIAA J. 42 (2), 289–295.CrossRefGoogle Scholar
12. Collier, J. 1972 Convection Boiling and Condensation, 2nd edn. McGraw Hill.Google Scholar
13. Concus, P. & Finn, R. 1969 On the behaviour of a capillary free surface in a wedge. Proc. Natl Acad. Sci. USA 63, 292–299.CrossRefGoogle Scholar
14. Concus, P. & Finn, R. 1990 Capillary surface in microgravity. In Low-Gravity Fluid Dynamics and Transport Phemomena, Progress in Astronautics and Aeronautics, vol. 130. AIAA.Google Scholar
15. Concus, P., Finn, R. & Weislogel, M. 2000 Measurement of critical contact angle in a microgravity experiment. Exp. Fluids 28 (3), 197–205.CrossRefGoogle Scholar
16. Dong, M. & Chatzis, I. 1995 The imbibition and flow of a wetting liquid along the corners of a square capillary tube. J. Colloid Interface Sci. 172 (2), 278–288.CrossRefGoogle Scholar
17. Finn, R. & Neel, R. W. 1999 C-singular solutions of the capillary problem. J. Reine Angew. Math. 512, 1–25.CrossRefGoogle Scholar
18. Griffith, P. & Wallis, J. D. 1960 The role of surface conditions in nucleate boiling. AIChE J. 56, 49–63.Google Scholar
19. Jenson, R. M., Weislogel, M. M., Tavan, N. T., Chen, Y., Semerjian, B., Bunnell, C. T., Collicott, S. H., Klatte, J. & Dreyer, M. E. 2009 The capillary flow experiments aboard the international space station: increments 9–15, August 2004–December 2007. Tech Rep. CR-2009-215586, NASA.Google Scholar
20. Kast, W. 1964 Beteutung der keimbildung und der instationanen wrmebertragung fur den wrmebertraga bei blasenverdampfung und tropfenkondensation. Chemie Ing. Teckn. 36 (9), 933–940.CrossRefGoogle Scholar
21. Khare, K., Brinkmann, M., Bruce, M., Law, B. M., Gurevich, E. L., Herminghaus, S. & Seemann, R. 2007 Dewetting of liquid filaments in wedge-shaped grooves. Langmuir 23, 12138–12141.CrossRefGoogle ScholarPubMed
22. Klatte, J., Haake, D., Weislogel, M. M. & Dreyer, M. E. 2008 A fast numerical procedure for steady capillary flow in open capillary channels. Acta Mech. 201, 269–276.CrossRefGoogle Scholar
23. Kovscek, A. R. & Radke, C. J. 1996 Gas bubble snap-off under pressure driven flow in constricted non-circular capillaries. Colloids Surf. 117, 56–76.CrossRefGoogle Scholar
24. de Lazzer, A., Langbein, D., Dreyer, M. & Rath, H. J. 1996 Mean curvature of liquid surfaces in cylindrical containers of arbitrary cross-section. Microgravity Sci. Technol. 9 (3), 208–219.Google Scholar
25. Lekan, J., Gotti, D., Jenkins, A., Owens, J. C. & Johnston, M. R. April 1996 Users guide for the 2.2 second drop tower of the NASA lewis research centre. Tech. Mem. 107090. NASA, Lewis Research Center.Google Scholar
26. Mumley, T. E., Radke, C. J. & Williams, M. C. 1986 Kinetics of liquid/liquid capillary rise, Parts i and ii. J. Colloid Interface Sci. 109 (2), 398–425.CrossRefGoogle Scholar
27. Ponomarenko, A., Clanet, C. & Quéré, D. 2011 Capillary rise in wedges. J. Fluid Mech. 666, 146–154.CrossRefGoogle Scholar
28. Ramé, E. & Weislogel, M. M. 2009 Gravity effects on capillary flows in sharp corners. Phys. Fluids 21 (4), 042106.CrossRefGoogle Scholar
29. Ransohoff, T. C. & Radke, C. J. 1988 Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied non-circular pore. J. Colloid Interface Sci. 121 (392).CrossRefGoogle Scholar
30. Romero, L. A. & Yost, F. G. 1996 Flow in an open channel capillary. J. Fluid Mech. 322, 109–129.CrossRefGoogle Scholar
31. Rosendahl, U., Ohlhoff, A. & Dreyer, M. E. 2004 Choked flows in open capillary channels: theory, experiment and computations. J. Fluid Mech. 518, 187–214.CrossRefGoogle Scholar
32. 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, 664–688.CrossRefGoogle Scholar
33. 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, 4498–4509.CrossRefGoogle Scholar
34. Tavan, N. 2009 Critical geometric wetting phenomena: study of capillary driven flow in the CFE Vane–Gap experiment aboard the International Space Station. Master’s thesis, Portland State University.Google Scholar
35. Wang, C. X., Xu, S. H., Sun, Z. W. & Hu, W. R. 2010 A study of the influence of initial liquid volume on the capillary flow in an interior corner under microgravity. Intl J. Heat Mass Transfer 53 (9–10), 1801–1807.CrossRefGoogle Scholar
36. Weislogel, M. M. 1996 Capillary flow in an interior corner. PhD thesis, Northwestern University.Google Scholar
37. Weislogel, M. M. 2001 Capillary flow in containers of polygonal section. AIAA J. 39 (12), 2320–2326.CrossRefGoogle Scholar
38. Weislogel, M. M. 2003 Some analytical tools for fluids management in space: isothermal capillary flows along interior corners. Adv. Space Res. 32 (2), 163–170.CrossRefGoogle Scholar
39. Weislogel, M. M. & Collicott, S. H. 2004 Capillary rewetting of vaned containers: spacecraft tank rewetting following thrust resettling. AIAA J. 42 (12), 2551–2561.CrossRefGoogle Scholar
40. Weislogel, M. M. & Lichter, S. 1998 Capillary flow in an interior corner. J. Fluid Mech. 373, 349–378.CrossRefGoogle Scholar
41. Weislogel, M. M. & Nardin, C. L. 2005 Capillary driven flow along interior corners formed by planar walls of varying wettability. Microgravity Sci. Technol. 17 (3), 45–55.CrossRefGoogle Scholar
42. Weislogel, M. M., Jenson, R. & Bolleddula, D. 2007 Capillary driven flows in weakly three-dimensional polygonal containers. AIAA Paper 2007-748, pp. 1–13. 45th AIAA Aerospace Sci. Meeting and Exhibit, Reno, Jan. 2007 .Google Scholar
43. Weislogel, M. M., Chen, Y & Bolledulla, D 2008 A better non-dimensionalization scheme for slender laminar flows: The Laplacian operator scaling method. Phys. Fluids 20 (2), 163–170.CrossRefGoogle Scholar
44. Weislogel, M. M., Chen, Y., Collicott, S. H., Bunnell, C. T., Green, R. D. & Bohman, D. Y. 2009 a More handheld fluid interface experiments for the International Space Station (CFE-2). AIAA Paper 2009-0615, pp. 1–10. 47th AIAA Aerospace Sciences Meeting, Orlando,.CrossRefGoogle Scholar
45. Weislogel, M. M., Thomas, E. A. & Graf, J. C. 2009b A novel device addressing design challenges for passive fluid phase separations aboard spacecraft. Microgravity Sci. Technol. 21 (3), 257–268.CrossRefGoogle Scholar
46. Yi, T. & Wong, H. 2007 Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films. J. Colloid Interface Sci. 313 (2), 579–591.CrossRefGoogle ScholarPubMed
47. Yonemoto, Y. & Kunugi, T. 2008 Reconsideration of Young’s equation. Thermal Sci. Engng 16 (1), 49–60.Google Scholar
48. Zhang, J., Watson, S. J. & Wong, H. 2007 Fluid flow and heat transfer in a dual-wet micro heat pipe. J. Fluid Mech. 589, 1–31.CrossRefGoogle Scholar