AIMS Biophysics, 2014, 1(1): 31-48. doi: 10.3934/biophy.2014.1.31

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Metastable capillary filaments in rectangular cross-section open microchannels

1 Department of Biotechnology, CEA/Université Grenoble-Alpes, 17 avenue des Martyrs, 38054, Grenoble, France;
2 Mathematics Department, Susquehanna University, 514 University Avenue, Selinsgrove, PA 17870, USA;
3 Department of Medical Microbiology and Immunology, University of Wisconsin-Madison, Madison, WI 53705, USA

Spontaneous capillary flow (SCF) in microchannels occurs for specific geometrical and wetting conditions. When the channel walls form corner angles with the channel bottom, liquid filaments may form in the corners. These capillary filaments are often called Concus-Finn (CF) filaments, and they can theoretically spread infinitely.In this work we consider rectangular open U-grooves of varying cross-section width, and we theoretically determine the flow conditions as a function of the aspect ratio of the channel and the liquid-solid contact angle. These flow conditions are numerically checked. Especially, we analyze the configurations where precursor capillary filaments form. We show that these filaments can be metastable, i.e. disappear into a bulk capillary flow if the proper conditions are met. A diagram of the flow regimes is deduced from theoretical developments and checked using numerical modeling.
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1. Kost GJ (2002) Principles and Practice of Point-of-Care Testing. Hagerstwon, MD: Lippincott Williams & Wilkins 3–12.

2. Yager P, Edwards T, Fu E, et al. (2006) Weigl, Microfluidic diagnostic technologies for global public health. Nature 442(7101): 412–418.

3. Martinez AW, Phillips ST, Whitesides GM (2010) Diagnostics for the developing world: microfluidic paper-based analytical devices. Anal Chem 82: 3–10.

4. Gervais L, de Rooij N, Delamarche E (2011) “Microfluidic chips for point-of-care immunodiagnostics”. Adv Mater 23 (24): H151–H176.

5. Gervais L, Delamarche E (2009) Toward one-step point-of-care immunodiagnostics using capillary-driven microfluidics and PDMS substrates. Lab Chip 9: 3330–3337.

6. Safavieh R, Juncker D (2013) Capillarics: pre-programmed, self-powered microfluidic circuits built from capillary elements. Lab Chip 13: 4180–4189.

7. Satoh W, Hosono H, Suzuki H (2005) On-Chip Microfluidic Transport and Mixing Using Electrowetting and Incorporation of Sensing Functions. Anal Chem 77: 6857–6863.

8. Casavant BP, Berthier E, Theberge AB, et al. (2013) Suspended microfluidics. Proc Natl Acad Sci110 (25): 10111–10116.

9. Berthier J, Brakke KA, Furlani EP, et al. (2014) Whole blood spontaneous capillary flow in narrow V-groove microchannels. Sensor Actuat B-Chem [impress].

10. Berthier J, Brakke KA, Gosselin D, et al. (2014) Suspended microflows between vertical parallel walls. Microfluid Nanofluid [impress].

11. Tung CK, Krupa O, Apaydin E, et al. (2013) A contact line pinning based microfluidic platform for modelling physiological flows. Lab Chip 13: 3876–3885.

12. Cox RG (1983) The spreading of a liquid on a rough solid surface. J Fluid Mech 131: 1–26.

13. Chen YK, Melvin LS, Rodriguez S, et al. (2009) Weislogel, Capillary driven flow in micro scale surface structures. Microelectron Eng 86: 1317–1320.

14. Rye RR, Yost FG, Mann J (1996) Wetting Kinetics in Surface Capillary Grooves. Langmuir 12:4625–4627.

15. Romero LA, Yost FG (1996) Flow in an open channel capillary. J Fluid Mechanics 322: 109–129.

16. Yost FG, Rye RR, Mann JA (1997) Solder wetting kinetics in narrow V-grooves. Acta Materialia45: 5337–5345.

17. Berthier J, Brakke KA, Berthier E (2014) A general condition for spontaneous capillary flow in uniform cross-section microchannels. Microfluid Nanofluid 16: 779–785.

18. Ouali FF, McHale G, Javed H, et al. (2013) Wetting considerations in capillary rise and imbibition in closed square tubes and open rectangular cross-section channels. Microfluid Nanofluid 15:309–326.

19. Concus P, Finn R (1969) On the behavior of a capillary surface in a wedge. Proc Natl Acad Sci63(2): 292–299.

20. Concus P, Finn R (1994) Capillary surfaces in a wedge—differing contact angles. Microgravity Sci Tec 7: 152–155.

21. Berthier J, Brakke KA (2012) The physics of microdrops. Scrivener-Wiley publishing.

22. Brakke KA (1992) Minimal surfaces, corners, and wires. J Geom Anal 2: 11–36.

23. Girardo S, Cingolani R, Chibbaro S, et al. (2009) Corner liquid imbibition during capillary penetration in lithographically made microchannels. Appl Phys Lett 94: 171901–171901–3.

24. Brakke KA (1992) The Surface Evolver. Exp Math 1(2): 141–165.

25. Seemann R, Brinkmann M, Kramer EJ, et al. (2005) Wetting morphologies at microstructured surfaces. Proc Natl Acad Sci 102(6): 1848–1852.

26. Gibbs JW (1873) A method of geometrical representation of the thermodynamic properties of substances by means of surfaces. T Connecticut Academy Arts Sciences 2: 382–404.

27. Jokinen V, Franssila S (2008) Capillarity in microfluidic channels with hydrophilic and hydrophobic walls. Microfluid Nanofluid 5: 443–448.

28. Bracke M, De Voeght E, Joos P (1989) The kinetics of wetting: the dynamic contact angle. Progr Colloid Polym Sci 79:142–149.

29. Seebergh JE, Berg JC (1992) Dynamic wetting in the low capillary number regime. Chem Eng Sci47 (17): 4455–4464.

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