Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-27T04:54:46.213Z Has data issue: false hasContentIssue false
  • English
  • Français

Equilibrium configurations of drops or bubbles in an eccentric annulus

Published online by Cambridge University Press:  29 January 2019

Negar Beheshti Pour Open the ORCID record for Negar Beheshti Pour [Opens in a new window]  and
David B. Thiessen Open the ORCID record for David B. Thiessen [Opens in a new window]
Negar Beheshti Pour
Affiliation:
Voiland School of Chemical Engineering and Bioengineering, Washington State University, Pullman, WA 99164, USA
David B. Thiessen*
Affiliation:
Voiland School of Chemical Engineering and Bioengineering, Washington State University, Pullman, WA 99164, USA
*
†Email address for correspondence: thiessen@wsu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The purpose of this paper is to find the zero-gravity equilibrium configurations of liquid drops or bubbles that have sufficient volume to form large-aspect-ratio bridging segments or occluding slugs in the eccentric annulus between two cylinders. In zero gravity, the static problem depends on the contact angle of the fluid segment on the solid support, and two geometric parameters: the radius ratio and the dimensionless distance between the cylinder centres. For both non-wetting and wetting liquids, we find regions of geometric parameter space where only occluding configurations occur, a bistable region where either configuration can occur, and a region where only the non-occluding bridging configuration can occur. For the non-occluding cases, we applied a large-aspect-ratio free-energy minimization approach to predict the cross-sectional shape of the liquid, and a finite element method was used to compute the interface shape of the occluding cases. A Surface Evolver model was used to simulate the three-dimensional shape of both occluding and non-occluding configurations. The simulation results support the theoretical predictions well. The fractional open area of the conduit was determined for both highly wetting and highly non-wetting minority phases. Optimization of the geometric parameters for a given wetting condition could facilitate the segregation and transport of two fluid phases in applications involving large aspect ratios and small pressure driving forces.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Liquid bridges
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 364 - 385
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Blackmore, W., Weislogel, M. M., Chen, Y., Kiewidt, L., Klatte, J. & Bunnell, C. T. 2011 The capillary flow experiments (CFE-2) on ISS: status. In 49th AIAA Aerospace Sciences Meeting. American Institute for Aeronautics and Astronautics.Google Scholar
Bostwick, J. B. & Steen, P. H. 2015 Stability of constrained capillary surfaces. Annu. Rev. Fluid Mech. 47, 539–568.10.1146/annurev-fluid-010814-013626Google Scholar
Brakke, K. A. 1992 The Surface Evolver. Exp. Maths. 1 (2), 141–165.10.1080/10586458.1992.10504253Google Scholar
Brakke, K. A. 1996 The Surface Evolver and the stability of liquid surfaces. Phil. Trans. R. Soc. Lond. A 354 (1715), 2143–2157.Google Scholar
Brinkmann, M., Kierfeld, J. & Lipowsky, R. 2004 A general stability criterion for droplets on structured substrates. J. Phys. A: Math. Gen. 37 (48), 11547–11573.10.1088/0305-4470/37/48/003Google Scholar
Brown, R. A. & Scriven, L. E. 1980 On the multiple equilibrium shapes and stability of an interface pinned on a slot. J. Colloid Interface Sci. 78 (2), 528–542.10.1016/0021-9797(80)90590-1Google Scholar
Cheah, M. J., Kevrekidis, I. G. & Benziger, J. B. 2013 Water slug formation and motion in gas flow channels: the effects of geometry, surface wettability, and gravity. Langmuir 29 (31), 9918–9934.10.1021/la4011967Google Scholar
Chen, Y. & Collicott, S. H. 2006 Study of wetting in an asymmetrical vane-wall gap in propellant tanks. AIAA J. 44 (4), 859–867.10.2514/1.15729Google Scholar
Chen, Y., Weislogel, M. M. & Nardin, C. L. 2006 Capillary-driven flows along rounded interior corners. J. Fluid Mech. 566, 235–271.10.1017/S0022112006001996Google Scholar
Collicott, S. H., Lindsley, W. G. & Frazer, D. G. 2006 Zero-gravity liquid–vapor interfaces in circular cylinders. Phys. Fluids 18 (8), 087109.10.1063/1.2345026Google Scholar
Concus, P. & Finn, R. 1969 On the behavior of a capillary surface in a wedge. Proc. Natl Acad. Sci. USA 63 (2), 292–299.10.1073/pnas.63.2.292Google Scholar
Concus, P. & Finn, R. 1990 Dichotomous behavior of capillary surfaces in zero gravity. Microgravity Science Technol. 3 (2), 87–92.Google Scholar
Faghri, A. 1995 Heat Pipe Sci. and Technology. Global Digital Press.Google Scholar
Finn, R. 1983 Existence criteria for capillary free surfaces without gravity. Indiana Univ. Math. J. 32 (3), 439–460.10.1512/iumj.1983.32.32032Google Scholar
Gau, H., Herminghaus, S., Lenz, P. & Lipowsky, R. 1999 Liquid morphologies on structured surfaces: from microchannels to microchips. Science 283 (5398), 46–49.10.1126/science.283.5398.46Google Scholar
Heil, M. 1999 Minimal liquid bridges in non-axisymmetrically buckled elastic tubes. J. Fluid Mech. 380, 309–337.10.1017/S0022112098003760Google Scholar
Jenson, R. M., Wollman, A. P., Weislogel, M. M., Sharp, L., Green, R., Canfield, P. J., Klatte, J. & Dreyer, M. E. 2014 Passive phase separation of microgravity bubbly flows using conduit geometry. Intl J. Multiphase Flow 65, 68–81.10.1016/j.ijmultiphaseflow.2014.05.011Google Scholar
Langbein, D. 1990 The shape and stability of liquid menisci at solid edges. J. Fluid Mech. 213, 251–265.10.1017/S0022112090002312Google Scholar
Liang, J., Luo, Y., Zheng, S. & Wang, D. 2017 Enhance performance of micro direct methanol fuel cell by in situ CO2 removal using novel anode flow field with superhydrophobic degassing channels. J. Power Sources 351, 86–95.10.1016/j.jpowsour.2017.03.099Google Scholar
Litterst, C., Eccarius, S., Hebling, C., Zengerle, R. & Koltay, P. 2006 Increasing 𝜇DMFC efficiency by passive CO2 bubble removal and discontinuous operation. J. Micromech. Microengng 16 (9), S248–S253.10.1088/0960-1317/16/9/S12Google Scholar
Lowry, B. J. & Thiessen, D. B. 2007 Fixed contact line helical interfaces in zero gravity. Phys. Fluids 19 (2), 022102.10.1063/1.2710518Google Scholar
Manning, R., Collicott, S. & Finn, R. 2011 Occlusion criteria in tubes under transverse body forces. J. Fluid Mech. 682, 397–414.10.1017/jfm.2011.230Google Scholar
Michael, D. H. 1981 Meniscus stability. Annu. Rev. Fluid Mech. 13 (1), 189–216.10.1146/annurev.fl.13.010181.001201Google Scholar
Oesterle, A.2015 Pipette cookbook 2015 p-97 and p-1000 micropipette pullers. Sutter Instrument, California.Google Scholar
Princen, H. M. 1970 Capillary phenomena in assemblies of parallel cylinders: III. Liquid columns between horizontal parallel cylinders. J. Colloid Interface Sci. 34 (2), 171–184.10.1016/0021-9797(70)90167-0Google Scholar
Protiere, S., Duprat, C. & Stone, H. A. 2013 Wetting on two parallel fibers: drop to column transitions. Soft Matt. 9 (1), 271–276.10.1039/C2SM27075GGoogle Scholar
Reyssat, E. 2015 Capillary bridges between a plane and a cylindrical wall. J. Fluid Mech. 773, R1.10.1017/jfm.2015.233Google Scholar
Roy, R. V. & Schwartz, L. W. 1999 On the stability of liquid ridges. J. Fluid Mech. 391, 293–318.10.1017/S0022112099005352Google Scholar
Schlitt, R.1994 Heat pipe with a bubble trap. US Patent 5,346,000.Google Scholar
Slobozhanin, L. A. & Alexander, J. I. D. 2003 Stability diagrams for disconnected capillary surfaces. Phys. Fluids 15 (11), 3532–3545.10.1063/1.1616557Google Scholar
Smedley, G. 1990 Containments for liquids at zero gravity. Microgravity Sci. Technol. 3, 13–23.Google Scholar
Wei, Y., Chen, X. & Huang, Y. 2011 Interior corner flow theory and its application to the satellite propellant management device design. Sci. China Technol. Sci. 54 (7), 1849–1854.10.1007/s11431-011-4374-4Google Scholar
Zhang, F. Y., Yang, X. G. & Wang, C. Y. 2006 Liquid water removal from a polymer electrolyte fuel cell. J. Electrochem. Soc. 153 (2), A225–A232.10.1149/1.2138675Google Scholar