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Dynamics in closed and open capillaries

  • T. S. Ramakrishnan (a1), P. Wu (a1) (a2), H. Zhang (a1) and D. T. Wasan (a2)


Capillary rise of a liquid displacing gas is analysed for both open and closed capillaries. We include menisci mass and hysteresis, and show that oscillations due to inertia are muted by friction at the advancing meniscus. From single-phase numerical computations in a no-slip/slip capillary, we quantify losses due to entry, flow development, meniscus slip, exit and acceleration of fluid within the reservoir. For closed capillaries, determining viscous drag due to gas requires inclusion of compressibility, and solving a moving boundary problem. This solution is derived through perturbation expansion with respect to two different small parameters for obtaining pressure above the liquid meniscus. Our rise predictions spanning a large range of experimental conditions and fluids for both open and closed capillaries match the data. The experimental data confirm the adequacy of the theoretically constructed dimensionless groups for predicting oscillatory behaviour.


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Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2002 Transport Phenomena, 2nd edn. John Wiley & Sons.
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid. Interface Sci. 299 (1), 113.
Blake, T. D. & Haynes, J. M. 1969 Kinetics of liquid/liquid displacement. J. Colloid Interface Sci. 30 (3), 421423.
Bosanquet, C. H. 1923 On the flow of liquids into capillary tubes. Lond. Edin. Dublin Phil. Mag. J. Sci. 45 (267), 525531.
Brochard-Wyart, F. & De Gennes, P. G. 1992 Dynamics of partial wetting. Adv. Colloid. Interface Sci. 39, 111.
Cox, R. G. 1986 The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J. Fluid Mech. 168, 169194.
Das, S. & Mitra, S. K. 2013 Different regimes in vertical capillary filling. Phys. Rev. E 87 (6), 063005.
Dorsey, N. E. 1926 Measurement of surface tension. NBS Sci. Papers 21, 563595.
Duvivier, D., Blake, T. D. & De Coninck, J. 2013 Toward a predictive theory of wetting dynamics. Langmuir 29 (32), 1013210140.
Fries, N. & Dreyer, M. 2008 The transition from inertial to viscous flow in capillary rise. J. Colloid. Interface Sci. 327, 125128.
Hamraoui, A. & Nylander, T. 2002 Analytical approach for the Lucas–Washburn equation. J. Colloid. Interface Sci. 250 (2), 415421.
Hartland, S. & Hartley, R. W. 1976 Axisymmetric Fluid–liquid Interfaces: Tables Giving the Shape of Sessile and Pendant Drops and External Menisci, with Examples of Their Use. Elsevier Science Ltd.
Heshmati, M. & Piri, M. 2014 Experimental investigation of dynamic contact angle and capillary rise in tubes with circular and noncircular cross sections. Langmuir 30 (47), 1415114162.
Hoffman, R. L. 1975 A study of the advancing interface. I. Interface shape in liquid–gas systems. J. Colloid. Interface Sci. 50 (2), 228241.
Hultmark, M., Aristoff, J. M. & Stone, H. A. 2011 The influence of the gas phase on liquid imbibition in capillary tubes. J. Fluid Mech. 678, 600606.
Jurin, J. 1717 An account of some experiments shown before the royal society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes. Phil. Trans. 30, 739747.
Katoh, K., Wakimoto, T., Yamamoto, Y. & Ito, T. 2015 Dynamic wetting behavior of a triple-phase contact line in several experimental systems. Exp. Therm. Fluid Sci. 60, 354360.
Kornev, K. G. & Neimark, A. V. 2001 Spontaneous penetration of liquids into capillaries and porous membranes revisited. J. Colloid. Interface Sci. 235 (1), 101113.
Lim, H., Tripathi, A. & Lee, J. 2014 Dynamics of a capillary invasion in a closed-end capillary. Langmuir 30 (31), 93909396.
Liu, S., Li, S. & Liu, J. 2018 Jurin’s law revisited: exact meniscus shape and column height. Eur. Phys. J. E 41 (3), 46.
Lucas, R. 1918 Rate of capillary ascension of liquids. Kolloid Z 23 (15), 1522.
Maggi, F. & Alonso-Marroquin, F. 2012 Multiphase capillary flows. Intl J. Multiphase Flow 42, 6273.
Masoodi, R., Languri, E. & Ostadhossein, A. 2013 Dynamics of liquid rise in a vertical capillary tube. J. Colloid Interface Sci. 389 (1), 268272.
Popescu, M. N., Ralston, J. & Sedev, R. 2008 Capillary rise with velocity-dependent dynamic contact angle. Langmuir 24 (21), 1271012716.
Quéré, D 1997 Inertial capillarity. Europhys. Lett. 39 (5), 533.
Quéré, D., Raphaël, É. & Ollitrault, J.-Y. 1999 Rebounds in a capillary tube. Langmuir 15 (10), 36793682.
Radiom, M., Chan, W. K. & Yang, C. 2010 Capillary filling with the effect of pneumatic pressure of trapped air. Microfluid Nanofluid 9 (1), 6575.
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 (2), 273278.
Verschaffelt, J. 1919 Applications of small drops and bubbles. K. Akad Amsterdam 21, 366374.
Voinov, O. V. 1976 Hydrodynamics of wetting. Fluid Dyn. 11 (5), 714721.
Walls, P. L. L., Dequidt, G. & Bird, J. C. 2016 Capillary displacement of viscous liquids. Langmuir 32 (13), 31863190.
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17 (3), 273.
Wu, P., Nikolov, A. D. & Wasan, D. T. 2017 Capillary rise: validity of the dynamic contact angle models. Langmuir 33 (32), 78627872.
Xiao, Y., Yang, F. & Pitchumani, R. 2006 A generalized analysis of capillary flows in channels. J. Colloid. Interface Sci. 298 (2), 880888.
Zhmud, B. V., Tiberg, F. & Hallstensson, K. 2000 Dynamics of capillary rise. J. Colloid Interface Sci. 228 (2), 263269.
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