The Role of the Capillary Pressure Component in the Displacement of Partially Wetting Liquid from the Capillary

The problem of modelling the process of displacement of partially wetting liquid by gas in a thin capillary is considered in this article. The results of numerical calculations for the investigated model are presented, taking into account the disjoining pressure in the three-phase contact area. Using the displacement of viscous partially wetting liquid by gas in a thin flat capillary as an example, the relative role of the pressure drop in the capillary is investigated. It is shown that a detailed account of the dependency of the dynamic contact angle on the meniscus speed is significant only at low relative speeds, in other words, at relatively small pressure drops in the capillary.

References

[1] Korol’kov A.V., Men’shikov V.A., Partola I.S., Sapozhnikov V.B. Razvitie idei professora V.M. Poliaeva po primeneniiu poristo-setchatykh materialov dlia vnutribakovykh ustroistv, obespechivaiushchikh mnogokratnyi zapusk ZhRD [Development of Ideas of Professor V.M. Polyaev on Application of Porous-meshed Materials for Internal Tank Devices Providing Repeated Many Times Start-up of Liquid Propellant Engines]. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie. [Herald of the Bauman Moscow State Technical University. Mechanical Engineering]. 2006, no. 2(63), pp. 78–88.

[2] Sapozhnikov V.B., Krylov V.I., Novikov Iu.M., Iagodnikov D.A. Nazemnaia otrabotka kapilliarnykh fazorazdelitelei na osnove kombinirovannykh poristo-setchatykh materialov dlia toplivnykh bakov zhidkostnykh raketnykh dvigatelei verkhnikh stupenei raket-nositelei, razgonnykh blokov i kosmicheskikh apparatov [Ground tests of capillary phase separators based on combined porous mesh material for fuel tanks of liquid propellant engine in propulsion installations of space crafts, top steps of carrier rockets and upper-stage rockets]. Inzhenernyi zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation]. 2013, no. 4(16). Available at: http://engjournal.ru/catalog/machin/rocket/707.html (accessed 20 August 2015).

[3] Romanov A.S., Semikolenov A.V. Modelirovanie gidrodinamiki rastekaniia kapli chastichno smachivaiushchei zhidkosti pod deistviem gorizontal’noi sily [Simulation of spreading hydrodynamics for a droplet of an incompletely wetting liquid under a horizontal force]. Zhurnal vychislitel’noi matematiki i matematicheskoi fiziki [Computational Mathematics and Mathematical Physics]. 1999, vol. 39, no. 7, pp. 1205–1210.

[4] Radoev B., Stockelhuber K.W., Tsekov R., Letocart P. Wetting film dynamics and stability. Colloid Stability and Application in Pharmacy, 2007, vol. 3, pp 151–172.

[5] Dai B., Leal L.G., Redondo A. Disjoining pressure for nonuniform thin films. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2008, vol. 78, iss. 6, article no. 061602.

[6] Saramago B. Thin liquid wetting films. Current Opinion in Colloid & Interface Science, 2010, vol. 15, no. 5, pp. 330–340.

[7] Ren W., Hu D. Continuum models for the contact line problem. Physics of Fluids, 2010, vol. 22, no. 10, pp. 102103-19.

[8] Patra A., Bandyopadhyay D., Tomar G., Sharma A., Biswas G. Instability and dewetting of ultrathin solid viscoelastic films on homogeneous and heterogeneous substrates. Journal of Chemical Physics, 2011, vol. 134, no. 6, pp. 064705-11.

[9] Boinovich L., Emelyanko A. Wetting and surface forces. Advances in Colloid and Interface Science, 2011, 165, pp. 60–69.

[10] Tsekov R., Toshev B.V. Capillary pressure of van der waals liquid nanodrops. Colloid Journal, 2012, vol. 74, no. 2, pp. 266–268.

[11] Colosqui C.E., Kavousanakis M.E., Papathanasiou A.G., Kevrekidis I.G. Mesoscopic model for microscale hydrodynamics and interfacial phenomena: Slip, films, and contact-angle hysteresis. Physical Review E – Statistical, Nonlinear, and Soft Matter Physics, 2013, vol. 87, no. 1, p. 013302.

[12] Nikolov A., Wasan D. Wetting-dewetting films: the role of structural forces. Advances in Colloid and Interface Science, 2014, vol. 206, pp. 207–221.

[13] Boinovich L., Emelyanenko A. The prediction of wettability of curved surfaces on the basis of the isotherms of the disjoining pressure. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2011, vol. 383, pp. 10–16.

[14] Popescu M.N., Oshanin G., Dietrich S., Cazabat A.-M. Precursor films in wetting phenomena. Journal of Physics Condensed Matter, 2012, vol. 24, p. 243102.

[15] Moulton D.E., Lega J. Effect of disjoining pressure in a thin film equation with nonuniform forcing. European Journal of Applied Mathematics, 2013, vol. 24, pp. 887–920.

[16] Snoeijer J.H., Andreotti B. Moving Contact Lines: Scales, Regimes, and Dynamical Transitions. Annual Review of Fluid Mechanics, 2013, vol. 45, pp. 269–292.

[17] Sibley D.N., Nold A., Savva N., Kalliadasis S. A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading. Journal of Engineering Mathematics, August 2014.

[18] Chaudhury K., Acharya P.V., Chakraborty S. Influence of disjoining pressure on the dynamics of steadily moving long bubbles inside narrow cylindrical capillaries. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2014, vol. 89, iss. 5, article no. 053002.

[19] Zhen P.Zh. Smachivanie: statika i dinamika [Wetting: statics and dynamics]. Uspekhi fizicheskikh nauk [Advances of Physical Sciences]. 1987, vol. 151, no. 4, pp. 619–681.

[20] Romanov A.S., Semikolenov A.V. Beznapornoe zapolnenie kapilliara v asimptoticheskoi teorii smachivaniia [Depressurized capillary filling in the asymptotic theory of wetting]. Inzhenernyi zhurnal: nauka i innovatsii [Engineering Journal: Science and Innovation]. 2013, no. 4. Available at: http://engjournal.ru/catalog/machin/rocket/699.html (accessed 20 August 2015).

[21] Romanov A.S. Ob odnom sposobe gidrodinamicheskogo opisaniia rastekaniia chastichno smachivaiushchei zhidkosti po ploskoi tverdoi poverkhnosti [A method of hydrodynamic description of partially wetting liquid spreading on a flat solid surface]. Kolloidnyi zhurnal [Colloid Journal]. 1990, vol. 52, no. 1, pp. 93–99.