Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries

doi:10.1016/j.cjche.2018.04.031

Chinese Journal of Chemical Engineering ›› 2018, Vol. 26 ›› Issue (10): 2014-2022.DOI: 10.1016/j.cjche.2018.04.031

• Fluid Dynamics and Transport Phenomena • 上一篇下一篇

Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries

Yicun Tang¹, Jingchun Min¹, Xuan Zhang², Guiling Liu¹

1 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
2 Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China

收稿日期:2018-02-26 修回日期:2018-04-16 出版日期:2018-10-28 发布日期:2018-11-14
通讯作者: Jingchun Min,E-mail address:minjc@tsinghua.edu.cn
基金资助:
Supported by the National Natural Science Foundation of China (51376103).

Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries

Yicun Tang¹, Jingchun Min¹, Xuan Zhang², Guiling Liu¹

1 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
2 Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China

Received:2018-02-26 Revised:2018-04-16 Online:2018-10-28 Published:2018-11-14
Contact: Jingchun Min,E-mail address:minjc@tsinghua.edu.cn
Supported by:
Supported by the National Natural Science Foundation of China (51376103).

摘要/Abstract

摘要： A numerical study has been conducted to simulate the liquid/gas interface (meniscus) behaviors and capillary pressures in various capillary channels using the volume of fluid (VOF) method. Calculations are performed for four channels whose cross-sectional shapes are circle, regular hexagon, square and equilateral triangle and for four solid/liquid contact angles of 30°, 60°, 120° and 150°. No calculation is needed for the contact angle of 90° because the liquid/gas interface in this case can be thought to be a plane surface. In the calculations, the liquid/gas interface in each channel is assumed to have a flat surface at the initial time, it changes towards its due shape thereafter, which is induced by the combined action of the surface tension and contact angle. After experiencing a period of damped oscillation, it stabilizes at a certain geometry. The interface dynamics and capillary pressures are compared among different channels under three categories including the equal inscribed circle radius, equal area, and equal circumscribed circle radius. The capillary pressure in the circular channel obtained from the simulation agrees well with that given by the Young-Laplace equation, supporting the reliability of the numerical model. The channels with equal inscribed circle radius yield the closest capillary pressures, while those with equal circumscribed circle radius give the most scattered capillary pressures, with those with equal area living in between. A correlation is developed to calculate the equivalent radius of a polygonal channel, which can be used to compute the capillary pressure in such a channel by combination with the Young-Laplace equation.

关键词: Capillary phenomenon, Polygonal channel, Meniscus shape, Capillary pressure

Abstract: A numerical study has been conducted to simulate the liquid/gas interface (meniscus) behaviors and capillary pressures in various capillary channels using the volume of fluid (VOF) method. Calculations are performed for four channels whose cross-sectional shapes are circle, regular hexagon, square and equilateral triangle and for four solid/liquid contact angles of 30°, 60°, 120° and 150°. No calculation is needed for the contact angle of 90° because the liquid/gas interface in this case can be thought to be a plane surface. In the calculations, the liquid/gas interface in each channel is assumed to have a flat surface at the initial time, it changes towards its due shape thereafter, which is induced by the combined action of the surface tension and contact angle. After experiencing a period of damped oscillation, it stabilizes at a certain geometry. The interface dynamics and capillary pressures are compared among different channels under three categories including the equal inscribed circle radius, equal area, and equal circumscribed circle radius. The capillary pressure in the circular channel obtained from the simulation agrees well with that given by the Young-Laplace equation, supporting the reliability of the numerical model. The channels with equal inscribed circle radius yield the closest capillary pressures, while those with equal circumscribed circle radius give the most scattered capillary pressures, with those with equal area living in between. A correlation is developed to calculate the equivalent radius of a polygonal channel, which can be used to compute the capillary pressure in such a channel by combination with the Young-Laplace equation.

Key words: Capillary phenomenon, Polygonal channel, Meniscus shape, Capillary pressure

Yicun Tang, Jingchun Min, Xuan Zhang, Guiling Liu. Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries[J]. Chinese Journal of Chemical Engineering, 2018, 26(10): 2014-2022.

Yicun Tang, Jingchun Min, Xuan Zhang, Guiling Liu. Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries[J]. Chin.J.Chem.Eng., 2018, 26(10): 2014-2022.

参考文献

[1] T.K. Tokunaga, K.R. Olson, J. Wan, Conditions necessary for capillary hysteresis in porous media:Tests of grain size and surface tension influences, Water Resour. Res. 40(2004), W05111.

[2] G.R. Jerauld, S.J. Salter, The effect of pore-structure on hysteresis in relative permeability and capillary pressure:Pore-level modeling, Transp. Porous Media 5(1990) 103-151.

[3] R.T. Armstrong, M.L. Porter, D. Wildenschild, Linking pore-scale interfacial curvature to column-scale capillary pressure, Adv. Water Resour. 46(2012) 55-62.

[4] E.C. Kumbur, K.V. Sharp, M.M. Mench, On the effectiveness of Leverett approach for describing the water transport in fuel cell diffusion media, J. Power Sources 168(2007) 356-368.

[5] E.C. Kumbur, K.V. Sharp, M.M. Mench, Validated Leverett approach for multiphase flow in PEFC diffusion media Ⅲ. Temperature effect and unified approach, J. Electrochem. Soc. 154(12) (2007) B1315-B1324.

[6] W.H. Green, G.A. Ampt, Studies on soil physics, J. Agric. Sci. (Camb.) 4(1911) 1-24.

[7] R. Lucas, Rate of capillary ascension of liquids, Kolloid Z. 23(15) (1918) 15-22.

[8] E.W. Washburn, The dynamics of capillary flow, Phys. Rev. 17(1921) 273-283.

[9] R. Masoodi, E. Languri, A. Ostadhossein, Dynamics of liquid rise in a vertical capillary tube, J. Colloid Interface Sci. 389(2013) 268-272.

[10] N. Fries, M. Dreyer, An analytic solution of capillary rise restrained by gravity, J. Colloid Interface Sci. 320(2008) 259-263.

[11] M. Lago, M. Araujo, Capillary rise in porous media, J. Colloid Interface Sci. 234(2001) 35-43.

[12] A. Siebold, M. Nardin, J. Schultz, A. Walliser, M. Oppliger, Effect of dynamic contact angle on capillary rise phenomena, Colloids Surf. A Physicochem. Eng. Asp. 161(2000) 81-87.

[13] N. Fries, Capillary transport processes in porous materials-experiment and model, (PhD Thesis) Cuvillier Verlag Göttingen, 2010.

[14] B.V. Zhmud, F. Tiberg, K. Hallstensson, Dynamics of capillary rise, J. Colloid Interface Sci. 228(2000) 263-269.

[15] M. Prat, On the influence of pore shape, contact angle and film flows on drying of capillary porous media, Int. J. Heat Mass Transf. 50(2007) 1455-1468.

[16] L.A. Segura, P.G. Toledo, Pore-level modeling of isothermal drying of pore networks:Effects of gravity and pore shape and size distributions on saturation and transport parameters, Chem. Eng. J. 111(2) (2005) 237-252.

[17] H. Wong, S. Morris, C.J. Radke, Three-dimensional menisci in polygonal capillaries, J. Colloid Interface Sci. 148(2) (1992) 317-336.

[18] G. Mason, N.R. Morrow, Meniscus curvatures in capillaries of uniform cross-section, J. Chem. Soc. Faraday Trans. 180(9) (1984) 2375-2393.

[19] A. Ishakoglu, A.F. Baytas, The influence of contact angle on capillary pressure-saturation relations in a porous medium including various liquids, Int. J. Eng. Sci. 43(2005) 744-755.

[20] Y.C. Tang, J.C. Min, X.M. Wu, Selection of convective moisture transfer driving potential and its impacts upon porous plate air-drying characteristics, Int. J. Heat Mass Transf. 116(2018) 371-376.

[21] J.C. Min, R.L. Webb, Condensate formation and drainage on typical fin materials, Exp. Thermal Fluid Sci. 25(3-4) (2001) 101-111.

[22] J.C. Min, R.L. Webb, Condensate carryover phenomena in dehumidifying finned tube heat exchangers, Exp. Thermal Fluid Sci. 22(3-4) (2000) 175-182.

[23] J.C. Min, R.L. Webb, H. Bemisderfer, Long-term hydraulic performance of dehumidifying heat-exchangers with and without hydrophilic coating, Int. J. HVAC&R Res. 6(3) (2000) 257-272.

[24] J.C. Min, X.M. Wu, L.F. Shen, F. Gao, Hydrophilic treatment and performance evaluation of copper finned tube evaporators, Appl. Therm. Eng. 31(14-15) (2011) 2936-2942.

[25] R. Masoodi, K.M. Pillai, A general formula for capillary suction-pressure in porous media, J. Porous Media 15(8) (2012) 775-783.

[26] E. Jettestuen, J.O. Helland, M. Prodanovi?, A level set method for simulating capillary-controlled displacements at the pore scale with nonzero contact angles, Water Resour. Res. 49(2013) 4645-4661.

[27] H.S. Suh, D.H. Kang, J. Jang, K.Y. Kim, T.S. Yun, Capillary pressure at irregularly shaped pore throats:Implications for water retention characteristics, Adv. Water Resour. 110(2017) 51-58.

[28] R. Sivanesapillai, N. Falkner, A. Hartmaier, H. Steeb, A CSF-SPH method for simulating drainage and imbibition at pore-scale resolution while tracking interfacial areas, Adv. Water Resour. 95(2016) 212-234.

[29] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39(1) (1981) 201-225.

[30] J.E. Pilliod Jr., E.G. Puckett, Second-order accurate volume-of-fluid algorithms for tracking material interfaces, J. Comput. Phys. 199(2) (2004) 465-502.

[31] S. Balachandran, Surfactant analysis of thin liquid film in the human trachea via application of volume of fluid (VOF), fluid dynamics, Comput. Model. Appl. (2012) 449-462.

[32] K. Samarpana, A. Konapala, D. Ramesh, Computational investigation of free surface flow around a ship hull, Int. J. Appl. Innov. Eng. Manag. 2(5) (2013) 98-107.

[33] D.L. Youngs, Time-dependent multi-material flow with large fluid distortion, Numer. Methods Fluid Dyn. 24(2) (1982) 273-285.

[34] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100(2) (1992) 335-354.

Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries

Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价