Prediction of Time of Capillary Rise in Porous Media Using Artificial Neural Network (ANN)

Document Type : Research Article


1 Department of Polymer and Color Engineering, Amirkabir University of Technology, P. O. Box 15875-4413 Tehran, I.R. IRAN

2 Department of Textile Engineering, Amirkabir University of Technology, P. O. Box 15875-4413 Tehran, I.R. IRAN


An Artificial Neural Network (ANN) was used to analyse the capillary rise in porous media. Wetting experiments were performed with fifteen liquids and fifteen different powders. The liquids covered a wide range  of  surface  tension ( 15.45-71.99  mJ/m2 )  and  viscosity (0.25-21 mPa.s). The powders also provided an acceptable range of particle size (0.012-45 μm) and surface free energy (25.54-63.90 mJ/m2). An artificial neural network was employed to predict the time of capillary rise for a known given height. The network's inputs were density, surface tension, and viscosity for the liquids and particle size, bulk density, packing density, and surface free energy for the powders. Two statistical parameters namely the product moment correlation coefficient (r2) and the performance factor (PF/3) were used to correlate the actual experimentally obtained times of capillary rise to: i) their equivalent values as predicted by a designed and trained artificial neural network; ii) their corresponding values as calculated by the Lucas-Washburn's equation as well as the equivalent values as calculated by its various other modified versions. It must be noted that for a perfect correlation r2=1 and PF/3=0. The results showed that only the present approach of artificial neural network was able to predict with superior accuracy (i.e. r2 = 0.91, PF/3=55) the time of capillary rise. The Lucas-Washburn's calculations gave the worst correlations (r2 = 0.11, PF/3 = 1016). Furthermore, some of the modifications of this equation as proposed by different workers did not seem to conspicuously improve the relationships giving a range of inferior correlations between the calculated and experimentally determined times of capillary rise (i.e. r2 = 0.24 to 0.44, PF/3 = 129 to 293).


Main Subjects

[1] Bell, J. M. and Cameron, F. K., The Flow of Liquids Through Capillary Spaces, J. Phys. Chem., 10, 658 (1906).
[2] Washburn, E. W., The Dynamics of Capillary Flow, Phys. Rev., 17, 273 (1921).
[3] Holland, F. A. and Bragg, R., “Fluid Flow for Chemical Engineers”, Edward Arnold Press: London, Chapter 1 (1995).
[4] Lucas, R., Ueber das Zeitgesetz des Kapillaren Aufstiegs von Flussigkeiten, Kolloid Z., 23, 15 (1918).
[5] Siebold, A., Nardin, M., Schultz, J., Walliser, A. and Oppliger, M., Effect of Dynamic Contact Angle on Capillary Rise Phenomena, Colloids Surfaces A: Physicochem. Eng. Aspects, 161, 81 (2000).
[6] Martic, G., Coninck, J. De and Blake, T.D., Influence of the Dynamic Contact Angle on the Charac-terization of Porous Media, J. Colloid  Interface Sci., 263, 213 (2003).
[7] Chibowski, E. and Holysz, L., Use of the Washburn Equation for Surface Free Energy Determination, Langmuir, 8, 710 (1992).
[8] Brakel, J. van and Heertjes, P. M., Capillary Rise in Porous Media Part III: Role of the Contact Angle, Powder Technol., 16, 91 (1977).
[9] Remoortere,  P. van  and  Joos, P., The Kinetics of Wetting: The Motion of a Three Phase Contactline in a Capillary, J. Colloid Interface Sci., 141, 348 (1991).
[10] Lockington, D.A. and Parlange, J.Y., A New Equation for Macroscopic Description of Capillary Rise in Porous Media, J. Colloid Interface Sci., 278, 404 (2004).
[11] Lago, M. and Araujo, M., Capillary Rise in Porous Media, Physica A, 289, 1 (2001).
[12] Delker,  T.,  Pengra,  D.  and  Wong, P. -z., Interface Pinning and the Dynamics of Capillary Rise in Porous Media, Phys. Rev. Lett., 76 , 2902 (1996).
[13] Noble, J. and Arnold, A., Experimental and Mathe-matical Modeling of Moisture Transport in Landfills, Chem. Eng. Commun., 100, 95 (1991).
[14] Tröger, J., Lunkwitz, K., Grundke, K. and Bürger, W., Determination of the Surface Tension of Microporous Membranes Using Wetting Kinetics Measurements, Colloids Surfaces A: Physicochem. Eng. Aspects, 134, 299 (1998).
[15] Schoelkopf, J., Gane, P. A. C., Ridgway, C.J. and Matthews, G.P., Practical Observation of Deviation from Lucas-Washburn Scaling in Porous Media, Colloids Surfaces A: Physicochem. Eng. Aspects, 206, 445 (2002).
[16] Bi, Z.C., Xu, F., Yang, P.H., Yu, J.Y. and Li, J.B., Mimic Oil Recovery with a SDBS-Dodecane-Silica Gel System, Colloids Surfaces A: Physicochem. Eng. Aspects, 180, 235 (2001).
[17] Bi, Z., Liao, W. and Qi, L., Wettability Alteration by CTAB Adsorption at Surfaces of SiO2 Film or Silica Gel Powder and Mimic Oil Recovery, Applied Surface Sci., 221, 25 (2004).
[18] Chibowski, E. and Perea-Carpio, R., Problems of Contact Angle and Solid Surface Free Energy Determination, Adv. Colloid Interface Sci., 98, 245 (2002).
[19] Cheever, G.D. and Ulicny, J.C., Interrelationships Between Pigment Surface Energies and Pigment Dispersions in Polymer Solutions, J. Coat. Technol., 55, 53 (1983).
[20] Tampy, G. K., Chen, W. -j., Prudich, M. E. and Savage, R.L., Wettability Measurements of Coal Using a Modified Washburn Technique, Energy Fuels, 2, 782 (1988).
[21] Dubé,  M.,   Rost,  M.  and   Alava,  M.,   Conserved Dynamics and Interface Roughening in Spontaneous  Imbibition: A Critical Overview, Eur. Phys. J. B, 15, 691 (2000).
[22] Rideal, E.K., On the Flow of Liquids Under Capillary Pressure, Phil. Mag., 44, 1152 (1922).
[23] Bosanquet, C.H., On the Flow of Liquids into Capillary Tubes, Phil. Mag., 45, 525 (1923).
[24] Szekely, J., Neumann, A.W. and Chuang, Y.K., The Rate of Capillary Penetration and the Applicability of the Washburn Equation, J. Colloid Interface Sci., 35, 273 (1971).
[25] Sorbie, K.S., Wu, Y.Z. and Mc Dougall, S.R., The Extended Washburn Equation and Its Application to the Oil/Water Pore Doublet Problem, J. Colloid Interface Sci., 174, 289 (1995).
[26] Kornev, K.G. and Neimark, A.V., Spontaneous Penetration of Liquids into Capillaries and Porous Membranes Revisited, J. Colloid Interface Sci., 235, 101 (2001).
[27] Kalra, R., Deo, M.C., Kumar, R. and Agarwal, V.K., Artificial Neural Network to Translate Offshore Satellite Wave Data to Coastal Locations, Ocean Eng., 32, 1917 (2005).
[28] Sözen, A.  and Arcakliogˇlu, E.,  Effect of Relative Humidity on Solar Potential, Applied Energy, 82, 345 (2005).
[29] Abbassi, A. and Bahar, L., Application of Neural Network for the Modeling and Control of Evaporative Condenser Cooling Load, Applied Thermal Eng., 25, 3176 (2005).
[30] Yang, J., Rivard, H. and Zmeureanu, R., On-line Building Energy Prediction Using Adaptive Artificial Neural Networks, Energy Buildings, 37, 1250 (2005).
[31] Peisheng, L., Youhui, X., Dunxi, Y. and Xuexin, S., Prediction of Grindability with Multivariable Regression and Neural Network in Chinese Coal, Fuel, 84, 2384 (2005).
[32] Yagci, O., Mercan, D.E.,  Cigizoglu,  H.K.  and Kabdasli, M. S., Artificial Intelligence Methods in Breakwater Damage Ratio Estimation, Ocean Eng., 32, 2088 (2005).
[33] Rezzi, S., Axelson, D.E., Héberger, K., Reniero, F., Mariani, C. and Guillou, C., Classification of Olive Oils Using High Throughput Flow HNMR Fingerprinting with Principal Component Analysis, Linear Discriminant Analysis and Probabilistic Neural Networks, Analytica Chimica Acta, 552, 13 (2005).
[34] Madan, A., Vibration Control of Building Structures Using Self-Organizing and Self-Learning Neural Networks, J. Sound Vibration,287, 759 (2005).
[35] Ahadian, S., The Attainment of Wetting Rate of Powders by Liquid Penetration Through the  Use  of       Artificial Neural Network (ANN), MSc Thesis, Department of Polymer and Color Engineering, Amirkabir University of Technology, Tehran, Iran (2006).
[36] Lange’s Handbook of Chemistry, Dean, J.A. Ed., McGraw-Hill: New York, Section 5 (1992).
[37] Labajos- Broncano, L., González- Martín, M. L., Bruque, J.M. and González-García, C.M., Comparison of the Use of Washburn's Equation in the Distance-Time and Weight-Time Imbibition Techniques, J. Colloid Interface Sci., 233, 357 (2001).
[38] Vargha-Butler, E.I., Zubovits, T.K., Hamza, H.A. and Neumann, A.W., Surface Tension Effects in the Sedimentation of the Polymer Particles in Various Liquid Mixtures, J. Dispers. Sci. Technol., 6, 357 (1985).
[39] Grundke, K., Bogumil, T., Gietzelt, T., Jacobasch, H. -j., Kwok, D.Y. and Neumann, A.W., Wetting Measurements on Smooth, Rough and Porous Solid Surfaces, Progr. Colloid Polym. Sci., 101, 58 (1996).
[40] Jacobasch , H. -j. , Grundke , K. , Augsburg , A. , Gietzelt , T.  and  Schneider , S. , Wetting  of  Solids  by  Liquids  with  Low  and  High  Viscosity , Progr.  Colloid  Polym.  Sci.105 , 44 ( 1997 ). 
[41] Grundke, K. and Augsburg, A., On the Determination of the Surface Energetics of Porous Polymer Materials, J. Adhes. Sci. Technol., 14, 765 (2000).
[42] Desai , T.R., Li, D., Finlay, W.H. and Wong, J.P., Determination of Surface Free Energy of Interactive Dry Powder Liposome Formulations Using Capillary Penetration Technique, Colloids Surfaces B: Biointerfaces, 22, 107 (2001).
[43] Aranberri-Askargorta, I., Lampke, T. and Bismarck, A., Wetting Behavior of Flax Fibers as Reinforcement for Polypropylene, J. Colloid Interface Sci., 263, 580 (2003). [44]  MATLAB Software, The Product of the MathWorks  Inc., Version 7.0 (2004).
[45] Guan, S.S. and Luo, M.R., Investigation of Parametric Effects Using Small Colour-Differences, Color Res. Appl., 24, 331 (1999).
[46] Coates, E., Fong, K.Y. and Rigg, B., Uniform Lightness Scales, J. S. D. C., 97, 179 (1981).
[47] Schultz,  W.,  The  Usefulness  of  Color  Difference Formulae for Fixing Color Tolerances, Color metrics (Soesterberg, Netherlands: AIC) 245 (1972).
[48] Cerepi, A., Humbert, L. and Burlot, R., Dynamics of  Capillary Flow and Transport Properties in Porous Media by Time-Controlled Porosimetry, Colloids Surfaces A: Physicochem. Eng. Aspects, 206, 425 (2002).
[49] Lindberg, B., Painting on Plastic Materials, J. O. C. C. A., 58, 408 (1975).