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Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity

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Abstract

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed in the Lucas–Washburn (L–W) equation. Commonly, to account for this deviation from the single equivalent hydraulic capillary, experimentalists propose an effective contact angle change. In this work, we consider rather the general term of the Wilhelmy wetting force regarding the wetting line length, and apply a proposed increase in the liquid–solid contact line and wetting force provided by the introduction of surface meso/nanoscale structure to the pore wall roughness. An experimental surface pore wall feature size regarding the rugosity area is determined by means of capillary condensation during nitrogen gas sorption in a ground calcium carbonate tablet compact. On this nano size scale, a fractal structure of pore wall is proposed to characterize for the internal rugosity of the porous medium. Comparative models based on the Lucas–Washburn and Bosanquet inertial absorption equations, respectively, for the short timescale imbibition are constructed by applying the extended wetting line length and wetting force to the equivalent hydraulic capillary observed at the long timescale imbibition. The results comparing the models adopting the fractal structure with experimental imbibition rate suggest that the L–W equation at the short timescale cannot match experiment, but that the inertial plug flow in the Bosanquet equation matches the experimental results very well. If the fractal structure can be supported in nature, then this stresses the role of the inertial term in the initial stage of imbibition. Relaxation to a smooth-walled capillary then takes place over the longer timescale as the surface rugosity wetting is overwhelmed by the pore condensation and film flow of the liquid ahead of the bulk wetting front, and thus to a smooth walled capillary undergoing permeation viscosity-controlled flow.

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Notes

  1. Acronal\(^{\textregistered }\) SA latex, S360D, BASF, Ludwigshafen, Germany

  2. Mangin, P., Mandelbrot, B. and coworkers, personal communication

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Acknowledgments

The authors express their thanks to Dr. Philip Gerstner, formerly of Aalto University, for providing the sample tablet formed formulations, and to Dr. Carlo Bertinetto, Aalto University, for his suggestions for the design of the matching algorithm of the fractal structure in MatLab. We also acknowledge the Scientific Research Program Funded by the Foundation (No. 201309) of Tianjin Key Laboratory of Pulp & Paper (Tianjin University of Science & Technology), P. R. China, supported by Shaanxi Provincial Education Department (Program No. 2014JK0636) and by the Research Projects of the Provincial Key Laboratory of Science and Technology Department of Shaanxi Province (2011HBSZS014).

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Authors and Affiliations

  1. College of Light Industry and Energy, Shaanxi University of Science and Technology, and Shaanxi Province Key Laboratory of Papermaking Technology and Specialty Paper, Xi’an , 710021, China

    Guodong Liu & Meiyun Zhang

  2. Department of Forest Products Technology, School of Chemical Technology, Aalto University, P.O. Box 16300, 00076 , Aalto, Finland

    Guodong Liu & Patrick Gane

  3. Tianjin Key Laboratory of Pulp & Paper, Tianjin University of Science & Technology, Tianjin , 300457, China

    Guodong Liu

  4. Omya International AG, 4665 , Oftringen, Switzerland

    Cathy Ridgway & Patrick Gane

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  1. Guodong Liu
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  2. Meiyun Zhang
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  3. Cathy Ridgway
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  4. Patrick Gane
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Correspondence to Guodong Liu.

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Liu, G., Zhang, M., Ridgway, C. et al. Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity. Transp Porous Med 104, 231–251 (2014). https://doi.org/10.1007/s11242-014-0331-6

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  • DOI: https://doi.org/10.1007/s11242-014-0331-6

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