Feuerzangenbowle - Imbibition and Porous Media Flow

This repository contains all my work regarding the Masterseminar about the topic of imbibition and porous media flow which covers the derivation of the "Lucas-Washburn Law" and the influence of geometrically variation of the capillary structure.

Abstract

Imbibtition is a process in which liquid gets sucked into porous media. This process is part of the everyday life and has many application in nature and industry. The dynamics of imbibition however can be understand with the dynamics of capillary flow in which the lenght of a column liquid follows a simple square root of time relation. Varying the geometry of the capillary results in the same relation for short times but changes the dynamics for long times with the outcome that more diverging geometry causes slower dynamics.

$l^2 = \left(\frac{\gamma}{\mu}\frac{\cos\theta}{2}\right)rt$

"Lucas Washburn Law"

Quicklinks

• Handout: PDF
• Presentation: PDF, PPTX

Literature

[1] J. M. Bell and F. K. Cameron, “The flow of liquids through capillary spaces,” The Journal of Physical Chemistry 10, 658–674 (1906).

[2] R. Lucas, “Über das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten,” Kolloid-Zeitschrift 23, 1435–1536 (1918).

[3] E. W. Washburn, “The dynamics of capillary flow,” Phys. Rev. 17, 273–283 (1921).

[4] D. I. Dimitrov, A. Milchev, and K. Binder, “Capillary rise in nanopores: Molecular dynamics evidence for the lucas-washburn equation,” Phys. Rev. Lett. 99, 054501 (2007).

[5] S. Gruener, T. Hofmann, D. Wallacher, A. V. Kityk, and P. Huber, “Capillary rise of water in hydrophilic nanopores,” Phys. Rev. E 79, 067301 (2009).

[6] S. Gruener and P. Huber, “Spontaneous imbibition dynamics of an n-alkane in nanopores: Evidence of meniscus freezing and monolayer sticking,” Phys. Rev. Lett. 103, 174501 (2009).

[7] M. Reyssat, L. Courbin, E. Reyssat, and H. A. Stone, “Imbibition in geome- tries with axial variations,” Journal of Fluid Mechanics 615, 335344 (2008).

[8] S. Gruener, Z. Sadjadi, H. E. Hermes, A. V. Kityk, K. Knorr, S. U. Egelhaaf, H. Rieger, and P. Huber, “Anomalous front broadening during spontaneous imbibition in a matrix with elongated pores,” Proceedings of the National Academy of Sciences 109, 10245–10250 (2012).

[9] F. Dullien, Porous Media - Fluid Transport and Pore Structure (Science Direct, 1991).