Capillarity-Driven Oil Flow in Nanopores: Darcy Scale Analysis of Lucas–Washburn Imbibition Dynamics

  • Simon Gruener
  • Patrick Huber


We present gravimetrical and optical imaging experiments on the capillarity-driven imbibition of silicone oils in monolithic silica glasses traversed by 3D networks of pores (mesoporous Vycor glass with 6.5 nm or 10 nm pore diameters). As evidenced by a robust square root of time Lucas–Washburn (L–W) filling kinetics, the capillary rise is governed by a balance of capillarity and viscous drag forces in the absence of inertia and gravitational effects over the entire experimental times studied, ranging from a few seconds up to 10 days. A video on the infiltration process corroborates a collective pore filling as well as pronounced imbibition front broadening resulting from the capillarity and permeability disorder, typical of Vycor glasses. The transport process is analyzed within a Darcy scale description, considering a generalized prefactor of the L–W law, termed Lucas–Washburn–Darcy imbibition ability. It assumes a Hagen–Poiseuille velocity profile in the pores and depends on the porosity, the mean pore diameter, the tortuosity and the velocity slip length and thus on the effective hydraulic pore diameter. For both matrices a reduced imbibition speed and thus reduced imbibition ability, compared to the one assuming the nominal pore diameter, bulk fluidity and bulk capillarity, can be quantitatively traced to an immobile, pore wall adsorbed boundary layer of 1.4 nm thickness. Presumably, it consists of a monolayer of water molecules adsorbed on the hydrophilic pore walls covered by a monolayer of flat-laying silicone oil molecules. Our study highlights the importance of immobile nanoscopic boundary layers on the flow in tight oil reservoirs as well as the validity of the Darcy scale description for transport in mesoporous media.


Imbibition Silicone oil Mesoporous silica Nanoporous media Darcy law 



This work has been supported by the Deutsche Forschungsgemeinschaft (DFG), Project Hu850/9-1, ”Oxidic 3d scaffold structures for wetting-assisted shaping and bonding of polymers”.

Supplementary material

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Authors and Affiliations

  1. 1.Sorption and Permeation LaboratoryBASF SELudwigshafenGermany
  2. 2.Institute of Materials Physics and TechnologyHamburg University of TechnologyHamburg-HarburgGermany

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