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

Abstract

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 pre-factor 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.

16 pages, 4 figures, 1 video as supplementary (enclosed as ancillary file), as resubmitted, in press, Transport in Porous Media (2018)

References in corpus (11)

• Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation
• Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media - topical review
• Switchable Imbibition in Nanoporous Gold
• Spontaneous Imbibition Dynamics of an n-Alkane in Nanopores: Evidence of Meniscus Freezing and Monolayer Sticking
• Capillary rise dynamics of liquid hydrocarbons in mesoporous silica as explored by gravimetry, optical and neutron imaging: Nano-rheology and determination of pore size distributions from the shape of imbibition fronts
• Hydraulic Transport Across Hydrophilic and Hydrophobic Nanopores: Flow Experiments with Water and n-Hexane
• Quantized Self-Assembly of Discotic Rings in a Liquid Crystal Confined in Nanopores
• Temperature dependence of the slip length in polymer melts at attractive surfaces
• Imbibition in mesoporous silica: rheological concepts and experiments on water and a liquid crystal
• Molecular dynamics of n-hexane: A quasi-elastic neutron scattering study on the bulk and spatially nanochannel-confined liquid
• A ferroelectric liquid crystal confined in cylindrical nanopores: Reversible smectic layer buckling, enhanced light rotation and extremely fast electro-optically active Goldstone excitations

Cited by in corpus (3)

• Conflicting Effects of Extreme Nanoconfinement on the Translational and Segmental Motion of Entangled Polymers
• Straight versus Spongy -- Effect of Tortuosity on Polymer Imbibition into Nanoporous Matrices Assessed by Segmentation-Free Analysis of 3D Sample Reconstructions
• Anomalous diffusion in an electrolyte saturated paper matrix