Gassmann Theory Applies to Nanoporous Media

Abstract

Recent progress in extraction of unconventional hydrocarbon resources has ignited the interest in the studies of nanoporous media. Since many thermodynamic and mechanical properties of nanoscale solids and fluids differ from the analogous bulk materials, it is not obvious whether wave propagation in nanoporous media can be described using the same framework as in macroporous media. Here we test the validity of Gassmann equation using two published sets of ultrasonic measurements for a model nanoporous medium, Vycor glass, saturated with two different fluids, argon and n-hexane. Predictions of the Gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements, and the bulk moduli of the solid and fluid constituents. The solid bulk modulus can be estimated from adsorption-induced deformation or from elastic effective medium theory. The fluid modulus can be calculated according to the Tait-Murnaghan equation at the solvation pressure in the pore. Substitution of these parameters into the Gassmann equation provides predictions consistent with measured data. Our findings set up a theoretical framework for investigation of fluid-saturated nanoporous media using ultrasonic elastic wave propagation.

arXiv commentIncludes Supporting Information

References in corpus (7)

• Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media - topical review
• Adsorption-Induced Deformation of Mesoporous Solids
• Elastic Response of Mesoporous Silicon to Capillary Pressures in the Pores
• 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
• Relation Between Pore Size and the Compressibility of a Confined Fluid
• Modulus-Pressure Equation for Confined Fluids
• Dynamic mechanical analysis of supercooled water in nanoporous confinement

Cited by in corpus (4)

• Laser-Excited Elastic Guided Waves Reveal the Complex Mechanics of Nanoporous Silicon
• Effect of Pore Geometry on the Compressibility of a Confined Simple Fluid
• Elastic Properties of Confined Fluids from Molecular Modeling to Ultrasonic Experiments on Porous Solids
• Ultrasonic Study of Water Adsorbed in Nanoporous Glasses