Elastic Properties of Confined Fluids in Nanopores: An Acoustic-Propagation Model

Following the compressibility route in statistical mechanics, the local isothermal modulus is derived for nanoconfined fluids. Based on this inhomogeneous modulus, an acoustic-propagation model (APM) is first proposed for averaged isothermal modulus in the pore. By utilizing the density profiles obtained from classical density functional theory, the inhomogeneous modulus of supercritical methane in the graphite slit pore is calculated. It is found that the profile of the modulus in the pore is out of phase with that of density. Further, employing the proposed APM method, the averaged isothermal modulus is calculated, and the effects of pressure, pore size, and temperature on the averaged modulus are investigated. It is found that (i) averaged modulus obtained from APM method still satisfies the Tait-Murnaghan (TM) equation, (ii) the averaged modulus is proportional to the reciprocal pore width for wider pores, while it oscillates with the reciprocal pore width for narrower pores, and (iii) the reciprocal modulus is proportional to temperature, while the linearization coefficient is insensitive to the pore size. These findings bear important implications for understanding the elasticity in fluid-saturated nanoporous media and may shed light on the capture or storage of special gases in the fields of geochemistry and geophysics.