Bulk Modulus of Not-So-Bulk Fluid

The velocity of ultrasonic waves in fluid-saturated porous media is a function of elastic moduli of solid and fluid constituents. Therefore, when the properties of a solid are known, ultrasonic measurements can provide information on the elastic modulus of the fluid in the pores. Recent ultrasonic experiments on fluid-saturated nanoporous glasses suggested that the elastic modulus of fluids in the pores is affected by confinement. Here we present theoretical predictions for the elastic modulus of liquid-like argon confined in spherical silica nanopores. We calculate the modulus using two different approaches. First we use the macroscopic thermodynamic definition of the modulus and calculate the modulus based on the derivative of the average fluid density, where the density of confined fluid is predicted by density functional theory. Second, we use the statistical mechanics approach and calculate the modulus from the fluctuations of number of molecules in the pore modeled using Monte Carlo molecular simulations in the grand canonical ensemble. We show that the predictions of the two approaches are consistent and close to the experimental results. Performing the calculations for a range of pore sizes we show that both methods predict that the modulus of confined argon is a linear function of the inverse pore size. Additionally we vary the solid-fluid interaction parameter, to represent solids other than silica. We show that the strong solid-fluid interactions (solvophilic confinement) make the fluid effectively stiffer, while the weak solid-fluid interactions (solvophobic confinement) make the fluid softer.