Wave Propagation in Surfactant-Containing Unsaturated Porous Media

Surfactants such as perfluoroalkyl and polyfluoroalkyl substances (PFAS) accumulate at the interface between the wetting and nonwetting fluids in an unsaturated porous medium and modify the interfacial tension and capillary pressure thereby influencing the poromechanical responses of the porous medium in general and the capillary wave behavior in particular. This paper first introduces a surfactant-modified capillary modulus in a Biot-type dynamic poroelasticity theory for unsaturated porous media. The wave speeds and attenuation behavior are then determined using a steady state propagating plane harmonic wave. Numerical results for both PFAS-contaminated clay-loam and loamy-sand textures indicate that generally the capillary wave speed decreases with an increase in the PFAS concentration although the speed reduction in the clay loam is not significant when the water saturation is near its residual value. In the meantime, presence of PFAS increases the attenuation coefficient for the capillary wave. For the clay-loam soil, the fast compressional wave speed also decreases with increasing PFAS concentration, but the speed reduction occurs in the low water saturation region. In general, the slow compressional and shear waves are not sensitive to the PFAS concentration. Finally, the sensitivity of capillary wave propagation to PFAS may be further explored to develop an acoustic sensing technology to detect PFAS concentrations in the vadose zone.