Oscillatory fluid flow in deformable tubes: Implications for pore-scale hydromechanics from comparing experimental...

Oscillatory flow of four fluids (air, water, two aqueous sodium-tungstate solutions) was excited at frequencies up to 250 Hz in tubes of two materials (steel, silicone) covering a wide range in length, diameter, and thickness. The hydrodynamical response was characterized by phase shift and amplitude ratio between pressures in an upstream (pressure excitation) and a downstream reservoir connected by the tubes. The resulting standing flow waves reflect viscosity-controlled diffusive behavior and inertia-controlled wave behavior for oscillation frequencies relatively low and high compared to Biot's critical frequency, respectively. Rigid-tube theories correspond well with the experimental results for steel tubes filled with air or water. The wave modes observed for silicone tubes filled with the rather incompressible liquids or air, however, require accounting for the solid's shear and bulk modulus to correctly predict speed of pressure propagation and deformation mode. The shear mode may be responsible for significant macroscopic attenuation in porous materials with effective frame-shear moduli lower than the bulk modulus of the pore fluid. Despite notable effects of the ratio of densities and of acoustic and shear velocity of fluid and solid, Biot's frequency remains an approximate indicator of the transition from the viscosity to the inertia controlled regime.