Acoustic waves in saturated porous media with gas bubbles.

The present framework employs various interface characteristics of gas bubbles into a continuum description of acoustics in porous media. It first extends the bubble compressibility in classic models by surface tension and higher-order curvature effects. This modelling extension is significantly relevant to estimate the impact of interface effects, e.

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

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.

The criterion of subscale sufficiency and its application to the relationship between static capillary pressure, saturation and interfacial areas.

Modern imaging techniques, increased simulation capabilities and extended theoretical frameworks, naturally drive the development of multiscale modelling by the question: which new information should be considered? Given the need for concise constitutive relationships and efficient data evaluation; however, one important question is often neglected: which information is sufficient? For this reason, this work introduces the formalized criterion of subscale sufficiency. This criterion states whether a chosen constitutive relationship transfers all necessary information from micro to macroscale within a multiscale framework. It further provides a scheme to improve constitutive relationships.

About the transition frequency in Biot's theory.

Biot's theory of wave propagation in porous media includes a characteristic frequency which is used to distinguish the low-frequency from the high-frequency range. Its determination is based on an investigation of fluid flow through different pore geometries on a smaller scale and a subsequent upscaling process. This idea is limited due to the assumptions made on the smaller scale.