Surface Poromechanics

Sponsor: Startup fund provided by CUBoulder, partial support by DOE-NEUP.

Objectives

One gram of some porous materials can contain surface area as large as that of a football field, yet surface forces such as surface tension and disjoining pressure have been routinely neglected in classical poromechanics theories. This research theme aims to enrich the thermodynamic basis of poromechanics to fundamentally incorporate the various surface phenomenon in modeling the macroscopic behavior of porous materials.

We extend Coussy’s macroscale theory for porous materials interacting with adsorptive fluid mixtures. The solid-fluid interface is treated as an independent phase that obeys its own mass, momentum and energy balance laws. As a result, a surface strain energy term appears in the free energy balance equation of the solid phase, which further introduces the so-called adsorption stress in the constitutive equations of the porous skeleton. This establishes a fundamental link between the adsorption characteristics of the solid-fluid interface and the mechanical response of the porous media. The thermodynamic framework is quite general in that it recovers the coupled conduction laws, Gibbs isotherm and the Shuttleworth’s equation for surface stress, and imposes no constraints on the magnitude of deformation and the functional form of the adsorption isotherms. A rich variety of coupling between adsorption and deformation is recovered as a result of combining different poroelastic models (isotropic vs. anisotropic, linear vs. nonlinear) and adsorption models (unary vs. mixture adsorption, uncoupled vs. stretch-dependent adsorption). These predictions are discussed against the backdrop of recent experimental data on coal swelling subjected to CO2 and CO2 –CH4 injections, showing the capability and versatility of the theory in capturing adsorption-induced deformation of porous materials.

Schematic of the system and the relevant pore-scale processes.

Publications

Zhang, Y. (2018). Mechanics of adsorption-deformation coupling in porous media. Journal of the Mechanics and Physics of Solids 114, 31-54.

Zhang, Y. (2019). Thermodynamic-consistent adsorption-swelling models for coal. In 53rd US Rock Mechanics/Geomechanics Symposium, New York City, NY.

Eskandari-Ghadi, M., Zhang, Y. (2021) Mechanics of shrinkage-swelling transition of microporous materials at the initial stage of adsorption. International Journal of Solids and Structures, p.111041, DOI: 10.1016/j.ijsolstr.2021.111041