Interfacial evolution explains the complex swelling-shrinkage responses of porous materials from vacuum-dry to full liquid saturation

Abstract

Adsorption-induced swelling occurs in a wide spectrum of natural and engineered porous materials. A key underlying mechanism is the monotonic reduction of solid-fluid surface energy upon fluid adsorption, which lowers the contractive adsorption stress and causes the porous skeleton to swell (Bangham and Fakhoury, 1928). Some mesoporous materials, however, deviate from the monotonic swelling pattern predicted by this mechanism, exhibiting an abrupt shrinkage at intermediate adsorbate partial pressures before swelling resumes and continues to full saturation. This behavior is commonly attributed to capillary condensation of the adsorbate from the vapor to the liquid phase within the pores. Understanding the stresses and the shrinkage induced by capillary condensation is critical in various industrial applications including micro-/nanofabrication, geotechnical engineering in collapsible soils, and sorption-driven actuation technologies. This work aims to develop a unified poromechanics theory that captures the full sequence of adsorption-induced deformation, including initial swelling, contraction during capillary condensation, and resumed expansion near full saturation. The formulation begins with a thermodynamic analysis of an unsaturated deformable porous solid, acknowledging the energetics of the solid-fluid (sl), solid-vapor (sv), and liquid-vapor (lv) interfaces. The resulting free energy balance permits the simultaneous derivation of the liquid retention characteristics curve and the coupled mechanical effects driven by adsorption and partial saturation. Within this framework, two strategies for constructing constitutive relations are examined: one explicitly resolves the dynamic evolution of sl-sv-lv interfacial areas to emphasize the underlying physics, while the other partially lumps the surface energies into a macroscopic capillary potential to facilitate model calibration using standard laboratory tests. The models are evaluated using datasets from two markedly different solid-fluid systems: N₂ gas adsorption on a hierarchical porous silica at 77 K and water adsorption on a carbon xerogel at 298 K. Both approaches effectively capture the complex, non-monotonic strain isotherms exhibited by the adsorbent. The adsorption-desorption hysteresis is also addressed in a thermodynamically consistent framework. The proposed theory demonstrates both robustness and unifying power in explaining the complex strain isotherms of porous materials along adsorption and desorption paths, covering the entire spectrum from vacuum-dry to fully liquid-saturated states.