PoroMechanics Research Group at Université Paris-Est
PoroMechanics and Surface Energy
At low temperatures benzene contracts when it solidifies, whereas water expands when freezing. But, at the same low temperatures, a sealed sample of benzene-saturated cement paste expands, whereas a water-saturated sample containing air voids contracts. A cement paste contains pores of various dimensions and, at small scales, the intermolecular forces play a major role in the pore deformation. Another example of such an impact of intermolecular forces relates to global warming issues: unmineable deep coal beds may be used as potential CO2 storage reservoirs, but coal swells when the methane saturating the pore space is replaced with supercritical carbon dioxide, which leads to a closure of the pore system and hinders further injection. This swelling is due to the change in surface energy due to the preferential absorption of CO2. In both cases the understanding of the macroscopic deformation requires a sound investigation at the pore scale, where the cost in surface energy governs confined phase transitions.
To address these problems the quantitative approach we develop combines three aspects: poromechanics at the macroscopic scale; the physics of interfaces at the microscopic scale; and molecular simulations at the nanoscopic scale. Poromechanics provides the host theory to formulate the macroscopic constitutive equations of partially liquid-saturated porous materials. Poromechanics includes the use of homogenization methods for the assessment of macroscopic poroelastic properties from the microscopic elastic properties of the solid matrix. The physics of interfaces allows us to analyze the interface energy effects related to in-pore phase transition of super-cooled water. It also enables the understanding of the formation of a pre-condensed film at a gas-solid interface and to determine how this thin liquid film affects the interface tension. At the nanoscopic scale, GCMC molecular simulations provide the tool to analyze the adsorption of CO2 and CH4 molecules in coal that contains both microscopic and nanoscopic pores.
Supersaturation quantifies the degree of super-cooling of confined water. The pore volume fraction remaining liquid, as a function of the super-saturation, has been shown to be a material macroscopic thermodynamic state function. Physics of interfaces has permitted the quantitative prediction of this state function from the sole knowledge of the pore size distribution. Experimental results using an original dielectric capacity device have confirmed this prediction. The mechanical behavior of freezing water-infiltrated materials was then determined with the help of original theoretical developments for unsaturated porous solids. Concerning the coal behavior, molecular simulations showed that the adsorption isotherms were mainly accounted for by the trapping of CO2 and CH4 molecules in the nanoscopic pores that constitute deep energy wells. The CO2-induced swelling of coal experimentally observed was successfully predicted as resulting from the surface tension acting as a pre-stress and significantly affected by CO2-adsorption.
The adequate combination of poromechanics, physics of interfaces, and GCMC molecular simulations provide a winning global strategy to predict quantitatively the mechanical behavior of unsaturated porous materials subjected to various in-pore phase transitions. Indeed, paraphrasing the poet John Donne, “no scale is an island”.
1. Coussy, O., Pereira, J.-M., Vaunat, J., “Revisiting the Thermodynamics of Plasticity for Unsaturated Soils”, Computer and Geotechnics, doi: 10.1016/j.compgeo.2009.09.003, 2009.
2. Coussy, O., Mechanics and Physics of Porous Solids, John Wiley and Sons, to appear in 2010.
3. Vandamme, M., Brochard, L., Lecampion, B., Coussy, O., “Adsorption and Deformation : the CO2-induced swelling of coal”, submitted to the Journal of Mechanics and Physics of Solids.
4. Coussy, O., “Poromechanics of freezing materials”, Journal of Mechanics and Physics of Solids, Vol 53/8, 1689-1718, 2005.
5. Fabbri, A., Coussy, O., Fen-Chong, T., Monteiro, P, “Are deicing salts necessary to promote scaling in concrete?” Journal of Engineering Mechanics, 134:7, 589-597, 2008.
6. Coussy, O., Brisard, S., “Prediction of drying shrinkage beyond the pore iso-deformation assumption“, Journal of Mechanics of Solids and Structures, Vol. 4, N°2, 263- 279, 2009.