Gibbs-Duhem equation is a fundamental relation of the thermodynamics of fluids that originates from the extensive behavior of fluids. Fluids adsorption in micro-porous media can break the extensivity with respect to volume, so that Gibbs-Duhem equation does not hold in general for adsorbed fluid. As a consequence, a total of 6 moduli are needed to fully describe the thermo-mechanics of an adsorbed fluid instead of 3 for bulk fluids (compressibility, thermal expansion, and heat capacity). In recent years, poromechanics theory has been extended to capture the effects of fluid adsorption in micro-porous media, but the non-validity of Gibbs-Duhem equation has been disregarded so far. We propose here a new formulation of poromechanics extended to adsorption which does not assume Gibbs-Duhem equation. The introduction of 6 fluid moduli instead of 3 is a rather fundamental change that requires to revisit the derivation from the fundamentals of poromechanics. In addition, the new poromechanics is formulated to capture thermo-mechanical couplings in double porosity media (micro- and macro-pores) with potential fluid transfers between the porosities. The final constitutive equations exhibit the same structure as in usual poromechanics, but with effective poromechanical properties that are affected by fluid confinement. The impact of assuming Gibbs-Duhem equation or not is discussed. In particular, we show that relaxing the assumption of Gibbs-Duhem may explain some experimental observations of adsorption-induced effects that are not captured by existing poromechanics. The proposed theory should improve our understanding of micro-porous materials with wide perspectives for applications (clay, cement, wood, bones, microporous carbons etc.).

Gibbs-Duhem方程是流体热力学的基本关系，其起源于流体的广泛行为。在微孔介质中吸附的流体可能会破坏体积的延伸性，因此对于所吸附的流体，Gibbs-Duhem方程通常不成立。结果，总共需要6个模数才能完整描述吸附流体的热力学，而不是散装流体的3个模数（可压缩性，热膨胀和热容）。近年来，多孔力学理论已被扩展以捕获微孔介质中流体吸附的影响，但迄今为止，吉布斯-杜海姆方程的无效性一直被忽略。在这里，我们提出了一种不考虑吉布斯-杜海姆方程的扩展到吸附的态力学的新公式。6模量而不是3模量的引入是一个相当根本的变化，需要重新考虑从微力学原理出发。另外，新的孔隙力学公式化了，以捕获双孔隙度介质（微孔和大孔）中的热力耦合，并在孔隙之间传递潜在的流体。最终的本构方程显示出与通常的poromechanics相同的结构，但具有受流体限制影响的有效poromechanical属性。讨论是否采用吉布斯-杜海姆方程的影响。尤其是，我们表明，放宽Gibbs-Duhem的假设可能可以解释一些实验性的观测结果，即现有的态力学无法捕捉到的吸附诱导作用。