Poromechanics Beyond the Second Law of Thermodynamics

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

The entire field of continuum mechanics has been developed subject to the axiom of the second law of thermodynamics. This axiom implies a non-negative rate of irreversible entropy production. Yet, the results of contemporary physics have shown that this law does not hold at very small spatial and/or temporal scales. The fluctuation theorem instead describes entropy as a stochastic quantity that is exponentially more likely to be positive than negative and, upon ensemble averaging, leads to the conventional second law inequality. This theorem has already replaced the second law in considerations of the rheological and thermal responses of liquids. Consequently, the continuum models for fluid filled porous media must be reformulated. The research outcomes would be significant both for the fundamental understanding of geological, biological and man-made materials. In particular, mechanistic description of the material responses will be modified according to the microstructure and its characteristic length scales. As a result, this research will provide new insight into the mechanics of highly complex media such as gels, fluid-saturated rock systems, cardiovascular and pulmonary tissues. The PI plans to offer short courses related to the mechanics of random and fractal materials and structures, and will expand the delivery of a high-school-level short course on fractals. Selected images and animations obtained through the research will be integrated into outreach programs to enrich the K-12 educational system. Research supported under this award seeks to define a paradigm shift in continuum mechanics and, especially, poromechanics. The research aims to answer the question how the consideration of the fluctuation theorem may alter our understanding of the continuum mechanics of porous media. A stochastic thermomechanics framework with internal variables considering the fluctuation theorem in place of the second law axiom will be formulated. The admission of random scatter in nanoscale systems, with possible violations of the Clausius-Duhem inequality, will lead to a modification of Darcy's law, of the poromechanical constitutive relations and of the heat conduction relations. The new formulation would explicitly account for scale dependence. The effective permeability and heat conduction moduli are expected to turn out to be higher than as dictated by classical continuum theories. Next, homogenized constitutive descriptions will be established based on a micropolar theory for the use in random, and possibly fractal, fluid-saturated media. New forms of field and differential equations will be derived and employed to derive solutions of relevant initial-boundary value problems, thereby modifying the conventional solutions of problems of continuum poromechanics.