Reports: ND849139-ND8: Modeling the Coupling of Elastic Anisotropy and Network Topology in Poroelastic Transport

Jeffrey Rickman, PhD , Lehigh University

Considerable progress has been made in elucidating the impact of a poroelastic medium on the transport behavior of the fluid. This coupling of fluid transport and material deformation is relevant in many physical situations including, for example, flow through gels, soil consolidation, and earth subsidence associated with oil recovery. Our program comprises several interrelated efforts.In some recent work, we have examined tracer diffusion in the presence of mobile obstacles. As hindered diffusion occurs in many different systems, we have chosen to focus on the particularly important case of tracer diffusion in a binary alloy. For this purpose, we have employed Monte Carlo simulation to describe the transport kinetics of the components of a two-dimensional lattice gas comprising two species, A and B, wherein one of the species (namely B) interacts with randomly-distributed line defects (such as dislocations) to form equilibrium (i.e., Cottrell) atmospheres at late times. Various kinetic assumptions and defect densities are explored to highlight the role of minority-atom mobility and interaction strength on the dynamics of the A atoms. From the calculated instantaneous diffusivity, several diffusive regimes are then identified and related to evolving segregation profiles and, in particular, to the free area available for diffusion. The results of this work were recently publish in Physica A.In a current, complementary effort, we seek to understand the diffusive flow of a fluid through a deformable crystalline solid at the atomic scale. More specifically, we employ both Monte Carlo (MC) and molecular dynamics (MD) simulations to model the diffusive behavior of small atoms through a crystalline solid comprising larger atoms. MC simulation is used to create a reservoir of small atoms having a fixed chemical potential that is attached to the crystal. Thus, MC simulation is used here to generate a grand-canonical ensemble so that the crystal is in contact with a mechanism that provides a driving force for diffusion. The dynamics of the small and host atoms in the crystal are simulated using MD and, in particular, we calculate the mean-squared displacement of the small atoms over a long time scale. Thus far we have written the necessary codes, and are now beginning the simulation of atomic transport.Our aim here is to describe fluid uptake in a deformable medium. It is expected that we will be able to identify two distinct regimes, a Fickian regime associated with the flow of relatively small spheres that create little distortion of the crystalline medium and a non-Fickian regime in which relatively large spheres generate self stresses in the crystal. In this latter regime one expects that diffusion may be spatially nonlocal as the concentration field of the diffusing species is coupled to the elastic field in the solid. If one assumes that the elastic fields relax quickly on the time scale of diffusive motion, then the associated diffusivity is modified by a chemical driving force that depends on the spatial distribution of the smaller atoms.The next step in this effort is the simulation of diffusion through a deformable porous network at the atomic scale. For this purpose, we will construct a hybrid model in which the small atoms move through an effective medium in which interactions are integrated over atomic planes. Thus, the diffusing species will be treated atomistically while the host medium will be described by an effective, Steele-like potential. Moreover, the host medium will be deformable as we will build into this description an energy penalty associated with changing the distance between the atomic planes. With this approach we will be able to construct porous networks with a desired distribution of pore sizes and connectivities and, in so doing, investigate the impact of pore network geometry on the diffusive transport of the smaller species.
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