Anomalies of molecular fluid flow through random media near their percolation threshold

• Applicant: Professor Dr. Felix Höfling
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 523950429

Fluid transport through porous media receives sustained research interest on the molecular scale, which is driven by, among other factors, its relevance for sustainability-related applications and the availability of tailored nano-porous materials. Despite much insight into continuum flows in random media, the interplay of fluid flow with a percolation transition and the repercussions of the molecular discreteness are poorly understood. In the vicinity of such a transition, the pore space exhibits a self-similar, maze-like structure and it is well-known, in equilibrium, that the Brownian motion of a single particle in such an environment leads to a series of intriguing anomalies; these include the emergence of sub-diffusion and persistent memory, which has received considerable scientific interest in recent years. The essence of this anomalous transport is condensed in the Lorentz gas model, a long-standing paradigm in statistical mechanics, which describes the dynamics of (non-interacting) gas particles confined to a random host structure. In this project, we replace the gas by a dense liquid, which introduces strong correlations into the confined fluid; in addition, we consider situations far from equilibrium by driving the fluid at the boundaries of the sample. The goal is a comprehensive understanding of the macroscopic, collective flow behaviour with focus on the critical regime at low porosity; in particular, one expects that some form of anomalous mass transport emerges near the percolation transition. Central questions to be clarified concern the factors and mechanisms that determine the flow. An example is the putative competition between excluded volume effects, slowing down the transport, and cooperative motion of fluid particles, potentially facilitating the flow. More fundamentally, we ask to what extent is the fluid flow, as a collective, non-equilibrium phenomenon, related to the tracer diffusion in equilibrium? How does the motion of a solute molecule that is carried along with the flow differ from the case of passive diffusion? The project is based on high-precision, non-equilibrium molecular dynamics simulations at large scales, combined with statistical characterisations and dynamic scaling analyses of the obtained data. This includes the calculation of permeability coefficients and non-linear flow–pressure relations beyond the Darcy regime, first-passage time distributions and break-through curves as well as heat dissipation within the porous medium. We anticipate that a scale invariance of the medium entails non-standard, universal spatial and temporal functional dependencies of these quantities. At a later stage of the project, we shall extend the study to specific chemical systems, which will allow us to connect the statistical physics insight obtained with concrete applications, such as phase separation processes of immiscible liquid mixtures by means of amorphous or heterogeneous molecular sieves.

• DFG Programme: Research Grants