Random walk with barriers: Diffusion restricted by permeable membranes

Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using a bulk transport measurement. Here we demonstrate how the long-range structural correlations introduced by permeable membranes give rise to distinct features of transport. We consider Brownian motion restricted by randomly placed and oriented permeable membranes and focus on the disorder-averaged diffusion propagator using a scattering approach. The renormalization group solution reveals a scaling behavior of the diffusion coefficient for large times, with a characteristically slow inverse square root time dependence. The predicted time dependence of the diffusion coefficient agrees well with Monte Carlo simulations in two dimensions. Our results can be used to identify permeable membranes as restrictions to transport in disordered materials and in biological tissues, and to quantify their permeability and surface area.Comment: 8 pages, 3 figures; origin of dispersion clarified, refs adde

Accurate phase-shift velocimetry in rock

AbstractSpatially resolved Pulsed Field Gradient (PFG) velocimetry techniques can provide precious information concerning flow through opaque systems, including rocks. This velocimetry data is used to enhance flow models in a wide range of systems, from oil behaviour in reservoir rocks to contaminant transport in aquifers. Phase-shift velocimetry is the fastest way to produce velocity maps but critical issues have been reported when studying flow through rocks and porous media, leading to inaccurate results. Combining PFG measurements for flow through Bentheimer sandstone with simulations, we demonstrate that asymmetries in the molecular displacement distributions within each voxel are the main source of phase-shift velocimetry errors. We show that when flow-related average molecular displacements are negligible compared to self-diffusion ones, symmetric displacement distributions can be obtained while phase measurement noise is minimised. We elaborate a complete method for the production of accurate phase-shift velocimetry maps in rocks and low porosity media and demonstrate its validity for a range of flow rates. This development of accurate phase-shift velocimetry now enables more rapid and accurate velocity analysis, potentially helping to inform both industrial applications and theoretical models

Quantitative permeability imaging of plant tissues

A method for mapping tissue permeability based on time-dependent diffusion measurements is presented. A pulsed field gradient sequence to measure the diffusion encoding time dependence of the diffusion coefficients based on the detection of stimulated spin echoes to enable long diffusion times is combined with a turbo spin echo sequence for fast NMR imaging (MRI). A fitting function is suggested to describe the time dependence of the apparent diffusion constant in porous (bio-)materials, even if the time range of the apparent diffusion coefficient is limited due to relaxation of the magnetization. The method is demonstrated by characterizing anisotropic cell dimensions and permeability on a subpixel level of different tissues of a carrot (Daucus carota) taproot in the radial and axial directions

Direct observation of ion dynamics in supercapacitor electrodes using in situ diffusion NMR spectroscopy

Ionic transport inside porous carbon electrodes underpins the storage of energy in supercapacitors and the rate at which they can charge and discharge, yet few studies have elucidated the materials properties that influence ion dynamics. Here we use in situ pulsed field gradient NMR spectroscopy to measure ionic diffusion in supercapacitors directly. We find that confinement in the nanoporous electrode structures decreases the effective self-diffusion coefficients of ions by over two orders of magnitude compared with neat electrolyte, and in-pore diffusion is modulated by changes in ion populations at the electrode/electrolyte interface during charging. Electrolyte concentration and carbon pore size distributions also affect in-pore diffusion and the movement of ions in and out of the nanopores. In light of our findings we propose that controlling the charging mechanism may allow the tuning of the energy and power performances of supercapacitors for a range of different applications