We present an experimental and numerical study of immiscible two-phase flow of Newtonian fluids in three-dimensional (3D) porous media to find the relationship between the volumetric flow rate (Q) and the total pressure difference () in the steady state. We show that in the regime where capillary forces compete with the viscous forces, the distribution of capillary barriers at the interfaces effectively creates a yield threshold (), making the fluids reminiscent of a Bingham viscoplastic fluid in the porous medium. In this regime, Q depends quadratically on an excess pressure drop (). While increasing the flow rate, there is a transition, beyond which the overall flow is Newtonian and the relationship is linear. In our experiments, we build a model porous medium using a column of glass beads transporting two fluids, deionized water and air. For the numerical study, reconstructed 3D pore networks from real core samples are considered and the transport of wetting and non-wetting fluids through the network is modeled by tracking the fluid interfaces with time. We find agreement between our numerical and experimental results. Our results match with the mean-field results reported earlier.Electronic supplementary materialThe online version of this article (doi:10.1007/s11242-017-0874-4) contains supplementary material, which is available to authorized users.

Sodium-ion batteries are a promising battery technology for their cost and sustainability. This has led to increasing interest in the development of new sodium-ion batteries and new analytical methods to non-invasively, directly visualise battery chemistry. Here we report operando 1 H and 23 Na nuclear magnetic resonance spectroscopy and imaging experiments to observe the speciation and distribution of sodium in the electrode and electrolyte during sodiation and desodiation of hard carbon in a sodium metal cell and a sodium-ion full-cell configuration. The evolution of the hard carbon sodiation and subsequent formation and evolution of sodium dendrites, upon over-sodiation of the hard carbon, are observed and mapped by 23 Na nuclear magnetic resonance spectroscopy and imaging, and their threedimensional microstructure visualised by 1 H magnetic resonance imaging. We also observe, for the first time, the formation of metallic sodium species on hard carbon upon first charge (formation) in a full-cell configuration.

Quantitative mapping of metal ions freely diffusing in solution is important across a diverse range of disciplines and is particularly significant for dissolution processes in batteries, metal corrosion, and electroplating/polishing of manufactured components. However, most current techniques are invasive, requiring sample extraction, insertion of an electrode, application of an electric potential or the inclusion of a molecular sensor. Thus, there is a need for techniques to visualize the distribution of metal ions non‐invasively, in situ, quantitatively, in three dimensions (3D) and in real time. Here we have used 1H magnetic resonance imaging (MRI) to make quantitative 3D maps showing evolution of the distribution of Cu2+ ions, not directly visible by MRI, during the electrodissolution of copper, with high sensitivity and spatial resolution. The images are sensitive to the speciation of copper, the depletion of dissolved O2 in the electrolyte and show the dissolution of Cu2+ ions is not uniform across the anode.

Quantitative mapping of metal ions freely diffusing in solution is important across ad iverse range of disciplines and is particularly significant for dissolution processes in batteries,m etal corrosion, and electroplating/polishing of manufactured components.H owever,m ost current techniques are invasive,r equiring sample extraction, insertion of an electrode,application of an electric potential or the inclusion of am olecular sensor.T hus,t here is an eed for techniques to visualize the distribution of metal ions non-invasively,i nsitu, quantitatively,inthree dimensions (3D) and in real time.Here we have used 1 Hm agnetic resonance imaging (MRI) to make quantitative 3D maps showing evolution of the distribution of Cu 2+ ions,n ot directly visible by MRI, during the electrodissolution of copper,w ith high sensitivity and spatial resolution. The images are sensitive to the speciation of copper,the depletion of dissolved O 2 in the electrolyte and showt he dissolution of Cu 2+ ions is not uniform across the anode.Inmany electrochemical experiments,i ti so ften assumed that the total measured current is distributed uniformly across the entire electrode surface.A ny evidence for an inhomogeneous distribution usually comes from post-mortem examination of electrode surfaces,w hich typically requires the system to be dismantled. This is adestructive process and can be,i nt he case of some batteries,p otentially dangerous. Hence,t here has long been considerable interest in the development of non-invasive,i nsitu measurements of local current distribution. One of the biggest challenges,i nt his respect, is the detection of the distribution of metal ions in solution, which is critical for the development of improved battery,anti-corrosion, and electroplating technologies.Thedetection of metal ions in solution can be performed either spectroscopically or electrochemically.I nsitu electrochemical detection typically uses ion-selective electrodes or scanning electrochemical microscopy [1] (SECM), which is often combined with anodic stripping voltammetry [2] (ASV) to detect metal-ion concentrations at the interface between the electrolyte and metal with as patial resolution on the order of tens of microns at concentrations in the parts per billion (ppb) to parts per trillion (ppt). However,a st he sample must be scanned relative to an electrode tip,t he technique is invasive,r esulting in the disturbance of mass transfer profiles,and images can be relatively slow to collect, cover arelatively small area (on the order 10 2 10 2 mm 2 )and are generally limited to atwo-dimensional (2D) region within the diffusion layer. In situ spectroscopic monitoring of electrochemical reactions [3] has employed av ariety of techniques,including UV/Vis,infrared (IR), and Raman spectroscopies.T he spectroscopic detection of metal ions is most commonly achieved through the use of molecular sensors, [4] which are typically probed using fluorescence spectroscopy or microscopy,enabling detection of the presence,concentration and envir...

Precipitation reactions influence transport properties in porous media and can be coupled to advective and dispersive transport. For example, in subsurface environments, mixing of groundwater and injected solutions can induce mineral supersaturation of constituents and drive precipitation reactions. Magnetic resonance imaging (MRI) and microcomputed tomography (μ-CT) were employed as complementary techniques to evaluate advection, dispersion, and formation of precipitate in a 3D porous media flow cell. Two parallel fluids were flowed concentrically through packed glass beads under two relative flow rates with NaCO and CaCl in the inner and outer fluids, respectively. CaCO became supersaturated and formed a precipitate at the mixing interface between the two solutions. Spatial maps of changing local velocity fields and dispersion in the flow cell were generated from MRI, while high resolution μ-CT imaging visualized the precipitate formed in the porous media. Formation of a precipitate minimized dispersive and advective transport between the two fluids and the shape of the precipitation front was influenced by the relative flow rates. This work demonstrates that the combined use of MRI and μ-CT can be highly complementary in the study of reactive transport processes in porous media.