Transport Diffusion Coefficient Research Articles

Relative contributions of mobility and partitioning to volatile fatty acid flux during electrodialysis

Economically valuable volatile fatty acids (VFAs) are sustainably produced via fermentation processes. To use VFAs downstream, they must be recovered using technologies like electrodialysis (ED). Solute transport properties (i.e., partition coefficient (K), diffusion coefficient (D), and permeability (P=KD)) govern flux in ED. Therefore, to advance understanding of VFA flux through anion exchange membranes (AEMs) in ED, we aimed to elucidate the relative contributions of VFA partitioning and mobility to their flux. Accordingly, for VFAs of different sizes (C1–C5) and inorganic anions (Cl–, Br–), we measured their fluxes during ED, permeabilities, and partition coefficients, and calculated the diffusion coefficients. We then evaluated the correlations between flux and transport properties and between transport properties and anion physicochemical properties. Results showed VFA flux had a strong correlation with permeability (R2=0.94, p<0.01), consistent with flux described by the Nernst-Planck equation. Further, while there was a negative correlation between VFA flux and partition coefficient (R2=0.46, p=0.21), there was a positive correlation between VFA flux and diffusion coefficient (R2=0.95, p<0.01) which showed VFA mobility governed VFA flux. We observed a negative correlation between VFA diffusion coefficient and carbon–chain length which was attributed to steric hindrance, and a positive correlation between partition coefficient and carbon chain-length which we attributed to hydrophobicity and polarizability. This work provides fundamental insight on interactions between VFAs and AEMs which affect anion flux during ED.

Shoreline evolution in adjacent to a coastal structure in Hiep Thanh commune, Duyen Hai district, Tra Vinh province

Coastal erosion is significant along the coastline in Hiep Thanh commune, Duyen Hai district, Tra Vinh province, Viet Nam. In order to address this severe coastal erosion, the local community has constructed a concrete embankment as an emergency solution to protect the coastline. However, this solution exacerbates the issue since the fundamental processes of coastal erosion remain inadequately explored and understood. Specifically, in beach sections without the concrete embankment, erosion still occurs. Therefore, this paper aims to investigate the shoreline changes adjacent to the embankment using an integrated approach with remote sensing and diffusion theory. The results show that beach erosion is occurring near the embankment at a rate of 44 meters per year, and the diffusion coefficient for longshore sand transport in the study area is 130 square meters per day. This study offers a practical approach to examining changes in the shoreline adjacent to a coastal structure, particularly valuable in situations where there is a scarcity of measured field data.

Experimental validation of momentum transport theory in the core of H-mode plasmas in the ASDEX Upgrade tokamak

This study employs the established momentum transport analysis at ASDEX Upgrade [Zimmermann et al., Nucl. Fusion 63, 124003 (2023)] to investigate the parametric variations of the momentum transport coefficients in the core of H-mode plasmas. These experimental results are compared to a comprehensive database of gyrokinetic calculations. Generally, good agreement between predicted and measured diffusive and convective transport coefficients is found. The predicted and measured Prandtl numbers correlate most dominantly with the magnetically trapped particle fraction. The experimentally inferred pinch numbers strongly depend on the logarithmic density gradient and magnetic shear, consistent with the theoretical predictions of the Coriolis pinch. The intrinsic torque from residual stress in the inner core is small, scales with the local logarithmic density gradient, and the data indicate a possible sign reversal. In the outer periphery of the core, the intrinsic torque is always co-current-directed and scales with the pressure gradient. This is consistent with prior experimental findings and global, non-linear gyrokinetic predictions. It suggests that profile shearing effects generate the intrinsic torque in the inner core. Toward the outer core, most likely, effects from E×B-shearing become more influential. These results offer the first comprehensive picture of this transport channel in the core plasma and contribute to validating the corresponding theoretical understanding. The derived scaling laws are used to construct a reduced momentum transport model, which has been validated against an additional dataset. This demonstrates that the model captures the essential contributions to momentum transport in the core of H-mode plasmas.

Spectrum of the Boltzmann collision operator for λϕ4 theory in the classical regime

We analytically determine all the eigenvalues and eigenfunctions of the linearized Boltzmann collision operator (computed using Boltzmann statistics) in massless scalar λϕ4 theory. This is used to determine this system's shear viscosity and particle diffusion transport coefficients in analytical form. The corresponding relaxation time approximation for this linearized Boltzmann equation is also derived.

Decoupling of ion-transport from polymer segmental relaxation and higher ionic-conductivity in poly(ethylene oxide)/succinonitrile composite-based electrolytes having low lithium salt doping.

Only limited enhancement in room-temperature ionic-conductivity for poly(ethylene oxide), PEO, based electrolytes is possible due to coupling between ionic-conductivity and segmental relaxation. In the present study, we have achieved ionic-conductivity of 1.07 × 10-3 and 6.20 × 10-4 S cm-1 at 313 and 298 K, respectively, by adding 45 wt% of succinonitrile (SN) in PEO having low LiTFSI loading (Li : EO = 1 : 20). This enhancement in the ionic-conductivity is attributed to faster ion transport (diffusion coefficient, D = 3.63 × 10-5 cm2 s-1) occurring through the ion-transport channels as confirmed by positron annihilation lifetime spectroscopy. The ionic-transport through these channels is observed to be highly decoupled from the segmental relaxations as confirmed using broadband dielectric spectroscopy through Ratner's approach. The observed decoupling of ionic-conductivity from PEO segmental relaxation in PEO-SN composite-based electrolytes would be useful to design rather inexpensive all solid-state polymer electrolytes for Li ion batteries.

Viscous QCD medium effects on the bottom quark transport coefficients

The bottom quark transport coefficients, i.e., drag and diffusion coefficients, have been studied for the collisional and soft gluon radiative processes within the viscous QCD medium. The thermal medium effects are incorporated using the effective fugacity quasiparticle model (EQPM). Both the shear and bulk viscous effects at leading order are embedded through the near-equilibrium distribution functions of the quark–gluon plasma (QGP) constituent quasiparticles. The transport coefficients’ dependence on the bottom quark’s initial momentum and QGP temperature have been investigated. The relative dominance of the radiative over the collisional process for the bottom quark seems to occur at a higher initial momentum compared to that of the charm quark. In contrast, the effect of the viscous corrections seems to be more for the charm quark. Furthermore, we also investigate the validity of the Einstein fluctuation–dissipation theorem for our analysis.

(Invited) Microelectrode-Based Diagnosis of Charge Propagation and Redox Transitions in Concentrated Polyoxometallate Electrolyte of Potential Utility for Redox Flow Battery

Concentrated solutions of Keggin-type silicotungstic acid, as well as the system’s single crystals (H4SiW12O40*31H2O) and their colloidal suspensions have been tested using the microelectrode methodology to determine mass-transport, electron self-exchange and apparent (effective) diffusion-type coefficients for charge propagation and homogeneous (electron self-exchange) rates of electron transfers. Silicotungstic acid facilitates proton conductivity, and undergoes fast, reversible, multi-electron electron transfers leading to the formation of highly conducting, mixed-valence (tungsten(VI,V) heteropoly blue) compounds. To develop useful electroanalytical diagnostic criteria, electroanalytical approaches utilizing microdisk electrodes have been adapted to characterize redox transitions of the system and to determine kinetic parameters. Combination of micoroelectrode-based experiments performed in two distinct diffusional regimes: radial (long-term experiment; e.g., slow scan rate voltammetry or long-pulse chronoamperometry) and linear (short-term experiment; e.g., fast scan rate voltammetry or short-pulse chronocoulometry) permits absolute determination of such parameters as effective concentration of redox centers (C0 ) and apparent transport (diffusion) coefficient (Dapp ). The knowledge of these parameters, in particular of [Dapp 1/2 C0 ] seems to be of importance to the evaluation of utility of redox electrolytes for charge storage.While current densities which reflect dynamics of electrochemical processes have an influence on the systems’ current densities, the viscosity of the electrolyte and the mass transport dynamics are also affected by the nature of the redox-active material and its concentration. Trying to develop useful electroanalytical diagnostic approaches, we have successfully utilized microelectrode-based probes, as well as the historical concepts of charge propagation in semi-solid or semi-liquid systems developed for mixed-valence polynuclear materials in order to characterize concentrated redox electrolytes. Among important parameters are concentration of redox centers (C0 ) and apparent transport (diffusion) coefficient (Dapp ). The knowledge of these parameters and, in particular of [Dapp 1/2 C0 ], are crucial when it comes to evaluation of the diffusional-type charge propagation dynamics in the concentrated electrolyte which may reflect both physical mass transport and electron self-exchange (electron-hopping) contributions. Both potential-step (chronocoulometry, chronoamperometry) and cyclic voltammetric experiments utilizing microdisk electrodes have been adapted to characterization (identification of redox transitions and determination of kinetic parameters) of model inorganic redox electrolytes, namely highly-concentrated solutions or colloidal suspensions of Keggin-type polyoxometallate, silicotungstic acid.

Molecular insights on influence of CO2 on CH4 adsorption and diffusion behaviour in coal under ultrasonic excitation

Decoupling the molecular structure from the pore structure is challenging under experimental conditions; this hinders the independent investigation of the effect of the changes in molecular structure on methane (CH4) transport. In this study, the molecular model of coal was reconstructed based on the test results of X-ray photoelectron spectroscopy (XPS) and 13C nuclear magnetic resonance (13C NMR). A grand canonical Monte Carlo (GCMC) based molecular dynamics (MD) simulation method was used to independently investigate the effect of CO2 on CH4 adsorption and diffusion behaviour in coal under changes in the molecular structure of coal after ultrasonic excitation. The experimental results show that, under ultrasonic excitation, the proportion of oxygen content in the coal increases and the oxygen-containing functional groups (carboxyl groups, ether bonds/hydroxyl groups) increase compared to the original coal. The simulation results show that the amount of CH4 adsorbed, the isosteric heat and the proportion of low-energy CH4 in the coal sample decrease after ultrasonic excitation for the same pore size. Furthermore, for the same pore size and CO2 partial pressure ratio, adsorption selectivity factor increases after ultrasonic treatment. Additionally, for the same pore size and the same CO2 partial pressure ratio, the interaction energy between CH4 and coal in the CH4–CO2–coal mixed system decreases and the density of high-energy CH4 increases after ultrasonic excitation; this leads to an increase in CH4 self-diffusion and transport diffusion coefficient. The presence of oxygen-containing functional groups causes a significant increase in the electrostatic potential difference between CO2 and coal as compared to that between CH4 and coal, which is the fundamental reason for the change in the effect of CO2 on the adsorption-diffusion behaviours of CH4. Our findings revealed the micro-mechanism of ultrasonic-assisted coalbed methane extraction and demonstrated the effectiveness of ultrasonic-CO2 collaborative technology.

Tracer diffusion coefficients in a moderately dense granular suspension: Stability analysis and thermal diffusion segregation

The diffusion transport coefficients of a binary granular suspension where one of the components is present in tracer concentration are determined from the (inelastic) Enskog kinetic equation. The effect of the interstitial gas on the solid particles is accounted for in the kinetic equation through two different terms: (i) a viscous drag force proportional to the particle velocity and (ii) stochastic Langevin-like term defined in terms of the background temperature. The transport coefficients are obtained as the solutions of a set of coupled linear integral equations recently derived for binary granular suspensions with arbitrary concentration [Gómez González et al., “Enskog kinetic theory for multicomponent granular suspensions,” Phys. Rev. E 101, 012904 (2020)]. To achieve analytical expressions for the diffusion coefficients, which can be sufficiently accurate for highly inelastic collisions and/or disparate values of the mass and diameter rations, the above integral equations are approximately solved by considering the so-called second Sonine approximation (two terms in the Sonine polynomial expansion of the distribution function). The theoretical results for the tracer diffusion coefficient D0 (coefficient connecting the mass flux with the gradient of density of tracer particles) are compared with those obtained by numerically solving the Enskog equation by means of the direct simulation Monte Carlo method. Although the first-Sonine approximation to D0 yields, in general, a good agreement with simulation results, we show that the second-Sonine approximation leads to an improvement over the first-Sonine correction, especially when the tracer particles are much lighter than the granular gas. The expressions derived here for the diffusion coefficients are also used for two different applications. First, the stability of the homogeneous steady state is discussed. Second, segregation induced by a thermal gradient is studied. As expected, the results show that the corresponding phase diagrams for segregation clearly differ from those found in previous works when the effect of gas phase on grains is neglected.

Fast transport diffusion of bound water in cellulose fiber network

AbstractA remarkable property of cellulose-based materials is that they can absorb huge amounts of water (25% of the dry mass) from ambient vapor, in the form of bound water confined at a nanoscale in the amorphous regions of the cellulose structure. The control of the dynamics of sorption and desorption of bound water is a major stake for the reduction of energy consumption and material or structure damages, but in the absence of direct observations this process is still poorly known. Here we present measurements of bound water transport thanks to Nuclear Magnetic Resonance relaxometry and Magnetic Resonance Imaging measurements. We show that the bound water is transported along the fibers and throughout the network of fibers in contact. For each material a single transport diffusion coefficient value allows to represent the processes over the whole range of saturation. The dependence of the transport diffusion coefficient on the fiber density and orientation is then analyzed to deduce the (elementary) transport diffusion coefficient of bound water along a cellulose fiber axis. This constitutes fundamental physical data which may be compared with molecular simulations, and opens the way to the prediction and control of sorption dynamics of all cellulosic materials or other hygroscopic materials.

Numerical modelling of heat transfer and simulation of a 5.56 mm rifle barrel

Numerical simulations tend to be useful to have a deep knowledge of phenomena difficult to be observed. In this context, the heat transfer in a 5.56 mm rifle barrel was modelled, simulated and analysed, coupling the Baer-Frankle interior ballistics approach with one and two-dimensional unsteady heat diffusion numerical models. The heat transfer coefficient correlation was obtained using Sutherland approximation of diffusive transport coefficient and output data from PRODAS interior ballistics simulation software. The one-dimensional heat transfer model was solved in MATLAB® environment while the two-dimensional heat transfer model was solved in COMSOL Multiphysics and Simulation Software. The results were verified, providing discrepancies minor than 7% in relation to reference data.

Revisiting the Mechanisms of Charge Transport in Solutions of Redox-Active Molecules Using Computer Simulations: When and Why Do Analytical Theories Fail?

Understanding charge transport is essential for the development of energy-storage applications. This work introduces a new theoretical methodology to model diffusive charge transport in solutions of redox-active molecules by combining Langevin dynamics for the spatial degrees of freedom and a master-equation formalism to describe the electron-hopping events between redox molecules. The model is used to analyze the effects of the concentration of the redox molecules and the strength of the intermolecular interactions on the charge-transport mechanism. In the past, the rate of charge transport has been modeled with the analytical Dahms-Ruff equation; however, this is a mean-field equation, whose range of validity has not been tested with less approximate theories. We show that the Dahms-Ruff equation fails to quantitatively predict the diffusion coefficient for charge transport for large concentrations of the redox species and high bimolecular electron-transfer rates, i.e., the most relevant conditions for energy-storage applications. Under these conditions, the diffusion coefficient for charge transport obtained from simulations is larger than that predicted from the Dahm-Ruff equation because of the formation of transient clusters of redox molecules. Also, intermolecular interactions, which are not taken into account by the Dahms-Ruff equation, play a central role in the charge transport of redox species. We show that the apparent diffusion coefficient experiences a maximum with respect to the strength of the intermolecular attractions. This maximum is traced back to the formation of clusters and their two opposite effects on the diffusion coefficient: electron hopping is fast within a cluster but inefficient between neighboring clusters.

Microelectrode-based probing of charge propagation and redox transitions in concentrated polyoxometallate electrolyte of potential utility for redox flow battery

Concentrated solutions of Keggin-type silicotungstic acid, as well as the system’s single crystals (H4SiW12O40*31H2O) and their colloidal suspensions have been tested using the microelectrode methodology to determine mass-transport, electron self-exchange and apparent (effective) diffusion-type coefficients for charge propagation and homogeneous (electron self-exchange) rates of electron transfers. Silicotungstic acid facilitates proton conductivity, and undergoes fast, reversible, multi-electron transfers leading to the formation of highly conducting, mixed-valence (tungsten(VI,V) heteropoly blue) compounds. To develop useful electroanalytical diagnostic criteria, electroanalytical approaches utilizing microdisk electrodes have been adapted to characterize redox transitions of the system and to determine kinetic parameters. Combination of microelectrode-based experiments performed in two distinct diffusional regimes: radial (long-term experiment; e.g., slow scan rate voltammetry or long-pulse chronoamperometry) and linear (short-term experiment; e.g., fast scan rate voltammetry or short-pulse chronocoulometry) permits absolute determination of such parameters as effective concentration of redox centers (C0) and apparent transport (diffusion) coefficient (Dapp). The knowledge of these parameters, in particular of [Dapp1/2 C0] seems to be of importance to the evaluation of utility of redox electrolytes for charge storage. For the colloidal suspension of silicotungstic acid (H4SiW12O40) crystals in the saturated solution, the following values have been obtained: Dapp = 1.8*10-6 cm2 s−1 and C0 = 1.1 mol dm−3, as well as the [Dapp1/2 C0] diagnostic parameter has reached the value as high as 6*10-3 mol/dm−3 cm s−1/2, provided that four electrons are involved in the H4SiW12O40 redox transitions. In this respect, the fact that crystals (dispersed solids) are characterized by high electron self-exchange rate (kex = 1.1*108 dm3 mol−1 s−1) and low activation energy (EA = 18.7 kJ mol−1) facilitating electron transfers between immobilized WVI and WV redox sites is also advantageous.

Electrochemical study of agarose hydrogels for natural convection on macroelectrodes and ultramicroelectrodes

Electrochemical measurements using an agarose hydrogel as a solid electrolyte and ferrocyanide as a redox probe were conducted to analyze transport properties and natural convection effects. The mass transport properties and diffusion coefficients of ferrocyanide were studied using various macroelectrodes and ultramicroelectrodes via cyclic voltammetry. The experimental results confirmed that the mass transfer behavior in agarose was similar to that in solution. The good linearity of the square root of the scan-rate-dependent peak current demonstrated that diffusion is dominant during mass transfer in agarose hydrogel owing to a reduction in other mass transport effects (i.e., migration and convection). Furthermore, chronoamperometry (CA) was performed to estimate the effects of natural convection in the solution and agarose hydrogel. CA curves and plots of current as a function of the inverse square root of time yielded irregular and irreproducible responses in the solution for relatively long-term electrochemistry. However, in the agarose hydrogel, the CA response was more regular and reproducible for > 300 s because of reduced natural convection, based on the Cottrell’s theory.

Molecular Study of Nonequilibrium Transport Mechanism for Proton and Water in Porous Proton Exchange Membranes

The transport process of proton and water through a porous proton exchange membrane (PEM) under pressure difference is significant to fuel cell performance. Nonequilibrium molecular dynamics simulations were conducted to investigate the diffusion mechanisms of hydronium ions and water molecules under pressure differences. Here, different driving forces (0.15 kcal/(mol·Å)–0.45 kcal/(mol·Å)) were applied to hydronium ions and water molecules as they transported through Nafion 117 membrane at temperatures between 300 K and 350 K. Results indicated that the transport diffusion coefficient of water molecules was larger than that of hydronium ions under different pressure drops due to the lower molecular weight and diffusion activation energy of water molecules (20.25 kJ/mol). Hydronium ions formed stronger hydrogen bonds with sulfonic acid groups than water molecules, which resulted in a higher diffusion activation energy for hydronium ions (21.15 kJ/mol). The proton conductivity rose with the increase in pressure difference. Moreover, the transport diffusion coefficient of water molecules and hydronium ions were positively correlated with temperature. This is because the kinetic energy of molecules increased and the pore size of the Nafion membrane enlarged at high temperatures. In addition, the dynamics of the hydrogen bond between hydronium ions and sulfonic acid groups/water molecules were accelerated at elevated temperatures, which further promoted proton transfer.

Simulated EIS and Trukhan model to study the ion transport parameters associated with Li+ ion dynamics in CS based polymer blends inserted with lithium nitrate salt

In the current work electrical and ion transport parameters of polymer electrolyte (PE) system of chitosan (Ch)/poly(2-oxazoline) (POZ)loaded with various concentrations of lithium nitrate (LiNO3) salt were studied. The EIS analysis shows that the load of LiNO3 improves the conductivity of the PE. The depressed semicircle of EIS which its center is below the Zr-axis and the distribution of relaxation time (τ) of the electrolytes verify the non-Debye behavior of the electrolytes. The maximum conducting system (CSPZLI5) shows the highest conductivity of 1.46 × 10−3 S/cm. Transport parameters (number density (n), mobility (μ), viscosity (η), and diffusion coefficient (D) of ions) are measured by Trukhan and EIS methods and compared agreeably and it is also consistent with the conductivity results. The determined n value from EIS was found to increase from 1.69 × 1016cm−3 to 9.5 × 1019 cm−3. Distinguished areas of stability attributed to DC involvement were marked from AC spectra. Dielectric parameters (i.e. ε' and ε'') are high at the low-frequency (fr) window due to electrode polarization (EP). The loss tangent (tan δ) is used to measure the relaxation time (τ) and ion transport parameters. The τ for the PEs is set off to decrease with increase of LiNO3 amount. The minimum τ of 4.08 × 10−7 s confirms the LiNO3 role in increasing ion migration. The transport parameters (n, μ, D, and η) are also in relationship with the dielectric and impedance analyses. From electric modulus examination it is found that the EP contribution can be minimized and relaxation attributing to bulk effects can be highlighted.

Ion Flux Self-Regulation Strategy with a Volume-Responsive Separator for Lithium Metal Batteries.

Lithium metal batteries (LMBs) are regarded as one of the most promising next-generation energy storage devices due to their high energy density. However, the conversion of LMBs from laboratory to factory is hindered by the formation of lithium dendrites and volume change during lithium stripping and deposition processes. In this work, a volume-responsive separator with core/shell structure thermoplastic polyurethane (TPU)/polyvinylidene fluoride (PVDF) fibers and SiO2 coating layers is designed to restrict dendrite growth. The TPU/PVDF-SiO2 separator can accommodate the volume change like an artificial lung and keep intimate contact with the electrodes, which leads to the formation of a uniform and high-density solid-electrolyte interphase. Meanwhile, the separator can regulate the transport channels and diffusion coefficients (D) of lithium ions with the change of porosity from both experimental and ab initio molecular dynamic analysis. The Li symmetric cells assembled with the TPU/PVDF-SiO2 can run for 1000 h at the current of 1.0 mA cm-2 without a short circuit. Moreover, the low melting point of PVDF can shut the ionic conduction down at 170 °C, guaranteeing the thermal safety of the batteries. With the above advantages, the TPU/PVDF-SiO2 separator presents great potential to promote the commercial and industrial application of LMBs.

Measuring Lithium-Ion Transport Properties in Electrolytes Via in Situ Infrared Spectroscopy

Electrolyte transport capability is a critical measure of battery function for both current Li-ion technology and chemistries beyond Li-ion. Ion transport plays a vital role in fast-charging, lithium plating, and performance under extreme temperature and cycling conditions. Though traditional electrolytes have been widely studied, current experimental methods do not allow for simple measurements of transport properties, often requiring large electrolyte volumes, long experiment times, and a dilute assumption. In this research, we developed analytical models that accurately predict apparent diffusion coefficient and transference number from numerical models of electrolyte ion concentrations in a lithium symmetric cell. The first analytical model utilized one-dimensional diffusion to predict the transient response of lithium concentration in the bulk electrolyte to an applied current. The second analytical model predicted lithium-ion concentration decay in a Li/Li cell at the electrode surface following a brief current pulse. The analytical models were used to fit numerical finite difference simulations of Li/Li cell performance to predict transport properties. This result suggests that current pulse methods can be applied to experimentally ascertain electrolyte diffusion properties. A new diagnostic is under development for characterizing electrolyte transport properties, diffusion coefficient and transference number, using the current pulse method applied to an in situ symmetric Li/Li cell. This diagnostic utilizes Fourier transform infrared spectroscopy and attenuated total reflectance to measure transport properties with low volumes of electrolyte and short experiment times. This capability may enable simple and rapid measurement of transport properties for electrolyte candidate screening and enrich broader understanding of electrolyte transport.

Ion alfvén velocity fluctuations and implications for the diffusion of streaming cosmic rays

The interstellar medium (ISM) of star-forming galaxies is magnetized and turbulent. Cosmic rays (CRs) propagate through it, and those with energies from ∼ GeV − TeV are likely subject to the streaming instability, whereby the wave damping processes balances excitation of resonant ionic Alfvén waves by the CRs, reaching an equilibrium in which the propagation speed of the CRs is very close to the local ion Alfvén velocity. The transport of streaming CRs is therefore sensitive to ionic Alfvén velocity fluctuations. In this paper we systematically study these fluctuations using a large ensemble of compressible MHD turbulence simulations. We show that for sub-Alfvénic turbulence, as applies for a strongly magnetized ISM, the ionic Alfvén velocity probability density function (PDF) is determined solely by the density fluctuations from shocked gas forming parallel to the magnetic field, and we develop analytical models for the ionic Alfvén velocity PDF up to second moments. For super-Alfvénic turbulence, magnetic and density fluctuations are correlated in complex ways, and these correlations as well as contributions from the magnetic fluctuations sets the ionic Alfvén velocity PDF. We discuss the implications of these findings for underlying “macroscopic” diffusion mechanisms in CRs undergoing the streaming instability, including modeling the macroscopic diffusion coefficient for the parallel transport in sub-Alfvénic plasmas. We also describe how, for highly-magnetized turbulent gas, the gas density PDF, and hence column density PDF, can be used to access information about ionic Alfvén velocity structure from observations of the magnetized ISM.

Ultramicroelectrode Based Approaches to Diagnose Utility of Redox Electrolytes in Flow Batteries

The proposed redox electrolyte system, concentrated solutions of Keggin type silicotungstic acid (H4SiW12O40), have been tested using the microelectrode methodology to determine mass-transport (effectively diffusional) coefficients for charge propagation and homogeneous (electron self-exchange) rates of electron transfers. Silicotungstic acid (H4SiW12O40) acts as proton conductors, and undergoes fast, reversible, multi-electron electron transfers leading to the formation of highly conducting, mixed-valence (tungsten(VI,V) heteropoly blue) compounds. To develop useful electroanalytical diagnostic criteria, electroanalytical approaches utilizing ultramicrodisk electrodes have been adapted to characterization of redox electrolytes. Combination of two parallel ultramicroelectrode-based experiments performed under radial (long-term experiment; e.g., slow scan rate) and linear (short-term experiment; e.g., fast scan rate) diffusion conditions permits determination of both effective concentration of redox centers and transport (diffusion) coefficient parameters, which are crucial to evaluation of the utility of a redox electrolyte for charge storage.