Laplace transform methods for transient diffusion; or, some good questions from Ralph White

Motivated by years of correspondence with Prof. Ralph White, I discuss two unconventional ways to solve diffusion problems with Laplace transforms. A method to derive error-function series, alternatives to Fourier series that converge rapidly and avoid the Gibbs phenomenon at short times, is illustrated by example. It is shown how Mittag-Leffler partial-fractions expansions can facilitate derivations of Fourier-series solutions from the same starting point. Several basic problems pertinent to electrochemical transport are analyzed, culminating in the development of a modified Cottrell equation applicable to thin films of unsupported electrolytic solutions sandwiched between planar electrodes

Overpotential from cosolvent imbalance in battery electrolytes: LiPF6 in EMC:EC

Most liquid lithium-ion-battery electrolytes incorporate cosolvent blends, but the dominant electrochemical transport models adopt a single-solvent approximation, which assumes in part that nonuniform cosolvent ratios do not affect cell voltage. For the popular electrolyte formulation based on ethyl-methyl carbonate (EMC), ethylene carbonate (EC), and LiPF6, we perform measurements with fixed-reference concentration cells, finding appreciable liquid-junction potentials when only the cosolvent ratio is polarized. A previously reported junction-potential correlation for EMC:LiPF6 is extended to cover much of the ternary composition space. We propose a transport model for EMC:EC:LiPF6 solutions grounded in irreversible thermodynamics. Thermodynamic factors and transference numbers are entwined in liquid-junction potentials, but concentration-cell measurements determine observable material properties we call junction coefficients, which appear in the extended form of Ohm’s law that accounts for how composition changes induce voltage drops. Junction coefficients of EC and LiPF6 are reported and illustrate the extent to which ionic current induces solvent migration

Drivers of membrane fouling in the vanadium acetylacetonate flow battery

Vanadium acetylacetonate (V(acac)3) disproportionation electrochemistry promises a crossover-tolerant, high-voltage flow battery, but exhibits low efficiency and short cycle life. We show that membrane fouling, rather than a parasitic side reaction, dominates early performance fade. Crossover rates through porous membranes were estimated from voltage transients with an adaptive observer while cycling flow-through reactors. For 0.1M V(acac)3 and 0.3M TEABF4 in acetonitrile flowed countercurrently at 5.0cms−1 parallel to the separator, fresh Daramic 175 and Celgard 4650 afforded active-species mass-transfer coefficients of 3.8μms−1 and 7.5μms−1, respectively, which decreased and became non-Fickian as cycling progressed. At ±10mAcm−2 from 0%–20% state of charge, voltage efficiency with Celgard fell from 96% to 60% over 27 cycles. Separator replacement restored the coulombic and voltage efficiencies, which repeated their first progression. Impedance spectra from series-connected canary cells reveal that separator resistances remain stable during open-circuit exposure to charged single electrolytes, but increase under applied current or open-circuit contact with differently charged electrolytes

Augmented saddle point formulation of the steady-state Stefan--Maxwell diffusion problem

We investigate structure-preserving finite element discretizations of the steady-state Stefan--Maxwell diffusion problem which governs diffusion within a phase consisting of multiple species. An approach inspired by augmented Lagrangian methods allows us to construct a symmetric positive definite augmented Onsager transport matrix, which in turn leads to an effective numerical algorithm. We prove inf-sup conditions for the continuous and discrete linearized systems and obtain error estimates for a phase consisting of an arbitrary number of species. The discretization preserves the thermodynamically fundamental Gibbs--Duhem equation to machine precision independent of mesh size. The results are illustrated with numerical examples, including an application to modelling the diffusion of oxygen, carbon dioxide, water vapour and nitrogen in the lungs.Comment: 27 pages, 5 figure

Structural electroneutrality in Onsager-Stefan-Maxwell transport with charged species

We present a method to embed local electroneutrality within Onsager-Stefan-Maxwell electrolytic-transport models, circumventing their formulation as differential systems with an algebraic constraint. Flux-explicit transport laws are formulated for general multicomponent electrolytes, in which the conductivity, component diffusivities, and transference numbers relate to Stefan-Maxwell coefficients through invertible matrix calculations. A construction we call a `salt-charge basis' implements Guggenheim's transformation of species electrochemical potentials into combinations describing a minimal set of neutral components, leaving a unique combination associated with electricity. Defining conjugate component concentrations and fluxes that preserve the structures of the Gibbs function and energy dissipation retains symmetric Onsager reciprocal relations. The framework reproduces Newman's constitutive laws for binary electrolytes and the Pollard-Newman laws for molten salts; we also propose laws for salt solutions in two-solvent blends, such as lithium-ion-battery electrolytes. Finally, we simulate a potentiostatic Hull cell containing a non-ideal binary electrolyte with concentration-dependent properties

Thyroid secretion rate of albino rats during growth, pregnancy and lactation

Publication authorized September 17, 1946.Digitized 2007 AES.Includes bibliographical references (pages 32-34)

The metabolism of thyroxine

Digitized 2007 AES.Includes bibliographical references (pages 69-76)

Finite element methods for multicomponent convection-diffusion

We develop finite element methods for coupling the steady-state Onsager--Stefan--Maxwell equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Developing a variational formulation for discretizing these equations is challenging: the formulation must balance physical relevance of the variables and boundary data, regularity assumptions, tractability of the analysis, enforcement of thermodynamic constraints, ease of discretization, and extensibility to the transient, anisothermal, and non-ideal settings. To resolve these competing goals, we employ two augmentations: the first enforces the mass-average constraint in the Onsager--Stefan--Maxwell equations, while its dual modifies the Stokes momentum equation to enforce symmetry. Remarkably, with these augmentations we achieve a Picard linearization of symmetric saddle point type, despite the equations not possessing a Lagrangian structure. Exploiting the structure of linear irreversible thermodynamics, we prove the inf-sup condition for this linearization, and identify finite element function spaces that automatically inherit well-posedness. We verify our error estimates with a numerical example, and illustrate the application of the method to non-ideal fluids with a simulation of the microfluidic mixing of hydrocarbons

Potentiometric MRI of a Superconcentrated Lithium Electrolyte: Testing the Irreversible Thermodynamics Approach.

Superconcentrated electrolytes, being highly thermodynamically nonideal, provide a stringent proving ground for continuum transport theories. Herein, we test an ostensibly complete model of LiPF6 in ethyl-methyl carbonate (EMC) based on the Onsager-Stefan-Maxwell theory from irreversible thermodynamics. We perform synchronous magnetic resonance imaging (MRI) and chronopotentiometry to examine how superconcentrated LiPF6:EMC responds to galvanostatic polarization and open-circuit relaxation. We simulate this experiment using an independently parametrized model with six composition-dependent electrolyte properties, quantified up to saturation. Spectroscopy reveals increasing ion association and solvent coordination with salt concentration. The potentiometric MRI data agree closely with the predicted ion distributions and overpotentials, providing a completely independent validation of the theory. Superconcentrated electrolytes exhibit strong cation-anion interactions and extreme solute-volume effects that mimic elevated lithium transference. Our simulations allow surface overpotentials to be extracted from cell-voltage data to track lithium interfaces. Potentiometric MRI is a powerful tool to illuminate electrolytic transport phenomena