Pedro E. Arce

Discharge Model for LiFePO4 Accounting for the Solid Solution Range

A comprehensive discharge model for LiFePO 4 electrode, including Li-ion diffusion in both the alpha and the beta solid solution phases, and phase transformation was developed. For the discharge model, the phase transformation, driven by the interfacial lithium concentration differences in both alpha and beta phases, was considered to be strongly dependent on the type of interface formed between the alpha and beta phases (coherent, semicoherent, and incoherent). By using the model as a tool, effects of extending the alpha and the beta solid solutions and reducing the particle size of LiFePO 4 on rate performance of LiFePO 4 were analyzed. The model developed in this article is applicable for predicting the discharge behavior of any other electrodes with phase transformation.

Effective Diffusivity Tensors of Point-Like Molecules in Anisotropic Porous Media by Monte Carlo Simulation

Monte Carlo simulations of random walks in anisotropic structured media are performed to determine the dependence of effective diffusivities on geometrical properties. The anisotropic media used in this study are periodic systems, which are generated by extending primitive, face-centered, and body-centered unit cells indefinitely in all axial directions. Results of simulations compare well with published experimental data and the calculations by the volume averaging method. In addition, these results suggest that if the 2D media with percolation thresholds subtantially differ from those of 3D, 2D approximations of 3D media are not satisfactory. When percolation thresholds are the same, the effective diffusivity tensors depend solely on the porosity. This fact has been suggested for isotropic media and it seems to hold for anisotropic media.

Role of Joule heating in dispersive mixing effects in electrophoretic cells: Convective-diffusive transport aspects

This contribution addresses the problem of solute dispersion in a free convection electrophoretic cell for the batch mode of operation, caused by the Joule heating generation. The problem is analyzed by using the two‐problem approach originally proposed by Bosse and Arce (Electrophoresis 2000, 21, 1018—1025). The approach identifies the carrier fluid problem and the solute problem. This contribution is focused on the latter. The strategy uses a sequential coupling between the energy, momentum and mass conservation equations and, based on geometrical and physical assumptions for the system, leads to the derivation of analytical temperature and velocity profiles inside the cell. These results are subsequently used in the derivation of the effective dispersion coefficient for the cell by using the method of area averaging. The result shows the first design equation that relates the Joule heating effect directly to the solute dispersion in the cell. Some illustrative results are presented and discussed and their implication to the operation and design of the device is addressed. Due to the assumptions made, the equation may be viewed as an upper boundary for applications such as free flow electrophoresis.

Applications of self-adjoint operators to electrophoretic transport, enzyme reactions, and microwave heating problems in composite media—II. Electrophoretic transport in layered membranes

The problem analyzed in this paper is a specific application of the general M-layered composite reaction/diffusion/convection formulation given by Locke and Arce. The analysis considers electrophoretic transport of a single solute species across a one-dimensional three-layered system and the solution is obtained using operator-theoretic methods. The geometrical structure of the spectrum of the operator is determined for the complete range of the various parameters including the distribution coefficients, applied electric field, electrophoretic mobilities, and diffusion coefficients. The structure of the spectrum allows a complete characterization of all the eigenvalues of the system in terms of all of these physical parameters. Calculation of the first eigenvalue for a number of cases shows its variation with the applied electrical field for various medium porosities and allows a priori estimates of the dynamics of the process. Concentration profiles are given to illustrate the solution.

The role of Joule heating in dispersive mixing effects in electrophoretic cells: hydrodynamic considerations.

The analysis described in this contribution is focused on the effect of Joule heating generation on the hydrodynamics of batch electrophoretic cells (i.e., cells that do not display a forced convective term in the motion equation). The hydrodynamics of these cells is controlled by the viscous forces and by the buoyancy force caused by the temperature gradients due to the Joule heating generation. The analysis is based on differential models that lead to analytical and/or asymptotic solutions for the temperature and velocity profiles of the cell. The results are useful in determining the characteristics of the temperature and velocity profiles inside the cell. Furthermore, the results are excellent tools to be used in the analysis of the dispersive‐mixing of solute when Joule heating generation must be accounted for. The analysis is performed by identifying two sequentially coupled problems. Thus, the “carrier fluid problem” and the “solute problem” are outlined. The former is associated with all the factors affecting the velocity profile and the latter is related to the convective‐diffusion aspects that control the spreading of the solute inside the cell. The analysis of this contribution is centered on the discussion of the “carrier fluid problem” only. For the boundary conditions selected in the contribution, the study leads to the derivation of an analytical temperature and a “universal” velocity profile that feature the Joule heating number. The Grashof number is a scaling factor of the actual velocity profile. Several characteristics of these profiles are studied and some numerical illustrations have been included.

Applications of self-adjoint operators to electrophoretic transport, enzyme reactions, and microwave heating problems in composite media. I: General formulation

Analytical solutions for transient and steady-state convection, diffusion, and reaction problems in one-dimensional M-layer composite media are developed. Three cases are considered: (1) electrophoretic transport; (2) first-order reactions; and (3) zero-order reactions. Solutions are obtained for both Dirichlet and generalized well-mixed boundary conditions. Operator-theoretic methods are utilized to solve the transient problems. The structure of the eigenvalue problem is considered in order to illustrate the methodology for the construction of the solutions to the transient problems. Steady-state solutions are presented for all the cases investigated.

Monitoring advanced oxidation of Suwannee River fulvic acid

Environmental context.Potentially toxic disinfection by-products form when water containing humic and fulvic acids is chlorinated to destroy pathogenic microorganisms. A pulsed electrical discharge was examined for its ability to destroy an aquatic fulvic acid by oxidation. Spectroscopically, changes in the organic structures were observed, but carbon content and disinfection by-products were not reduced. Abstract.A pilot-scale pulsed electrical discharge (PED) system was used to treat Suwannee River fulvic acid (SRFA) as a representative precursor material for the formation of disinfection by-products (DBPs), specifically trihalomethane compounds. Ultraviolet-visible and fluorescence spectroscopy, dissolved organic carbon (DOC), and the trihalomethane formation potential (THMFP) were used as analytical parameters to monitor the effects of treatment on the substrate. The potential for SRFA degradation (5 mg L–1 DOC) was examined over 60 min at each of four operational configurations, varying pulse energy and frequency (0.15 J and 60 Hz, 0.15 J and 120 Hz, 0.4 J and 60 Hz, and 0.4 J and 120 Hz) in a factorial design. Statistically significant changes occurred for UV254, EX254EM460, and EX328EM460 under selected conditions; however, concomitant changes in DOC and THMFP were not observed. The composition of SRFA changed, but organic carbon was not mineralised to carbon dioxide. In addition to showing degradation by PED, the significance of the preliminary findings of this research was to demonstrate that spectroscopic monitoring of precursor degradation alone can be misleading, and that whereas ultraviolet-visible and fluorescence spectroscopy indicated degradation of precursor compounds, DOC and THMFP measurements were unchanged and did not support the occurrence of mineralisation in this system.

An integral-spectral approach for convective-diffusive mass transfer with chemical reaction in Couette flow Mathematical formulation and numerical illustrations

Abstract The convective-diffusive mass transfer problem with chemical reaction in a Couette planar flow has been analyzed in terms of the integralspectral methods originally introduced by Arce et al. (Comput. Chem. Eng. 2(11) (1988) 1103). The problem is solved by inverting the differential model into an integral equation of a Volterra type, in the axial variable, and of the Fredholm type, in the radial coordinate. The kernel of such an integral equation is given by the Green function which does not contain any of the kinetic parameters of the (homogeneous and/or heterogeneous) reaction term. This Green function is computed in terms of the eigenfunctions and eigenvalues of the Sturm-Liouville problem associated with the radial variable. The Sturm-Liouville problem is solved (analytically) by using Airy functions and the final integral equation must be solved by an iteration procedure. Several of the mathematical formulation details are discussed and many numerical examples are presented to illustrate the technique: for example, concentration profiles for systems with heterogeneous (wall) catalytic reactions, homogenous (global) reactions and simultaneous (global and wall catalytic) reactions with kinetics of a general form, i.e. power-law and Langmuir-Hinshelwood types of functions are investigated. The solutions to the class of problems considered here are obtained as particular cases of the general integral equation solution of the differential model discussed in the article. The effects of relevant parameters in the system on the computational algorithm with respect to convergence and (numerical) stability characteristics are discussed.

Effect of capillary geometry on predicting electroosmotic volumetric flowrates in porous or fibrous media.

Electrokinetic-based methods are used in a variety of applications including drug delivery and separation of biomolecules, among others. Many of these applications feature a fibrous or a porous medium that can be modeled by using capillary bundle models to predict the behavior of the electroosmotic flow within the particular system. The role of geometry in predicting volumetric flowrates in porous media is investigated by modeling the electroosmotic flow in idealized capillaries of rectangular, cylindrical, and annular geometries. This is achieved by the coupling of electrostatics and continuum hydrodynamics to obtain analytical expressions that govern the electrokinetically - driven volumetric flow within these idealized capillary geometries. A previous study developed a model to compare the cylindrical and annular capillary geometries by utilizing two methods that compare the areas of the two geometries. The methods used in this previous work will also be used in the present contribution to compare the volumetric flowrates in the cylindrical and annular capillaries with a rectangular capillary. Illustrative results will be presented to aid in the understanding of the influence of the various geometrical and electrostatic parameters that arise from the analysis of these volumetric flowrates. It was found that the electroosmotic volumetric flowrates are significantly affected by the capillary geometry.

Dispersive mixing in a batch electrophoretic cell with Eyring fluids

The main objective of this study is analysis of dispersive mixing inside a batch electrophoretic cell due to Joule heating, especially for the case of non‐Newtonian carriers. To this end, a carrier fluid that follows the Eyring rheological model is used in the analysis of the species convective‐diffusive equation that describes the solute motion inside the device. The hydrodynamic problem (Bosse, M. A. et al., Electrophoresis 2002, 23, 2149–2156) of the electrophoretic cell is sequentially coupled to this equation. Then, by following a procedure based on the area‐averaging method, an effective diffusion coefficient is obtained. This equation is the first a priori design equation for devices such as the ones analyzed in this contribution. It is useful in determining mixing conditions for the values of the relevant parameters of the physical system. The results of this analysis are used to study the cell behavior under several conditions imposed by their main parameters. Finally, some suggestions are offered about the use of Eyring fluids as potential carriers useful for controlling dispersive mixing in batch electrophoretic cells.