arXiv subjects

Cristian F. Guajardo Yévenes

Publications and source records attributed to Cristian F. Guajardo Yévenes.

3 recordsLinked to original sources

arXiv2021

Analytical solution for two-dimensional Laplace's equation in a shallow domain containing coplanar interdigitated boundaries

Laplace's equation appears frequently in physical applications involving conservable quantities. Among these applications, miniaturized devices have been of interest, in particular those using interdigitated arrays. Therefore, we solved the two-dimensional Laplace's equation for a shallow or finite domain consisting of interdigitated boundaries. We achieved this by using Jacobian elliptic functions to conformally transform the interdigitated domain into a parallel plates domain. The obtained expressions for potential distribution, flux density and flux allow for arbitrary domain height, different band widths and asymmetric potentials at the interdigitated array, besides considering fringing effects at both ends of the array. All these expressions depend only on relative dimensions, instead of absolute ones. With these results we showed that the behavior in shallow or finite domains approaches that of a semi-infinite domain, when its height is greater than the separation between the centers of consecutive bands. We also found that, for any desired but fixed flux, bands of equal width minimize the total surface of the interdigitated array. Finally, we present approximate expressions for the flux, based on elementary functions, which can be applied to ease the calculation of currents (faradaic or non-faradaic), capacitances and resistances among other possible applications.

physics.class-ph↗

arXiv2019

Steady-state theory of interdigitated array of electrodes in confined spaces: Case of pure diffusion and reversible electrode reactions

Analytical equations were found for interdigitated electrodes, which considered reversible electrode reactions and pure diffusion within confined spaces. A conformal transformation, obtained by the use of Jacobian elliptic functions, was applied to solve the diffusion equation in steady state. The obtained steady-state current depends on the ratio of elliptic integrals of the first kind, in which their moduli are functions of the relative dimensions of the cell. The current is smaller for shallower cells, but approaches similiar values to those of semi-infinite geometries when the cell is sufficiently tall. Approximations using trigonometric and hyperbolic expressions were also found for the steady-state current in the cases of shallow and tall cells respectively.

physics.chem-ph↗

arXiv2018

Properties of coplanar periodic electrodes in confined spaces: Case of two-dimensional diffusion

Periodic configurations of electrodes, in particular of microelectrodes, have been of interest since the advent of microfabrication. In this report, theory which is common to any periodic cell (or any cell that can be extended periodically) with finite height and two-dimensional symmentry was derived. The diffusion equation in this cell was solved and the concentration profile was obtained in terms of its Fourier coefficients and as a function of an arbitrary current density. From this base result, a set of properties were derived which are fairly general, since they don't assume restrictions such as reversible electrode reactions (Nernst equation valid when current circulates). These properties involve: horizontal averages and (weighted) sum of concentrations, both with a close connection to the net current and accumulation of species in the cell. The derived properties allow: to explain qualitative aspects of collection efficiency and limiting currents, to predict the concentration on counter electrodes and non-linearities caused by depletion of species at extremely polarized electrodes, and to estimate the time required by the current to reach steady state in potential controlled experiments. The theoretical results are illustrated analytically and numerically for the concrete case of interdigitated array of electrodes.

physics.chem-ph↗