Analysis of diffuse-layer effects on time-dependent interfacial kinetics

We investigate the subtle effects of the diffuse charged layer on interfacial kinetics by solving the governing equations for ion transport (Nernst–Planck) with realistic boundary conditions representing reaction kinetics (Butler–Volmer) and compact-layer capacitance (Stern) in the asymptotic limit =λ_D/L→0, where λ_D is the Debye screening length and L is the distance between the working and counter electrodes. Using the methods of singular perturbation theory, we derive the leading-order steady-state response to a nonzero applied current in the case of the oxidation of a neutral species into cations, without any supporting electrolyte. In certain parameter regimes, the theory predicts a reaction-limited current smaller than the classical diffusion-limited current; this over potential effect is not due to ohmic drop effects in the bulk of the cell but rather to antagonist processes involved in the surface charge transfer and diffuse layer charging respectively. We demonstrate that the charging of diffuse charge, since it is intimately coupled to the surface reaction and cannot be considered independently, plays a fundamental role in nonequilibrium surface reactions when the transport of one of the reacting species is coupled to the total interfacial response of the compact and diffuse layers.     

Imbricate continuum and progressive fracturing of concrete and geomaterials

Meccanica - After giving an overview of the recent results at Northwestern University on mathematical models for fracturing heterogeneous materials, the lecture addresses the problem of a continuum...     

A one-parameter formula for estimating the Λ well depth

A one parameter, semi-empirical formula for Λ-binding energy of heavy hypernuclei in the inverse powers of core mass number (A _c) has been developed in the framework of the folding model. Unlike similar calculations reported by other authors (Deloff 1971; Daskaloyanniset al 1985), we are able to take into account the effect arising from the difference in the number of protons and neutrons of the core nuclei having same mass number. The radius and diffuseness are parametrized using the experimentally known charge density data of a fairly large number of medium and heavy nuclei. The well depth parameter (i.e. Λ-binding energy in infinite nuclear matter) in the formula is obtained from a fit to theB _Λ data of _Λ ²⁸ Si, _Λ ⁴⁰ Ca, _Λ ⁵¹ V and _Λ ³⁹ Y. Using the original Λ-nucleus potential, theB _Λ of ground and the experimentally known excited states of these hypernuclei have also been calculated by solving numerically the two-body Schrödinger equation. The agreement with the experimental data is satisfactory.     

Theoretical prediction of fast 3D AC electro-osmotic pumps

AC electro-osmotic (ACEO) pumps in microfluidics currently involve planar electrode arrays, but recent work on the underlying phenomenon of induced-charge electro-osmosis (ICEO) suggests that three-dimensional (3D) geometries may be exploited to achieve faster flows. In this paper, we present some new design principles for periodic 3D ACEO pumps, such as the "fluid conveyor belt" of ICEO flow over a stepped electrode array. Numerical simulations of these designs (using the standard low-voltage model) predict flow rates almost twenty times faster than existing planar ACEO pumps, for the same applied voltage and minimum feature size. These pumps may enable new portable or implantable lab-on-a-chip devices, since rather fast (mm s(-1)), tuneable flows should be attainable with battery voltages (<10 V).     

Average shape of transport-limited aggregates

We study the relation between stochastic and continuous transport-limited growth models. We derive a nonlinear integro-differential equation for the average shape of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation. Focusing on the advection-diffusion-limited aggregation (ADLA) model, we show that the average shape of the stochastic growth is similar, but not identical, to the corresponding continuous dynamics. Similar results should apply to DLA, thus explaining the known discrepancies between average DLA shapes and viscous fingers in a channel geometry.