Research Spotlights

Abstract

This issue's Research Spotlights article by Wei, Zheng, Chen, and Xia highlights the significance of charge transport and specifically centers on multiscale models capable of providing comprehensive predictions in complex settings. As the article states, charge transport is “omnipresent in nature and man-made devices” and includes a diverse range of applications from metal oxide semiconductors to fuel/solar/battery cells to “nature-made nano-bio transistors” or ion channels which effectively maintain ion concentrations within cells, the basic unit of structure and function in all living things. To appreciate the challenges associated with charge transport systems such as those found in sophisticated nano devices (mechanical, optical, electronic, and biological), the article underscores the importance of properly accounting for intricate molecular mechanisms, sophisticated material structures, chemical reactions, and potentially large spatial dimensions when these devices are embedded within large systems, e.g., fuel cells. The article then proceeds to develop variational multiscale models with a focus on addressing heterogeneous chemical and biological systems that are far from equilibrium. Numerous examples are discussed, including fuel cells, a host of nanofluidic devices, and in particular ion channels which are used to validate the variational multiscale models. Derivations are given for coupled Laplace--Beltrami (LB) and Poisson--Nernst--Planck (PNP) equations as well as coupled Laplace--Beltrami and Poisson--Boltzmann--Nernst--Planck (PBNP) equations and also Laplace--Beltrami coupled with Poisson--Nernst--Planck and Navier--Stokes equations. The authors demonstrate two important model features: (1) consistency between equilibrium LP and Poisson--Boltzmann theory and nonequilibrium LP and PNP theory at equilibrium, and (2) how the reduced equations associated with the LB and PBNP formulation can capture behavior obtained from the coupled LB-PNP equations in nonequilibrium settings. The differential geometry of surfaces as a means of separating macroscopic and microscopic domains also plays a prominent role in the paper. The article concludes with computational algorithms that implement the multiscale models and a number of interesting numerical experiments which include comparisons with experimental measurements of current-voltage curves for a specific ion channel.