Direct numerical simulation of electrokinetic transport phenomena: variational multi-scale stabilization and octree-based mesh refinement

Finite element modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS) equation. Direct numerical simulation (DNS) to accurately capture the spatio-temporal variation of ion concentration and current flux remains challenging due to the (a) small critical dimension of the electric double layer (EDL), (b) stiff coupling, large advective effects, and steep gradients close to boundaries, and (c) complex geometries exhibited by electrochemical devices. In the current study, we address these challenges by presenting a direct numerical simulation framework that incorporates: (a) a variational multiscale (VMS) treatment, (b) a block-iterative strategy in conjunction with semi-implicit (for NS) and implicit (for PNP) time integrators, and (c) octree based adaptive mesh refinement. The VMS formulation provides numerical stabilization critical for capturing the electro-convective instabilities often observed in engineered devices. The block-iterative strategy decouples the difficulty of non-linear coupling between the NS and PNP equations and allows using tailored numerical schemes separately for NS and PNP equations. The carefully designed second-order, hybrid implicit methods circumvent the harsh timestep requirements of explicit time steppers, thus enabling simulations over longer time horizons. Finally, the octree-based meshing allows efficient and targeted spatial resolution of the EDL. These features are incorporated into a massively parallel computational framework, enabling the simulation of realistic engineering electrochemical devices. The numerical framework is illustrated using several challenging canonical examples

Protein Transport through Nanopores Illuminated by Long-Time-Scale Simulations

The transport of molecules through nanoscale confined space is relevant in biology, biosensing, and industrial filtration. Microscopically modeling transport through nanopores is required for a fundamental understanding and guiding engineering, but the short duration and low replica number of existing simulation approaches limit statistically relevant insight. Here we explore protein transport in nanopores with a high-throughput computational method that realistically simulates hundreds of up to seconds-long protein trajectories by combining Brownian dynamics and continuum simulation and integrating both driving forces of electroosmosis and electrophoresis. Ionic current traces are computed to enable experimental comparison. By examining three biological and synthetic nanopores, our study answers questions about the kinetics and mechanism of protein transport and additionally reveals insight that is inaccessible from experiments yet relevant for pore design. The discovery of extremely frequent unhindered passage can guide the improvement of biosensor pores to enhance desired biomolecular recognition by pore-tethered receptors. Similarly, experimentally invisible nontarget adsorption to pore walls highlights how to improve recently developed DNA nanopores. Our work can be expanded to pressure-driven flow to model industrial nanofiltration processes

Physics of Ionic Conduction in Narrow Biological and Artificial Channels

The book reprints a set of important scientific papers applying physics and mathematics to address the problem of selective ionic conduction in narrow water-filled channels and pores. It is a long-standing problem, and an extremely important one. Life in all its forms depends on ion channels and, furthermore, the technological applications of artificial ion channels are already widespread and growing rapidly. They include desalination, DNA sequencing, energy harvesting, molecular sensors, fuel cells, batteries, personalised medicine, and drug design. Further applications are to be anticipated.The book will be helpful to researchers and technologists already working in the area, or planning to enter it. It gives detailed descriptions of a diversity of modern approaches, and shows how they can be particularly effective and mutually reinforcing when used together. It not only provides a snapshot of current cutting-edge scientific activity in the area, but also offers indications of how the subject is likely to evolve in the future

Transient electrohydrodynamic flow with concentration dependent fluid properties: modelling and energy-stable numerical schemes

Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles. This results in a generalized Navier-Stokes-Poisson-Nernst-Planck system, where fluid properties such as density and permittivity depend on the ion concentration fields. We propose strategies for constructing numerical schemes for this set of equations, where solving the electrochemical and the hydrodynamic subproblems are decoupled at each time step. We provide time discretizations of the model that suffice to satisfy the same energy dissipation law as the continuous model. In particular, we propose both linear and non-linear discretizations of the electrochemical subproblem, along with a projection scheme for the fluid flow. The efficiency of the approach is demonstrated by numerical simulations using several of the proposed schemes

Physics of Ionic Conduction in Narrow Biological and Artificial Channels

This is a book about ion channels. It has been written mostly by physical scientists and mathematicians, even though the most widespread and important manifestation of ion channels is in biology, where they are essential to life in all its forms. How do non-biologists get involved in such investigations? Everyone will have their own particular story but, for ourselves, it was the heady combination of scientific curiosity, a wish to contribute to the fundamental understanding of natural phenomena that clearly have crucially important applications, and the realisation that some of our physics knowledge and expertise might be relevant

Multi-Scale Computational Studies of Calcium (Ca\u3csup\u3e2+\u3c/sup\u3e) Signaling

Ca2+ is an important messenger that affects almost all cellular processes. Ca2+ signaling involves events that happen at various time-scales such as Ca2+ diffusion, trans-membrane Ca2+ transport and Ca2+-mediated protein-protein interactions. In this work, we utilized multi-scale computational methods to quantitatively characterize Ca2+ diffusion efficiency, Ca2+ binding thermodynamics and molecular bases of Ca2+-dependent protein-protein interaction. Specifically, we studied 1) the electrokinetic transport of Ca2+ in confined sub-µm geometry with complicated surfacial properties. We characterized the effective diffusion constant of Ca2+ in a cell-like environment, which helps to understand the spacial distribution of cytoplasmic Ca2+. 2) the association kinetics and activation mechanism of the protein phosphatase calcineurin (CaN) by its activator calmodulin (CaM) in the presence of Ca2+. We found that the association between CaM and CaN peptide is diffusion-limited and the rate could be tuned by charge density/distribution of CaN peptite. Moreover, we proposed an updated CaM/CaN interaction model in which a secondary interaction between CaN’s distal helix motif and CaM was highlighted. 3) the roles of Mg2+ and K+ in the active transport of Ca2+ by sarco/endoplasmic reticulum Ca2+-ATPase (SERCA) pump. We found that Mg2+ most likely act as inhibitor while K+ as agonist in SERCA’s transport process of Ca2+. Results reported in this work shed insights into various aspects of Ca2+ signaling from molecular to cellular level

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer