Electrokinetic Problems Research Articles

Numerical Modeling of Floating Potentials in Electrokinetic Problems Using an Asymptotic Method

Floating potentials appear in electrokinetic problems when isolated high-conductive materials are included in a dielectric or weakly conductive ambient medium. The large contrast of conductivities generates numerical issues that make hard the computation of the electric potential. This article proposes a rigorous numerical method to tackle this kind of problem. Interestingly, a correction to the case of a perfect conductor is given in order to improve the accuracy of the computation. The method involves a cascade of two elementary problems set, respectively, in the ambient medium and in the high-conductive inclusions. An example is proposed with a 4-electrode system designed to both induce electroporation in a biological tissue sample and measure the resulting impedance. The approach is extended to a nonlinear problem by taking advantage of the iterative scheme that is necessarily applied in this case.

Fault Identification on a Fuel Cell by 3-D Current Density Reconstruction From External Magnetic Field Measurements

An original approach of fuel cell diagnosis is presented. It is based on the solving of an inverse linear problem linking the magnetic field signature outside of the fuel cell to the current density distribution inside. The searched solution is a linear combination of conservative current distribution obtained by a set of electrokinetic problems solved by a finite face element method. As the problem is ill-posed, the solution is stabilized using a truncated singular value decomposition. The approach is validated to reconstruct a 3-D current density distribution in a stack simulator and in a fuel cell stack operating in the laboratory conditions.

Fault detection for polymer electrolyte membrane fuel cell stack by external magnetic field

An original non-invasive approach of fuel cell diagnosis is proposed in order to locate different kinds of faults in PEMFC stacks from magnetic field measurements. The method is based on the solving of an inverse linear problem linking the magnetic field signature outside of the fuel cell to the current density distribution inside. The searched solution is a linear combination of conservative current distribution obtained by a set of electrokinetic problems solved by a finite face element method. As the problem is ill-posed, the solution is stabilized using a truncated singular value decomposition. In this work, 30 sensors are used to perform the magnetic tomography of a PEMFC stack consisting of 100 cells with a large active area of 220 cm2. External magnetic measurement makes possible to identify 2D or 3D changes of current density distribution induced either by a cell flooding or membrane drying as well as by material degradation in a PEMFC stack.

ESPResSo 4.0 – an extensible software package for simulating soft matter systems

ESPResSo 4.0 is an extensible simulation package for research on soft matter. This versatile molecular dynamics program was originally developed for coarse-grained simulations of charged systems Limbach et al., Comput. Phys. Commun. 174, 704 (2006). The scope of the software has since broadened considerably: ESPResSo can now be used to simulate systems with length scales spanning from the molecular to the colloidal. Examples include, self-propelled particles in active matter, membranes in biological systems, and the aggregation of soot particles in process engineering. ESPResSo also includes solvers for hydrodynamic and electrokinetic problems, both on the continuum and on the explicit particle level. Since our last description of version 3.1 Arnold et al., Meshfree Methods for Partial Differential Equations VI, Lect. Notes Comput. Sci. Eng. 89, 1 (2013), the software has undergone considerable restructuring. The biggest change is the replacement of the Tcl scripting interface with a much more powerful Python interface. In addition, many new simulation methods have been implemented. In this article, we highlight the changes and improvements made to the interface and code, as well as the new simulation techniques that enable a user of ESPResSo 4.0 to simulate physics that is at the forefront of soft matter research.

MOR-Based Approach to Uncertainty Quantification in Electrokinetics With Correlated Random Material Parameters

A strategy for uncertainty quantification in electrokinetic problems with correlated random material parameters is proposed. Such approach exploits a reduced-order model and a polynomial spectral approximation of the deterministic parametric electrokinetic problem for accurately and efficiently estimating the statistics of the quantities of interest.

О выборе методов решения уравнения Пуассона в общем случае распределения объемной плотности заряда и о постановке краевых условий в электрокинетических задачах (обзор)

О выборе методов решения уравнения Пуассона в общем случае распределения объемной плотности заряда и о постановке краевых условий в электрокинетических задачах (обзор)

Nonlinear electrophoresis at arbitrary field strengths: small-Dukhin-number analysis

Smoluchowski’s formula for thin-double-layer electrophoresis does not apply for highly charged particles, where surface conduction modifies the electrokinetic transport in the electro-neutral bulk. To date, systematic studies of this nonzero Dukhin-number effect have been limited to weak fields. Employing our recent macroscale model [O. Schnitzer and E. Yariv, “Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction,” Phys. Rev. E 86, 021503 (2012)], valid for arbitrary Dukhin numbers, we analyze herein particle electrophoresis at small (but finite) Dukhin numbers; valid for arbitrary fields, this asymptotic limit essentially captures the practical range of parameters quantifying typical colloidal systems. Perturbing about the irrotational zero-Dukhin-number flow, we derive a linear scheme for calculating the small-Dukhin-number correction to Smoluchowski’s velocity. This scheme essentially amounts to the solution of a linear diffusion–advection problem governing the salt distribution in the electro-neutral bulk. Using eigenfunction expansions, we obtain a semi-analytic solution for this problem. It is supplemented by asymptotic approximations in the respective limits of weak fields, small ions, and strong fields; in the latter singular limit, salt polarization is confined to a diffusive boundary layer. With the salt-transport problem solved, the velocity correction is readily obtained by evaluating three quadratures, corresponding to the contributions of (i) electro- and diffuso-osmotic slip due to polarization of both the Debye layer and the bulk; (ii) a net Maxwell force on the electrical double layer; and (iii) Coulomb body forces acting on the space charge in the “electro-neutral” bulk. The velocity correction calculated based upon the semi-analytic solution exhibits a transition from the familiar retardation at weak fields to velocity enhancement at moderate fields; this transition is analytically captured by the small-ion approximation. At stronger fields, the velocity correction approaches a closed-form asymptotic approximation which follows from an analytic solution of the diffusive boundary-layer problem. In this régime, the correction varies as the 3/2-power of the applied field. Our small-Dukhin-number scheme, valid at arbitrary field strengths, naturally lends itself to a tractable analysis of nonlinear surface-conduction effects in numerous electrokinetic problems.

Robust and high‐resolution simulations of nonlinear electrokinetic processes in variable cross‐section channels

We present a model and an associated numerical scheme to simulate complex electrokinetic processes in channels with nonuniform cross-sectional area. We develop a quasi-1D model based on local cross-sectional area averaging of the equations describing unsteady, multispecies, electromigration-diffusion transport. Our approach uses techniques of lubrication theory to approximate electrokinetic flows in channels with arbitrary variations in cross-section; and we include chemical equilibrium calculations for weak electrolytes, Taylor-Aris type dispersion due of nonuniform bulk flow, and the effects of ionic strength on species mobility and on acid-base equilibrium constants. To solve the quasi-1D governing equations, we provide a dissipative finite volume scheme that adds numerical dissipation at selective locations to ensure both unconditional stability and high accuracy. We couple the numerical scheme with a novel adaptive grid refinement algorithm that further improves the accuracy of simulations by minimizing numerical dissipation. We benchmark our numerical scheme with existing numerical schemes by simulating nonlinear electrokinetic problems, including ITP and electromigration dispersion in CZE. Simulation results show that our approach yields fast, stable, and high-resolution solutions using an order of magnitude less grid points compared to the existing dissipative schemes. To highlight our model's capabilities, we demonstrate simulations that predict increase in detection sensitivity of ITP in converging cross-sectional area channels. We also show that our simulations of ITP in variable cross-sectional area channels have very good quantitative agreement with published experimental data.

Parallel Direct Solver for the Finite Integration Technique in Electrokinetic Problems

The finite integration technique allows the simulation of real-world electromagnetic field problems with complex geometries. It provides a discrete reformulation of Maxwell's equations in their integral form suitable for numerical computing. The resulting matrix equations of the discretized fields can be used for efficient numerical simulations on modern computers and can be exploited to use a parallel computing. In fact, by reordering the unknowns by the nested dissection method, it is possible to directly construct the lower triangular matrix of the Cholesky factorization with many processors without assembling the matrix system. In this paper, a parallel algorithm is proposed for the direct solution of large sparse linear systems with the finite integration technique. This direct solver has the advantage of handling singularities in the matrix of linear systems. The computational effort for these linear systems, often encountered in numerical simulation of electromagnetic phenomena by finite integration technique, is very significant in terms of run-time and memory requirements. Many numerical tests have been carried out to evaluate the performance of the parallel direct solver.

Electrokinetic control of sample splitting at a channel bifurcation using isotachophoresis

We present a novel method for accurately splitting ionic samples at microchannel bifurcations. We leverage isotachophoresis (ITP) to focus and transport sample through a one-inlet, two-outlet microchannel bifurcation. We actively control the proportion of splitting by controlling potentials at end-channel reservoirs (and thereby controlling the current ratio). We explore the effect of buffer chemistry and local electric field on splitting dynamics and propose and validate a simple Kirchoff-type rule controlling the split ratio. We explore the effects of large applied electric fields on sample splitting and attribute a loss of splitting accuracy to electrohydrodynamic instabilities. We propose a scaling analysis to characterize the onset of this instability. This scaling is potentially useful for other electrokinetic flow problems with self-sharpening interfaces.

Transport of electric charge in low dielectric constant fluids

Electrokinetic phenomena in fluids have usually been described mathematically in terms of the electrical potential distribution within, and at the surfaces of the fluid. In this paper an alternative description of electrokinetic phenomena in terms of the charge distribution within the fluid and at its surfaces, applicable when the dielectric constant of the fluid is low, is given. This takes the form of a linear partial differential equation for the transport of electric charge by diffusion, conduction, and convection in the fluid. The principle of similarity is applied to the equation; types of electrokinetic phenomena to be expected in a given system are characterized in terms of two ratios of characteristic lengths, the Reynolds number, and the Schmidt number. Three examples in which the equation is solved, subject to appropriate boundary conditions, are presented. A comparison with previous work by the author on charge generation and transport in turbulent flow of hydrocarbons through tubes is made. The theory developed may be applied to electrokinetic problems in hydrocarbon systems and should be applicable to problems in atmospheric electricity.