Next Article in Journal / Special Issue
Grand Canonical Monte Carlo Simulation of Nitrogen Adsorption in a Silica Aerogel Model
Previous Article in Journal
Current Issues in Finite-T Density-Functional Theory and Warm-Correlated Matter †
Previous Article in Special Issue
Bonding Strength Effects in Hydro-Mechanical Coupling Transport in Granular Porous Media by Pore-Scale Modeling
Article Menu

Export Article

Open AccessArticle
Computation 2016, 4(2), 17; doi:10.3390/computation4020017

Analytical Results on the Behavior of a Liquid Junction across a Porous Diaphragm or a Charged Porous Membrane between Two Solutions According to the Nernst–Planck Equation

Università degli Studi di Milano, Dipartimento di Matematica, via Saldini 50, Milano 20133, Italy
*
Author to whom correspondence should be addressed.
Academic Editors: Qinjun Kang and Li Chen
Received: 21 December 2015 / Revised: 7 March 2016 / Accepted: 25 March 2016 / Published: 30 March 2016
(This article belongs to the Special Issue Advances in Modeling Flow and Transport in Porous Media)
View Full-Text   |   Download PDF [630 KB, uploaded 30 March 2016]   |  

Abstract

We model the behavior of an ideal liquid junction, across a porous and possibly charged medium between two ion-containing solutions, by means of the Nernst–Planck equation for the stationary state, in conditions of local electroneutrality. An analytical solution of the equation was found long ago by Planck for the uncharged junction with only ions of valences +1 and −1. Other analytical results, which have later been obtained also for more general situations, seem impractical for performing calculations. In this paper, we obtain analytical solutions for systems with up to three valence classes, which can be applied to perform numerical calculations in a straightforward way. Our method provides a much larger amount of information on the behavior of the system than the well-known Henderson’s approximation. At the same time, it is more simple and reliable, and much less demanding in terms of computational effort, than the nowadays commonly employed numerical methods, typically based on discrete integration and trial-and-error numerical inversions. We present some examples of practical applications of our results. We study in particular the uphill transport (i.e., the transport from the lower-concentration to the higher-concentration region) of a divalent cation in a liquid junction containing also other univalent anions and cations. View Full-Text
Keywords: liquid junction; membrane; Nernst–Planck equation; uphill transport; 66.10.Ed, 82.45.Gj liquid junction; membrane; Nernst–Planck equation; uphill transport; 66.10.Ed, 82.45.Gj
Figures

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Marino, M.; Brogioli, D. Analytical Results on the Behavior of a Liquid Junction across a Porous Diaphragm or a Charged Porous Membrane between Two Solutions According to the Nernst–Planck Equation. Computation 2016, 4, 17.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Computation EISSN 2079-3197 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top