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Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle
The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9416042/ https://www.ncbi.nlm.nih.gov/pubmed/36014348 http://dx.doi.org/10.3390/molecules27165108 |
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author | Ohshima, Hiroyuki |
author_facet | Ohshima, Hiroyuki |
author_sort | Ohshima, Hiroyuki |
collection | PubMed |
description | The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general expression for the Laplace transform of the transient electrophoretic mobility, we present an approximation method to avoid the numerical inverse Laplace transformation and derive a simple approximate analytic mobility expression for a weakly charged particle without involving numerical inverse Laplace transformations. The transient electrophoretic mobility can be obtained directly from this approximate mobility expression without recourse to the numerical inverse Laplace transformation. The results are found to be in excellent agreement with the exact numerical results obtained by Huang and Keh. |
format | Online Article Text |
id | pubmed-9416042 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-94160422022-08-27 Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle Ohshima, Hiroyuki Molecules Article The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general expression for the Laplace transform of the transient electrophoretic mobility, we present an approximation method to avoid the numerical inverse Laplace transformation and derive a simple approximate analytic mobility expression for a weakly charged particle without involving numerical inverse Laplace transformations. The transient electrophoretic mobility can be obtained directly from this approximate mobility expression without recourse to the numerical inverse Laplace transformation. The results are found to be in excellent agreement with the exact numerical results obtained by Huang and Keh. MDPI 2022-08-11 /pmc/articles/PMC9416042/ /pubmed/36014348 http://dx.doi.org/10.3390/molecules27165108 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Ohshima, Hiroyuki Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle |
title | Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle |
title_full | Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle |
title_fullStr | Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle |
title_full_unstemmed | Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle |
title_short | Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle |
title_sort | approximate analytic expression for the time-dependent transient electrophoretic mobility of a spherical colloidal particle |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9416042/ https://www.ncbi.nlm.nih.gov/pubmed/36014348 http://dx.doi.org/10.3390/molecules27165108 |
work_keys_str_mv | AT ohshimahiroyuki approximateanalyticexpressionforthetimedependenttransientelectrophoreticmobilityofasphericalcolloidalparticle |