{"title":"Electrokinetic Power-Series Solution in Narrow Cylindrical Capillaries for All Zeta Potentials.","authors":"Sam Khalifa, Arturo Villegas, Francisco J Diez","doi":"10.1002/elps.202400183","DOIUrl":null,"url":null,"abstract":"<p><p>Work from Rice and Whitehead showed the results of electrokinetic flow in a capillary tube under the assumption of low zeta potential <math><semantics><mo><</mo> <annotation>$<$</annotation></semantics> </math> 25 mV, limiting the approximation's usability. Further research conducted by Philip and Wooding provided an alternative solution that assumes high zeta potentials <math><semantics><mo>></mo> <annotation>$>$</annotation></semantics> </math> 25 mV and relies on Rice and Whitehead's solution for lower ranges. However, this solution is presented as a piecewise function, where the functions change based on the zeta potential and the <math> <semantics><mrow><mi>κ</mi> <mi>a</mi></mrow> <annotation>$\\kappa a$</annotation></semantics> </math> parameter, introducing infinite values for the zeta potential and discontinuities in the derived functions. This paper aims to provide a singular equation solution to the full Poisson-Boltzmann equation for a long cylindrical capillary for all zeta potentials. This solution is a single, continuous, and finite function that produces exact results instead of approximations for all ranges of zeta potential. This exact solution is compared against published approximate solutions for large zeta potentials shown by comparing the large zeta potential approximation with the new exact solution. Important parameters such as volume transport and apparent viscosity were found to have errors of up to 9.76%-57.4%, respectively. The function <math> <semantics><mrow><mi>f</mi> <mo>(</mo> <mi>κ</mi> <mi>a</mi> <mo>,</mo> <msub><mi>ψ</mi> <mn>0</mn></msub> <mo>,</mo> <mi>β</mi> <mo>)</mo></mrow> <annotation>$f(\\kappa a, \\psi _0, \\beta)$</annotation></semantics> </math> has errors of up to 10.5% compared to our full solution.</p>","PeriodicalId":11596,"journal":{"name":"ELECTROPHORESIS","volume":" ","pages":""},"PeriodicalIF":3.0000,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ELECTROPHORESIS","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1002/elps.202400183","RegionNum":3,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"BIOCHEMICAL RESEARCH METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Work from Rice and Whitehead showed the results of electrokinetic flow in a capillary tube under the assumption of low zeta potential 25 mV, limiting the approximation's usability. Further research conducted by Philip and Wooding provided an alternative solution that assumes high zeta potentials 25 mV and relies on Rice and Whitehead's solution for lower ranges. However, this solution is presented as a piecewise function, where the functions change based on the zeta potential and the parameter, introducing infinite values for the zeta potential and discontinuities in the derived functions. This paper aims to provide a singular equation solution to the full Poisson-Boltzmann equation for a long cylindrical capillary for all zeta potentials. This solution is a single, continuous, and finite function that produces exact results instead of approximations for all ranges of zeta potential. This exact solution is compared against published approximate solutions for large zeta potentials shown by comparing the large zeta potential approximation with the new exact solution. Important parameters such as volume transport and apparent viscosity were found to have errors of up to 9.76%-57.4%, respectively. The function has errors of up to 10.5% compared to our full solution.
期刊介绍:
ELECTROPHORESIS is an international journal that publishes original manuscripts on all aspects of electrophoresis, and liquid phase separations (e.g., HPLC, micro- and nano-LC, UHPLC, micro- and nano-fluidics, liquid-phase micro-extractions, etc.).
Topics include new or improved analytical and preparative methods, sample preparation, development of theory, and innovative applications of electrophoretic and liquid phase separations methods in the study of nucleic acids, proteins, carbohydrates natural products, pharmaceuticals, food analysis, environmental species and other compounds of importance to the life sciences.
Papers in the areas of microfluidics and proteomics, which are not limited to electrophoresis-based methods, will also be accepted for publication. Contributions focused on hyphenated and omics techniques are also of interest. Proteomics is within the scope, if related to its fundamentals and new technical approaches. Proteomics applications are only considered in particular cases.
Papers describing the application of standard electrophoretic methods will not be considered.
Papers on nanoanalysis intended for publication in ELECTROPHORESIS should focus on one or more of the following topics:
• Nanoscale electrokinetics and phenomena related to electric double layer and/or confinement in nano-sized geometry
• Single cell and subcellular analysis
• Nanosensors and ultrasensitive detection aspects (e.g., involving quantum dots, "nanoelectrodes" or nanospray MS)
• Nanoscale/nanopore DNA sequencing (next generation sequencing)
• Micro- and nanoscale sample preparation
• Nanoparticles and cells analyses by dielectrophoresis
• Separation-based analysis using nanoparticles, nanotubes and nanowires.