Electrokinetic Power-Series Solution in Narrow Cylindrical Capillaries for All Zeta Potentials.

IF 3 3区 生物学 Q2 BIOCHEMICAL RESEARCH METHODS ELECTROPHORESIS Pub Date : 2024-12-16 DOI:10.1002/elps.202400183
Sam Khalifa, Arturo Villegas, Francisco J Diez
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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 κ a $\kappa a$ 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 f ( κ a , ψ 0 , β ) $f(\kappa a, \psi _0, \beta)$ has errors of up to 10.5% compared to our full solution.

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赖斯和怀特海德的研究表明,在低 zeta 电位为 25 mV 的假设条件下,毛细管中的电动流动结果,限制了近似值的可用性。菲利普和伍丁进行的进一步研究提供了另一种解决方案,即假设高 zeta 电位 >$>$ 25 mV,并在较低范围内依赖赖斯和怀特海德的解决方案。然而,这种解决方案是以片断函数的形式呈现的,其中的函数根据zeta电位和κ a $k\appa a$参数而变化,从而引入了zeta电位的无限值和导出函数的不连续性。本文旨在为所有zeta 电位下的长圆柱毛细管全泊松-波尔兹曼方程提供一个奇异方程解。该解法是一个单一、连续和有限的函数,可产生精确的结果,而不是所有zeta电位范围内的近似值。通过将大 zeta 电位近似值与新的精确解进行比较,可以将这种精确解与已公布的大 zeta 电位近似值进行比较。结果发现,体积传输和表观粘度等重要参数的误差分别高达 9.76%-57.4% 。函数 f ( κ a , ψ 0 , β ) $f(\kappa a, \psi _0, \beta)$ 与我们的完整解相比误差高达 10.5%。
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来源期刊
ELECTROPHORESIS
ELECTROPHORESIS 生物-分析化学
CiteScore
6.30
自引率
13.80%
发文量
244
审稿时长
1.9 months
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.
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