{"title":"Transport of solute in an unsteady electroosmotic flow of Casson fluid through a micro-channel","authors":"Sudip Debnath, Sachin Shaw, Ashis Kumar Roy","doi":"10.1007/s13367-025-00119-3","DOIUrl":null,"url":null,"abstract":"<div><p>The study aims to analyse the importance of electroosmotic force on the solute dispersion in a microchannel where the carrier fluid is defined by non-Newtonian Casson rheology. The Electric-double layer (EDL) is considered near the channel walls. Flow unsteadiness due to the electric force leads to a highly non-linear momentum equation, which is solved using a regular perturbation method. However, Gill’s generalized dispersion technique is used to discuss the solute dispersion mechanism. The velocity profile, along with the advection, dispersion coefficients and mean concentration, is discussed with different rheological and controlled parameters. The impact of key control parameters, i.e., thickness of the EDL, yield stress, and Péclet number, on the dispersion coefficient, advection coefficient, and mean concentration is examined. A wide range of parameters is considered based on the experimental and physical database from different literatures. Although the transport coefficients are evaluated analytically, numerical tests have also been conducted, producing results that match very well. The existence of electroosmotic force (higher Debye–Hückel electro-osmotic parameter, <i>κ</i>) raises the advection coefficient, and this impact is more noticeable for lower <i>κ</i> values. The dispersion coefficient (<span>\\(K_{2}\\)</span>) diminishes nonlinearly with increasing <i>κ</i> and eventually converges to a specific value with larger <i>κ</i>. The mean concentration variation is more pronounced at lower values of <i>κ</i>, showing a 50% increase as <i>κ</i> rises from 10 to 50, while the variation is only 7% when <i>κ</i> changes from 50 to 100. Understanding dispersion phenomena controlled by electroosmotic force and pulsatility is a challenging task, mainly due to its nonlinearity, and as a result, this area has not been extensively explored. This type of study may have wide applications in biomedical engineering, human blood flow analysis, and beyond. The present simulation will thus be valuable in understanding mass transfer processes.</p><h3>Graphical abstract</h3><p>Schematic diagram of the proposed geometry\n</p><div><figure><div><div><picture><img></picture></div></div></figure></div></div>","PeriodicalId":683,"journal":{"name":"Korea-Australia Rheology Journal","volume":"37 2","pages":"145 - 158"},"PeriodicalIF":2.6000,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Korea-Australia Rheology Journal","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s13367-025-00119-3","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The study aims to analyse the importance of electroosmotic force on the solute dispersion in a microchannel where the carrier fluid is defined by non-Newtonian Casson rheology. The Electric-double layer (EDL) is considered near the channel walls. Flow unsteadiness due to the electric force leads to a highly non-linear momentum equation, which is solved using a regular perturbation method. However, Gill’s generalized dispersion technique is used to discuss the solute dispersion mechanism. The velocity profile, along with the advection, dispersion coefficients and mean concentration, is discussed with different rheological and controlled parameters. The impact of key control parameters, i.e., thickness of the EDL, yield stress, and Péclet number, on the dispersion coefficient, advection coefficient, and mean concentration is examined. A wide range of parameters is considered based on the experimental and physical database from different literatures. Although the transport coefficients are evaluated analytically, numerical tests have also been conducted, producing results that match very well. The existence of electroosmotic force (higher Debye–Hückel electro-osmotic parameter, κ) raises the advection coefficient, and this impact is more noticeable for lower κ values. The dispersion coefficient (\(K_{2}\)) diminishes nonlinearly with increasing κ and eventually converges to a specific value with larger κ. The mean concentration variation is more pronounced at lower values of κ, showing a 50% increase as κ rises from 10 to 50, while the variation is only 7% when κ changes from 50 to 100. Understanding dispersion phenomena controlled by electroosmotic force and pulsatility is a challenging task, mainly due to its nonlinearity, and as a result, this area has not been extensively explored. This type of study may have wide applications in biomedical engineering, human blood flow analysis, and beyond. The present simulation will thus be valuable in understanding mass transfer processes.
该研究旨在分析电渗透力对微通道中溶质分散的重要性，其中载体流体由非牛顿卡森流变学定义。双电层（EDL）在通道壁附近被考虑。由电磁力引起的流动不稳定性导致了一个高度非线性的动量方程，该方程采用正则摄动法求解。然而，采用吉尔广义色散技术来讨论溶质色散机理。讨论了不同流变参数和控制参数下的速度分布、平流、弥散系数和平均浓度。考察了EDL厚度、屈服应力和psamclet数等关键控制参数对扩散系数、平流系数和平均浓度的影响。基于不同文献的实验和物理数据库，考虑了广泛的参数范围。虽然对输运系数进行了解析计算，但也进行了数值试验，得出了非常吻合的结果。电渗透力（较高的debye - hckel电渗透参数κ）的存在提高了平流系数，且这种影响在较低的κ值下更为明显。色散系数（\(K_{2}\)）随着κ的增大呈非线性减小，并随着κ的增大最终收敛到某一特定值。κ值越低，平均浓度变化越明显，为50% increase as κ rises from 10 to 50, while the variation is only 7% when κ changes from 50 to 100. Understanding dispersion phenomena controlled by electroosmotic force and pulsatility is a challenging task, mainly due to its nonlinearity, and as a result, this area has not been extensively explored. This type of study may have wide applications in biomedical engineering, human blood flow analysis, and beyond. The present simulation will thus be valuable in understanding mass transfer processes.Graphical abstractSchematic diagram of the proposed geometry
期刊介绍：
The Korea-Australia Rheology Journal is devoted to fundamental and applied research with immediate or potential value in rheology, covering the science of the deformation and flow of materials. Emphases are placed on experimental and numerical advances in the areas of complex fluids. The journal offers insight into characterization and understanding of technologically important materials with a wide range of practical applications.
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