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 (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13367_2025_119_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">$K_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>) 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. Graphical abstract Schematic diagram of the proposed geometry

Transport of solute in an unsteady electroosmotic flow of Casson fluid through a micro-channel

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发表日期：

2025年3月13日

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Sudip Debnath,
Sachin Shaw,
Ashis Kumar Roy

摘要

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 ( $K_{2}$ $K_{2}$ ) 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.

Graphical abstract

Schematic diagram of the proposed geometry