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Taylor dispersion analysis in a viscoelastic fluid through arbitrarily shaped axisymmetric channels

Published online by Cambridge University Press:  12 December 2025

Carlos Teodoro Open the ORCID record for Carlos Teodoro [Opens in a new window] ,
Oscar Bautista Open the ORCID record for Oscar Bautista [Opens in a new window]  and
Federico Méndez Open the ORCID record for Federico Méndez [Opens in a new window]
Carlos Teodoro*
Affiliation:
ESIME Azcapotzalco, Instituto Politécnico Nacional, Avenida de las Granjas 682, Colonia Santa Catarina, Alcaldía Azcapotzalco, 02250 Ciudad de México, CDMX, Mexico Tecnológico Nacional de México, Tecnológico de Estudios Superiores de Ecatepec, Av. Tecnológico S/N Colonia Valle de Anáhuac, Sec. Fuentes, 55210 Ecatepec de Morelos, Estado de México, Mexico
Oscar Bautista*
Affiliation:
ESIME Azcapotzalco, Instituto Politécnico Nacional, Avenida de las Granjas 682, Colonia Santa Catarina, Alcaldía Azcapotzalco, 02250 Ciudad de México, CDMX, Mexico
Federico Méndez
Affiliation:
Departamento de Termofluidos, Facultad de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyoacán, 04510 Ciudad de México, CDMX, Mexico
*
Corresponding authors: Carlos Teodoro, carlos_teo@tese.edu.mx; Oscar Bautista, obautista@ipn.mx
Corresponding authors: Carlos Teodoro, carlos_teo@tese.edu.mx; Oscar Bautista, obautista@ipn.mx
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Abstract

The dispersion of solutes has been extensively studied due to its important applications in microfluidic devices for mixing, separation and other related processes. Solute dispersion in fluids can be analysed over multiple time scales; however, Taylor dispersion specifically addresses long-term behaviour, which is primarily influenced by advective dispersion. This study investigates Taylor–Aris dispersion in a viscoelastic fluid flowing through axisymmetric channels of arbitrary shape. The fluid’s rheology is described using the simplified Phan-Thien–Tanner (sPTT) model. Although the channel walls are axisymmetric, they can adopt any geometry, provided they maintain small axial slopes. Drawing inspiration from the work of Chang & Santiago (2023 J. Fluid Mech. vol. 976, p. A30) on Newtonian fluids, we have developed a governing equation for solute dynamics that accounts for the combined effects of fluid viscoelasticity, molecular diffusivity and channel geometry. This equation is expressed using key dimensionless parameters: the Weissenberg number, the Péclet number and a shape-dependent dimensionless function. Solving this model allows us to analyse the temporal evolution of the solute distribution, including its mean and variance. Our analysis shows that viscoelasticity significantly decreases the effective solute diffusivity compared with that observed in a Newtonian fluid. Additionally, we have identified a specific combination of parameters that results in zero or negative transient growth of the variance. This finding is illustrated in a phase diagram and provides a means for transient control over dispersion. We validated our results against Brownian dynamics simulations and previous literature, highlighting potential applications for the design and optimisation of microfluidic devices.

JFM classification

Mass Transport: Dispersion Non-Newtonian Flows: Viscoelasticity Mass Transport: Coupled diffusion and flow

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1025 , 25 December 2025 , A9
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© The Author(s), 2025. Published by Cambridge University Press

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