Yielding-dependent Taylor dispersion in electrokinetic-magnetohydrodynamic Casson microflows
Abstract
Longitudinal dispersion in a yielding fluid depends on the velocity distribution and on how the flow is maintained. We study a neutral tracer in pressure-assisted electrokinetic and magnetohydrodynamic flow of a Casson fluid through a slit microchannel. The nonlinear stress and velocity equations determine the yielded layers, the unyielded core and the axial flow. Mei's multiple-scale homogenization of the advection-diffusion equation then separates transverse relaxation, mean drift and longitudinal spreading, yielding the Taylor-Aris auxiliary problem and effective diffusivity. An exact pressure-driven solution gives cubic decay of the mean velocity and eighth-power decay of the dispersion enhancement near flow arrest. Under fixed pressure and electrical forcing, increasing the yield parameter from Y=0 to $0.7$ moves the optimum Hartmann number from Hap=0.696 to $2.634$, while the corresponding normalized diffusivity decreases from DTC=1.454 to $1.015$. At fixed mean throughput and Hap=1, the trend reverses: DTC increases from $1.000433$ to $1.002311$. The homogenized energy identity traces this difference to the velocity departure from the sectional mean, including that within the unyielded core. Analytical limiting solutions, direct concentration calculations, numerical convergence studies and a coupled Casson shear test support the reduced-flow predictions. An electrolyte-based dimensional assessment identifies the magnetic optima as theoretical forcing states for representative aqueous microchannels. These results are relevant to predicting longitudinal tracer spreading in microchannels carrying fluids with a yield stress, whether pressure or throughput is controlled.
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BibTeX
@misc{poddar2026yieldingdependent,
title = {{Yielding-dependent Taylor dispersion in electrokinetic-magnetohydrodynamic Casson microflows}},
author = {Nanda Poddar and Debabrata Das and Suman Chakraborty},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25433},
eprint = {2610.25433},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25433},
}
RIS
TY - UNPB
TI - Yielding-dependent Taylor dispersion in electrokinetic-magnetohydrodynamic Casson microflows
AU - Nanda Poddar
AU - Debabrata Das
AU - Suman Chakraborty
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25433
UR - https://arxiv.org/abs/2610.25433
AB - Longitudinal dispersion in a yielding fluid depends on the velocity distribution and on how the flow is maintained. We study a neutral tracer in pressure-assisted electrokinetic and magnetohydrodynamic flow of a Casson fluid through a slit microchannel. The nonlinear stress and velocity equations determine the yielded layers, the unyielded core and the axial flow. Mei's multiple-scale homogenization of the advection-diffusion equation then separates transverse relaxation, mean drift and longitudinal spreading, yielding the Taylor-Aris auxiliary problem and effective diffusivity. An exact pressure-driven solution gives cubic decay of the mean velocity and eighth-power decay of the dispersion enhancement near flow arrest. Under fixed pressure and electrical forcing, increasing the yield parameter from Y=0 to $0.7$ moves the optimum Hartmann number from Ha_p=0.696 to $2.634$, while the corresponding normalized diffusivity decreases from D_T^C=1.454 to $1.015$. At fixed mean throughput and Ha_p=1, the trend reverses: D_T^C increases from $1.000433$ to $1.002311$. The homogenized energy identity traces this difference to the velocity departure from the sectional mean, including that within the unyielded core. Analytical limiting solutions, direct concentration calculations, numerical convergence studies and a coupled Casson shear test support the reduced-flow predictions. An electrolyte-based dimensional assessment identifies the magnetic optima as theoretical forcing states for representative aqueous microchannels. These results are relevant to predicting longitudinal tracer spreading in microchannels carrying fluids with a yield stress, whether pressure or throughput is controlled.
ER -