Catheter-modulated transient solute dispersion in micropolar annular flow with a retentive and absorptive arterial wall
Abstract
We study transient solute dispersion in pressure-driven micropolar flow through a concentric annulus representing a catheterized artery. The catheter is impermeable to solute, whereas the arterial wall combines irreversible removal with reversible surface retention. The exact steady micropolar velocity field is coupled to the Gill-Sankarasubramanian generalized-dispersion framework; the resulting bulk-surface hierarchy is advanced with Rannacher-damped Crank-Nicolson time stepping to determine K0(t), K1(t) and K2(t). The exchange coefficient is independent of the micropolar parameters and satisfies −K0(0+)=2(β+θDa)/(1−λ2), whereas K2−Pe−2∼σv2t initially, so the leading short-time dispersion is hydrodynamic and independent of wall kinetics. In the weak-reaction regime, micropolarity modifies convection approximately linearly and shear dispersion quadratically through the velocity-amplitude factor. A narrow-gap analysis with ε=1−λ gives v̅∼(2−Nc)ε2/6 and K2−Pe−2∼(2−Nc)2ε6/7560 for a fixed pressure gradient, revealing a sixth-power suppression of shear dispersion as the catheter approaches the arterial wall. Increasing λ from $0.01$ to $0.30$ reduces effective convection by about a factor of $2.45$, while chemically passive shear-induced dispersion falls by a factor of $24$. The coupled formulation also yields the exact partition Φm+Φs+Φa=1, separating mobile, reversibly retained and irreversibly absorbed solute. The reconstructed field quantifies reaction-modulated transverse non-uniformity, while the results distinguish hydrodynamic effects of confinement and microrotation from kinetic wall effects.
Related
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BibTeX
@misc{ahmed2026cathetermodulated,
title = {{Catheter-modulated transient solute dispersion in micropolar annular flow with a retentive and absorptive arterial wall}},
author = {Sohel Ahmed and Nanda Poddar and Kajal Kumar Mondal and Subham Dhar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38423},
eprint = {2609.38423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38423},
}
RIS
TY - UNPB
TI - Catheter-modulated transient solute dispersion in micropolar annular flow with a retentive and absorptive arterial wall
AU - Sohel Ahmed
AU - Nanda Poddar
AU - Kajal Kumar Mondal
AU - Subham Dhar
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38423
UR - https://arxiv.org/abs/2609.38423
AB - We study transient solute dispersion in pressure-driven micropolar flow through a concentric annulus representing a catheterized artery. The catheter is impermeable to solute, whereas the arterial wall combines irreversible removal with reversible surface retention. The exact steady micropolar velocity field is coupled to the Gill-Sankarasubramanian generalized-dispersion framework; the resulting bulk-surface hierarchy is advanced with Rannacher-damped Crank-Nicolson time stepping to determine K_0(t), K_1(t) and K_2(t). The exchange coefficient is independent of the micropolar parameters and satisfies −K_0(0^+)=2(β+θDa)/(1−λ^2), whereas K_2−Pe^−2∼σ_v^2t initially, so the leading short-time dispersion is hydrodynamic and independent of wall kinetics. In the weak-reaction regime, micropolarity modifies convection approximately linearly and shear dispersion quadratically through the velocity-amplitude factor. A narrow-gap analysis with ε=1−λ gives v̅∼(2−N_c)ε^2/6 and K_2−Pe^−2∼(2−N_c)^2ε^6/7560 for a fixed pressure gradient, revealing a sixth-power suppression of shear dispersion as the catheter approaches the arterial wall. Increasing λ from $0.01$ to $0.30$ reduces effective convection by about a factor of $2.45$, while chemically passive shear-induced dispersion falls by a factor of $24$. The coupled formulation also yields the exact partition Φ_m+Φ_s+Φ_a=1, separating mobile, reversibly retained and irreversibly absorbed solute. The reconstructed field quantifies reaction-modulated transverse non-uniformity, while the results distinguish hydrodynamic effects of confinement and microrotation from kinetic wall effects.
ER -