https://doi.org/10.1140/epjp/s13360-025-07221-z
Regular Article
Asymptotic analysis of a multi-layered model of KL-Newtonian fluids for blood flow dynamics in microvessels: a varying viscosity and permeability approach
1
Department of Mathematics, Birla Institute of Technology and Science Pilani, 333031, Pilani, Rajasthan, India
2
Department of Mathematics, VIT-AP University, 522237, Amaravati, Andhra Pradesh, India
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Received:
16
February
2025
Accepted:
15
December
2025
Published online:
3
January
2026
Abstract
The present study investigates the flow dynamics of a two-fluid model based on KL-Newtonian fluids mimicking the blood flow through microvessels. The model distinguishes between the central region of the vessel occupied with the red blood cells and the outer plasma region, where the flow is governed by the Kuang and Luo (K–L) and the Newtonian fluids, respectively. Due to the presence of the glycocalyx layer and impurities near the vessel wall, the plasma region is further divided into three subregions, i.e., a non-porous layer adjacent to the central region, an intermediate transition Brinkman layer, and an outer Brinkman–Forchheimer region. The model accounts for spatial variations in permeability and fluid viscosity in the two outer porous regions. The regular perturbation method for high permeabilities and the singular perturbation method with matched asymptotic expansions for low permeabilities are applied to solve the momentum equations in porous regions to acquire the asymptotic solutions. The effect of external body forces has been studied through Froude number. The dependence of velocity, flow rate, and flow resistance on the numerous control parameters such as Froude number, Reynolds number, Kuang and Luo (K–L) fluid parameters, viscosity, and the porous medium parameters is analyzed graphically. Although the porous plasma region is thin, changes in its permeability measurably affect the velocity profile and derived flow quantities. The variation of plug-core velocity with Froude number indicates an increasing influence of inertial forces relative to gravitational forces. Specifically, as the Froude number increases, the flow profile experiences a deceleration, indicating that inertial effects become increasingly influential. The explanations could be informative for clinical applications, such as pulmonary hemodynamics and gastrointestinal anatomy. However, empirical validation remains an essential step in establishing the applicability of the results.
Mathematics Subject Classification: 76D07 / 76M45 / 76T06
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
