TITLE:
Analysis of the Linear Temporal Stability of Blood Flow under the Influence of a Magnetic Field in Microvessels
AUTHORS:
Toha François Lihonou, Kalil Pierre Mathos, Hilaire Segning, Abdelghani Laouer, Casimir Raymond Tefo, Amoussou Laurent Hinvi
KEYWORDS:
Linear Temporal Stability, Blood Flow, Microvessels, BVP4C Technique, Spectral Collocation Method
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.16 No.3,
September
10,
2026
ABSTRACT: In this work, we study the linear temporal stability of a unidirectional Poiseuille blood flow under the influence of the magnetic parameter and the Reynolds number. Blood is modeled as a spatially inhomogeneous fluid, with its viscosity dependent on the red blood cell concentration. We focus on small blood vessels, such as the terminal branches of arteries, arterioles, and small veins. For the basic flow, assumed to be laminar and two-dimensional, the basic velocity profiles were obtained numerically, including the magnetic effect, using the BVP4C method in Matlab. Stability analysis was performed using classical linear temporal analysis in terms of normal modes, leading to a fourth-order eigenvalue problem solved numerically using the Chebyshev spectral collocation method. The results indicate that the flow is unconditionally unstable. However, increasing the magnetic parameter or the Reynolds number, coupled with decreasing red blood cell concentration, reduces the degree of flow instability. The stabilization of blood flow in microvessels is essential for protecting the vascular walls.