Linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles: application to controlled drug delivery

Abstract

Purpose For this purpose, a linear stability analysis based on the Navier–Stokes and Maxwell equations is made leading to an eigenvalue differential equation of the modified Orr–Sommerfeld type which is solved numerically by the spectral collocation method based on Chebyshev polynomials. Unlike previous studies, blood is considered as a non-Newtonian fluid. The effects of various parameters such as volume fraction of nanoparticles, Casson parameter, Darcy number, Hartmann number on flow stability were examined and presented. This paper aims to investigate a linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles with an application to controlled drug delivery. Design/methodology/approach Targeted delivery of therapeutic agents such as stem cells and drugs using magnetic nanoparticles with the help of external magnetic fields is an emerging treatment modality for many diseases. To this end, controlling the movement of nanoparticles in the human body is of great importance. This study investigates controlled drug delivery by using magnetic nanoparticles in a porous artery under the influence of a magnetic field. Findings It was found the following: the Casson parameter affects the stability of the flow by amplifying the amplitude of the disturbance which reflects its destabilizing effect. It emerges from this study that the taking into account of the non-Newtonian character is essential in the modeling of such a system, and that the results can be very different from those obtained by supposing that the blood is a Newtonian fluid. The presence of iron oxide nanoparticles in the blood increases the inertia of the fluid, which dampens the disturbances. The Strouhal number has a stabilizing effect on the flow which makes it possible to say that the oscillating circulation mechanisms dampen the disturbances. The Darcy number affects the stability of the flow and has a stabilizing effect, which makes it possible to increase the contact surface between the nanoparticles and the fluid allowing very high heat transfer rates to be obtained. It also emerges from this study that the presence of the porosity prevents the sedimentation of the nanoparticles. By studying the effect of the magnetic field on the stability of the flow, it is observed that the Hartmann number keeps the flow completely stable. This allows saying that the magnetic field makes the dissipations very important because the kinetic energy of the electrically conductive ferrofluid is absorbed by the Lorentz force. Originality/value The originality of this paper resides on the application of the linear stability analysis for controlled drug delivery.

The impact of strut profile geometry and malapposition on the haemodynamics and drug-transport behaviour of arteries treated with drug-eluting stents

“…Blood was modelled with uniform density, r = 1060 kg/m 3 , and laminar flow conditions were assumed due to the low Reynolds numbersless than 1300 (Yamamoto et al, 2004) in the renal vasculature. Numerical studies have shown that factors including the non-Newtonian properties of blood and body accelerations can affect solute dispersion in blood flow (Saadun et al, 2021); non-Newtonian properties have also been shown to be essential when modelling targeted delivery of therapeutic agents (Tiam Kapen et al, 2022). Nonetheless, a constant viscosity of m = 0.00345 Pa•s, based on blood's lowest viscosity limit, was ascribed to the blood for three main reasons: it yields more exaggerated flow disturbances than non-Newtonian blood rheological models (Vijayaratnam et al, 2015); the wall shear stress thresholds used in the present study were originally obtained (Chen et al, 2015;LaDisa et al, 2004), and; the choice of blood rheological model has negligible impact on the drug transport behaviour in the context of stented arteries (Vijayaratnam et al, 2015(Vijayaratnam et al, , 2019.…”

Analysis of Nanodrug Delivery in Blood Flowing through Blood Vessels Using Machine Learning Models

“…Sutterby fluid acted as a base fluid that was non-Newtonian in nature. Tiam et al [8] analyzed the linear stability of blood flow consisting of magnetic nanoparticles and investigated the controlled drug delivery taking place in a porous artery in the presence of a magnetic field. Their study placed importance on controlling the mobility of the nanoparticles.…”