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.

中文翻译：

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用磁性纳米粒子对非牛顿血流进行线性稳定性分析：在受控药物输送中的应用

目的

为此，基于 Navier-Stokes 和 Maxwell 方程进行线性稳定性分析，得到修正的 Orr-Sommerfeld 型特征值微分方程，该方程通过基于 Chebyshev 多项式的谱搭配方法进行数值求解。与之前的研究不同，血液被认为是一种非牛顿流体。检查并展示了各种参数，例如纳米颗粒的体积分数、卡森参数、达西数、哈特曼数对流动稳定性的影响。本文旨在研究使用磁性纳米粒子对非牛顿血流的线性稳定性分析，并将其应用于受控药物递送。

设计/方法/方法

在外部磁场的帮助下，使用磁性纳米粒子靶向递送治疗剂（例如干细胞和药物）是许多疾病的新兴治疗方式。为此，控制纳米粒子在人体内的运动非常重要。本研究通过在磁场影响下的多孔动脉中使用磁性纳米颗粒来研究受控药物递送。

发现

结果表明：卡森参数通过放大反映其不稳定效应的扰动幅度来影响流动的稳定性。从这项研究中可以看出，在这种系统的建模中考虑非牛顿特性是必不可少的，并且结果可能与假设血液是牛顿流体所获得的结果大不相同。血液中氧化铁纳米颗粒的存在增加了流体的惯性，从而抑制了干扰。Strouhal 数对流动具有稳定作用，这使得可以说振荡循环机制抑制了扰动。达西数影响流动的稳定性并具有稳定作用，这使得增加纳米颗粒和流体之间的接触表面成为可能，从而获得非常高的传热率。该研究还表明，孔隙的存在阻止了纳米颗粒的沉降。通过研究磁场对流动稳定性的影响，观察到哈特曼数使流动完全稳定。这允许说磁场使耗散非常重要，因为导电铁磁流体的动能被洛伦兹力吸收。据观察，哈特曼数保持流动完全稳定。这允许说磁场使耗散非常重要，因为导电铁磁流体的动能被洛伦兹力吸收。据观察，哈特曼数保持流动完全稳定。这允许说磁场使耗散非常重要，因为导电铁磁流体的动能被洛伦兹力吸收。

原创性/价值

本文的独创性在于线性稳定性分析在受控药物递送中的应用。