Biological flows under the effect of strong magnetic fields with micropolar theory

Abstract

This doctoral thesis is focused on examining the effect of strong externally applied magnetic fields on blood flows using micropolar fluid theory. Micropolar fluid theory developed by Eringen in 1998 is an extension of the classical model for Newtonian fluids, i.e. the Navier–Stokes equations. The main feature of micropolar fluids is microrotation, a vector field that represents the particles’ average rotational velocity and is solved in addition to the fluid’s velocity. Blood is a popular example of a micropolar fluid, due to the existence of the blood cells in the plasma. Moreover, blood contains the erythrocytes (red blood cells), which contain the hemoglobin molecule, an iron oxide that behaves like a ferromagnetic particle. Such particles exhibit strong forces because of the magnetic polarization (magnetization) when an external magnetic field is applied. In general, the magnetization tends to relax with the externally applied magnetic field. Due to this misalignment, a magnetic torque arises, which also affects the microrotation of the erythrocytes. This phenomenon is called micromagnetorotation (MMR). In most theoretical and numerical studies that study the effect of applied magnetic fields on blood flows, micromagnetorotation is ignored, due to the assumption that a magnetic field cannot influence erythrocytes’ microrotation. On the other hand, there are experimental studies that show a significant velocity reduction in blood flows and symptoms such as vertigo and nausea that cannot be explained only by the effect of the Lorentz force, due to the small electrical conductivity of blood. In this manner, this doctoral thesis is dedicated to the study of the effect of micromagnetorotation on micropolar blood flows under the effect of externally applied magnetic fields, focusing on possible mechanisms of diffusion/ interruption of blood, when a body is imported in MRI scanners. Finally, the effect of micromagnetorotation on pathological conditions, such as stenosis is also examined.