Author(s)

Agnès Drochon^1*, Manon Beuque², Dima Abi-Abdallah Rodriguez³

¹UMR CNRS 7338, Université de Technologie de Compiègne, Galileo Galilei Sorbonne Universités, Compiègne, France.
²Université de Technologie de Compiègne, Compiègne, France.
³IR4M, Université Paris Sud-Paris Saclay, Orsay, France.

The aim of this paper is to provide an advanced analysis of the shear stresses exerted on vessel walls by the flowing blood, when a limb or the whole body, or a vessel prosthesis, a scaffold… is placed in an external static magnetic field B₀. This type of situation could occur in several biomedical applications, such as magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering, mechanotransduction studies… Since blood is a conducting fluid, its charged particles are deviated by the Hall effect, and the equations of motion include the Lorentz force. Consequently, the velocity profile is no longer axisymmetric, and the velocity gradients at the wall vary all around the vessel. To illustrate this idea, we expand the exact solution given by Gold (1962) for the stationary flow of blood in a rigid vessel with an insulating wall in the presence of an external static magnetic field: the analytical expressions for the velocity gradients are provided and evaluated near the wall. We demonstrate that the derivative of the longitudinal velocity with respect to the radial coordinate is preponderant when compared to the θ-derivative, and that elevated values of B₀ would be required to induce some noteworthy influence on the shear stresses at the vessel wall.

Magnetohydrodynamic Flow of Blood, Wall Shear Stresses, Magnetic Fields in Biomedical Applications

Drochon, A. , Beuque, M. and Rodriguez, D. (2017) Impact of an External Magnetic Field on the Shear Stresses Exerted by Blood Flowing in a Large Vessel. Journal of Applied Mathematics and Physics, 5, 1493-1502. doi: 10.4236/jamp.2017.57122.