Author(s)

Agnès Drochon¹, Vincent Robin², Odette Fokapu¹, Dima Abi-Abdallah Rodriguez³

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

The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several biomedical applications: magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold (1962) (with the induced fields not neglected) is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.

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

Drochon, A. , Robin, V. , Fokapu, O. and Rodriguez, D. (2016) Stationary Flow of Blood in a Rigid Vessel in the Presence of an External Magnetic Field: Considerations about the Forces and Wall Shear Stresses. Applied Mathematics, 7, 130-136. doi: 10.4236/am.2016.72012.