Abstract
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.
Highlights
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 inducing electrical currents and voltages along the vessel walls and in the neighboring tissues
The analysis presented in this paper is based on the exact solution given by Gold [14] for the stationary blood flow in a rigid vessel with insulating wall in the presence of an external static magnetic field
Summary
The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B0. The analysis presented in this paper is based on the exact solution given by Gold [14] for the stationary blood flow in a rigid vessel with insulating wall in the presence of an external static magnetic field. This analysis completes a previous one [15]. Since the magnetic field breaks the flow axisymmetry, it is interesting to study in details the velocities, pressure, forces, induced fields and currents in a vessel cross section Such integrations over the cross-section of the vessel would be necessary in order to explore the feasibility of deriving 1-D equations [16] for this type of flow
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