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 d...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.展开更多
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...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.展开更多
The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to b...The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible, and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability, Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress.展开更多
文摘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.
文摘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.
文摘The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible, and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability, Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress.
