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A Review of Some Reference Analytic Solutions for the Magnetohydrodynamic Flow of Blood

Applied Mathematics 2018年第10期9卷 1179-1192页

作者： Agnès Drochon manon beuque Dima Abi-Abdallah Rodriguez Université de Technologie de Compiègne Galileo Galilei Sorbonne Universités Compiègne France Université de Technologie de Compiègne Compiègne France IR4M Paris-Sud University Université Paris Saclay Orsay France

A short review of some reference solutions for the magnetohydrodynamic flow of blood is proposed in this paper. We present in details the solutions of Hartmann (1937), of Vardanyan (1973) and of Sud et al. (1974). In each case, a comparison is provided with the corresponding solution for the flow without any external magnetic field, namely Poiseuille (plane or cylindrical) and Womersley. We also present a synopsis of some other solutions for people who would like to go further in this topic. The interest in MHD flow of blood may be motivated by many reasons, such as Magnetic Resonance Imaging (MRI), Pulse Wave Velocity measurement, magnetic drug targeting, tissue engineering, mechanotransduction studies, and blood pulse energy harvesting… These fundamental solutions should also be used as particular limiting cases to validate any proposed more elaborated solutions or to validate computer codes.

关键词： Magnetohydrodynamic Flow of Blood Magnetic Field in Biomedical Applications Hartmann Womersley

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Impact of an External Magnetic Field on the Shear Stresses Exerted by Blood Flowing in a Large Vessel

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Journal of Applied Mathematics and Physics 2017年第7期5卷 1493-1502页

作者： Agnès Drochon manon beuque Dima Abi-Abdallah Rodriguez UMR CNRS 7338 Université de Technologie de Compiègne Galileo Galilei Sorbonne Universités Compiègne France Université de Technologie de Compiègne Compiègne France IR4M 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.

关键词： Magnetohydrodynamic Flow of Blood Wall Shear Stresses Magnetic Fields in Biomedical Applications

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