Numerical Simulation of Magneto-Rheological Fluids: A Continuum Medium Approach

This work pertains to modern, interdisciplinary research trends in nanomaterials. The author presents a novel method with major potential for various applications such as ferromagnetic brakes and valves; nanosized shock absorbers, and in the medical field, heart valves and medical nanorobots. A mathematical model is constructed with numerical solutions proposed for the system of equations describing the model. The underlying assumption is that a ferromagnetic suspension can be regarded as a continuous medium. Such an assumption was originally suggested in Peskin¿s Immersed Boundary (IB) method. The IB method is coupled with Chorin¿s Projection method to construct a finite differences scheme for solving a boundary value case. The application and the calculations are done to a first order approximation, hence fluid flow is treated as a Stokes flow. The integration of the rheological behavior is implicit, through the force density field. This method can easily extend to an entire class of Newtonian and non-Newtonian ferromagnetic real fluids, whose shear viscosity depend upon the magnetic field, and upon the modulus of the strain rate tensor.

Constantin C. Nichita, Ph.D., studied Mathematics at University of Buffalo. He has a M.S. in Mechanical Engineering from University of Buffalo. Professional experience Postdoctoral Research in Geophysical Mass Flows at University of Buffalo and Postdoctoral Research in Artificial Intelligence at Petroleum-Gas University of Ploiesti.