On the development of OpenFOAM solvers for simulating MHD micropolar fluid flows with or without the effect of micromagnetorotation

Abstract

Any micropolar fluid containing magnetic particles, such as blood or ferrofluids, subjected to an external magnetic field experiences a magnetic torque due to the misalignment between particle magnetization and the magnetic field. This effect, known as micromagnetorotation (MMR), remains underexplored in blood flows where erythrocyte magnetization is often neglected. To investigate this, two transient OpenFOAM solvers were developed: epotMicropolarFoam, for incompressible, laminar magnetohydrodynamic (MHD) micropolar flows, and epotMMRFoam, which extends it by incorporating MMR. Both solvers use the PISO algorithm for pressure-velocity coupling and adopt the low magnetic Reynolds number approximation. Micropolar effects are modeled by including the microrotation-vorticity difference in the momentum equation and solving the internal angular momentum equation. In epotMMRFoam, the MMR term is added to this equation, and a constitutive equation for magnetization is also solved. Validation against analytical MHD micropolar Poiseuille flow showed excellent accuracy (error less than 2 percent). Including MMR led to notable reductions in velocity (up to 40 percent) and microrotation (up to 99.9 percent), especially under strong magnetic fields and high hematocrit. Without MMR, magnetic effects were minimal due to the low electrical conductivity of blood. Simulations of 3D MHD artery and 2D MHD aneurysm flows confirmed these findings. In aneurysm geometries, MMR suppressed vortex cores, indicating strong stabilizing and shear-dampening effects. These solvers show high potential for biomedical applications such as magnetic hyperthermia and targeted drug delivery.