A numerical model for aggregations formation and magnetic driving of spherical particles based on OpenFOAM®

Abstract

Background and objective This work presents a numerical model for the formation of particle aggregations under the influence of a permanent constant magnetic field and their driving process under a gradient magnetic field, suitably created by a Magnetic Resonance Imaging (MRI) device. Methods The model is developed in the OpenFOAM platform and it is successfully compared to the existing experimental and numerical results in terms of aggregates size and their motion in water solutions. Furthermore, several series of simulations are performed for two common types of particles of different diameter in order to verify their aggregation and flow behaviour, under various constant and gradient magnetic fields in the usual MRI working range. Moreover, the numerical model is used to measure the mean length of aggregations, the total time needed to form and their mean velocity under different permanent and gradient magnetic fields. Results The present model is found to predict successfully the size, velocity and distribution of aggregates. In addition, our simulations showed that the mean length of aggregations is proportional to the permanent magnetic field magnitude and particle diameter according to the relation : l¯a=7.5B0di 3/2. The mean velocity of the aggregations is proportional to the magnetic gradient, according to : u¯a=6.63G˜B0 and seems to reach a steady condition after a certain period of time. The mean time needed for particles to aggregate is proportional to permanent magnetic field magnitude, scaled by the relationship : t¯a∝7B0. Conclusions A numerical model to predict the motion of magnetic particles for medical application is developed. This model is found suitable to predict the formation of aggregations and their motion under the influence of permanent and gradient magnetic fields, respectively, that are produced by an MRI device. The magnitude of the external constant magnetic field is the most important parameter for the aggregations formation and their driving. © 2017 Elsevier B.V.