Study about the structure and dynamics of magnetic nanofluids using a mesoscopic simulation approach

Modelling of magnetic bead transport in a microvascular network

“…where  is the bead mass (assumed the same for all the beads), N is the total number of beads, 𝐅 , is the viscous drag force, 𝐅 , is the magnetic force due to applied magnetic fields, 𝐅 , is the force related to the magnetic dipole-dipole interactions between the i-th and j-th beads and 𝐅 , is the steric repulsive force that occurs when the surfactant layers of the i-th and j-th beads are going to overlap [18,19]. In the following, the different force contributions are briefly described.…”

“…where 𝐫 = 𝐫 − 𝐫 is the vector distance between beads barycenters, with the corresponding unit vector 𝐞 = 𝐫 [19,20]. When the distance between two beads is larger than 12 times the bead radius, we consider the contribution from the dipole-dipole interaction negligible.…”

“…To preserve ferrofluid stability and limit aggregation phenomena, MNPs and magnetic beads are generally coated with a surfactant layer, which is responsible for a steric repulsion force, whose effect becomes important when particles are so close that their coating layers start overlapping [18,19].…”

“…The model combines the Navier-Stokes equations, to simulate blood flow, with classical Newtonian dynamics [17], to calculate the trajectory of each bead. As factors of influence of bead motion, we consider the magnetic force, which is generated by a permanent magnet outside the vessel, the hydrodynamic force, the magnetic dipole-dipole interactions between beads and the steric repulsion effects due to bead surfactant layer, generally added to preserve colloidal stability [18,19].…”

Tuning the dimensional order in self-assembled magnetic nanostructures: theory, simulations, and experiments

“…Recent studies have revealed that self-assembly can occur through inherent magnetic interactions, even in the absence of external magnetic fields. [20][21][22] Moreover, several measurements [23][24][25] have provided evidence that the resulting magnetic properties critically depend on the configurations of the nanoparticles in the final structures. These findings have significantly contributed to our fundamental understanding of the magnetic properties exhibited by MNPs and their arrangements.…”