Dynamics of rotating paramagnetic particle chains simulated by particle dynamics, Stokesian dynamics and lattice Boltzmann methods

Abstract

Paramagnetic particles, when subjected to external unidirectional rotating magnetic fields, form chains which rotate along with the magnetic field. In this paper three simulation methods, particle dynamics (PD), Stokesian dynamics (SD) and lattice Boltzmann (LB) methods, are used to study the dynamics of these rotating chains. SD simulations with two different levels of approximations-additivity of forces (AF) and additivity of velocities (AV)-for hydrodynamic interactions have been carried out. The effect of hydrodynamic interactions between paramagnetic particles under the effect of a rotating magnetic field is analyzed by comparing the LB and SD simulations, both of which include hydrodynamic interactions, with PD simulations in which hydrodynamic interactions are neglected. It was determined that for macroscopically observable properties like average chain length as a function of Mason number, reasonable agreement is found between all the three methods. For microscopic properties like the force distribution on each particle along the chain, inclusion of hydrodynamic interaction becomes important to understand the underlying physics of chain formation.

Numerical and experimental study of a rotating magnetic particle chain in a viscous fluid

“…Thus, the expression for the magnetic interaction force F m i acting on the i th super-paramagnetic particle in a collection of N particles equals [9,13]:…”

“…The excluded-volume force is implemented to model 'hard' sphere particles and thus to prevent them from overlapping [9,13]:…”

“…Rotational dynamics of isolated magnetic particle chains have also been studied extensively [10][11][12][13]. The rotating chains are observed to undergo a process of dynamic growth and fragmentation that is dependent on the frequency of the applied field.…”

“…Typical structures such as linear chains and S-shaped chains are noted. Yadav et al [12] and Krishnamurthy et al [13] observed that the particle dynamics method is able to predict the macroscopic chain dynamics accurately. But, for microscopic properties, inclusion of hydrodynamic interactions becomes important.…”

Self-organizing magnetic beads for biomedical applications

“…6) is used to calculate the force F d on an object in a fluid, with particle radius r, density ρ and viscosity η of the fluid and the relative velocity v of the particle. Krishnamurthy et al [7] show that Stokes drag is a good approximation for the force acting on the beads.…”