Numerical simulation of particles movement in cellular flows under the influence of magnetic forces

A numerical model of particle motion in fluid flow under the influence  of hydrodynamic and magnetic forces is presented. The  Lagrangian particle tracking algorithm was developed being capable  of simulating dilute suspensions of particles in viscous flows where  gravity, buoyancy, drag, pressure gradient, added mass and  magnetophoretic forces are taken into account. The method is used   to study the behaviour of magnetite particles in a periodic cellular  flow field under the influence of a magnetic field produced by electric  wires placed in cell centres. For such a flow field it is known  that particles in steady state merge into individual trajectories. The   influence of the magnetic field on the particle trajectories is examined  and an exponential model for the time evolution of the  fraction of adhered particles to the electric wires is proposed. Three  particle Stokes number values are considered: 0.01, 0.1 and 1. The   existence of a critical magnetic pressure coefficient was found, at  which all particles end up to be adhered to the wires. The critical  magnetic pressure coefficient was found to be proportional to the   Stokes number. For sub-critical magnetic pressure coefficient, the  particle trajectories are significantly altered by the magnetic field,   both in their shape and in their number. Furthermore, in the   sub-critical regime, the minimal distance of particles to the cell   centres is larger for particles with smaller Stokes numbers.