Force acting on a cluster of magnetic nanoparticles in a gradient field: A Langevin dynamics study

•Magnetophoretic force on the cluster of nanoparticles is obtained numerically.•For a given particle number, the force decreases with concentration.•Simulation results are interpreted analytically.•New analytical expression for the magnetophoretic mobility is proposed. Magnetophoretic force acting on a rigid spherical cluster of single-domain nanoparticles in a constant-gradient weak magnetic field is investigated numerically using the Langevin dynamics simulation method. Nanoparticles are randomly and uniformly distributed within the cluster volume. They interact with each other via long-range dipole-dipole interactions. Simulations reveal that if the total amount of particles in the cluster is kept constant, the force decreases with increasing nanoparticle concentration due to the demagnetizing field arising inside the cluster. Numerically obtained force values with great accuracy can be described by the modified mean-field theory, which was previously successfully used for the description of various dipolar media. Within this theory, a new expression is derived, which relates the magnetophoretic mobility of the cluster with the concentration of nanoparticles and their dipolar coupling parameter. The expression shows that if the number of particles in the cluster is fixed, the mobility is a nonmonotonic function of the concentration. The optimal concentration values that maximize the mobility for a given amount of magnetic phase and a given dipolar coupling parameter are determined.