Development of stepwise particle dosing algorithm in magnetic solution deposition to clarify maximum area fraction points

We investigated sedimentation in a colloidal dispersion composed of spherical ferromagnetic particles using Brownian dynamic simulations. We developed an algorithm to derive the maximum surface integral rate points, which is the area fraction that prevents the formation of a thin film under each condition, to clarify the conditions for forming a desired thin film in which spherical ferromagnetic particles settle down and exist separately. We derived the maximum surface integral rate points by dosing spherical ferromagnetic particles according to the formation of clusters under each of the 10000 total conditions, by varying the applied magnetic field, magnetic force between the particles, mass density, and temperature of the solution. The main results are summarized as follows. When the strength of the applied magnetic field is increased, the magnetic moment of the particle is strongly restrained in the direction of the magnetic field. Therefore, only the repulsive force caused by the magnetic moment of the particle is applied in the horizontal direction of the particle, leading to the formation of thin films with maximum surface integral rate points of less than 0.243. However, higher-density limiting points were undesirable. Therefore, increasing the random force improved the number of conditions in which the maximum surface integral rate points were greater than 0.243. In the condition where the strength of the applied magnetic field and the random force are large, the maximum surface integral rate points tend to be large; however, the force applied to the particle is large. Depending on the magnitude of the magnetic force between particles, there are conditions where the balance of the force is unstable and the maximum surface integral rate points decrease significantly. However, as the mass density increased, the maximum surface integral rate points increased. We found that by dosing particles according to cluster formation, we could reach a maximum area fraction of 0.322, even though we could not reach an area fraction of 0.403 when all particles formed a thin film.