The size ratio effect on the microstructure and magnetization of a bidisperse magnetic colloidal suspension

This research examines how the size ratio influences the microstructure and time-dependent magnetization in a bidisperse magnetic colloidal suspension under a uniform magnetic field. Two types of particles model the bidisperse suspension: the small particles of radius R_s and the large particles of radius R_l. The size ratio, ξ = R_l/R_s, defines the particle size difference. The total volume fraction of the suspension, ϕ, is obtained from ϕ = ϕ_s + ϕ_l, where ϕ_s and ϕ_l are the volume fractions of the small and large particles, respectively. The magnetic dipole-dipole interaction among the small particles and the large ones is characterized by the dipolar coupling parameters λ_s and λ_l, respectively. The interactions among the applied magnetic field and the magnetic dipoles of the small and large particles are measured by the Langevin parameters α_s and α_l, respectively. This study performs Brownian dynamics (BD) simulations of a bidisperse suspension comprising N = 1000 particles, with ϕ = 10^-3 and ϕ_s = ϕ_l = 5 × 10^-4. Also, α_s ranges from 0 to 1000, and λ_s from 5 to 30. The size ratio, ξ, takes values of 1, 2 and 3. The values of λ_l and α_l are computed by the parameters aforementioned by assuming that all particles exhibit the same saturation magnetization. Our results show a rich variability in the microstructure as ξ increases. As the large particles increase in size, they exhibit a greater magnetic dipole moment, which induces a non-uniform local magnetic field around them. The surrounding small particles then aggregate with the large ones, driven by this local magnetic field. Small α_s values lead to the formation of flux-closure structures such as rings of small and large particles as well as shell-like structures, which consist of small particles surrounding the large ones. The formation of these microstructures directly affects time-dependent magnetization of the suspension, which exhibits a decay with time in the limit of long times. These findings have important implications for synthesizing magnetic colloidal suspensions with enhanced properties.