Simulation of the optimal diameter and wall thickness of hollow Fe₃O₄ microspheres in magnetorheological fluids

Abstract

This work reported a simulation study on the optimal diameter (D) and wall thickness (H) of hollow Fe3O4 microspheres to improve the magnetorheological (MR) effect. Modified formulae for the magnetic dipolar force, van der Waals force, and hydrodynamic drag force were employed in the simulation model. Typical evolution of shear stress and microstructures in steady shear flow was obtained. The shear stress-strain curve was divided into linear, fluctuant, and homeostasis regions, which were related to the inclination of particle chains and the lateral aggregation. For hollow Fe3O4 microspheres with different diameters and wall thicknesses, the shear stress curves collapsed onto a quadratic master curve. The best wall thickness was H = 0.39D for a 20 wt% MR fluid and H = 0.35D for a 40 wt% MR fluid, while the optimal diameter was D = 1000 nm and D = 100 nm, respectively. The maximum shear stress of the 40 wt% MR fluid was twice that of the 20 wt% MR fluid. The change of shear stress was due to the competition that results among the magnetic interaction, number of neighbors, tightness, and orientation of the particle chains. Simulated dimensionless viscosity data as a function of Mason number for various diameters, wall thicknesses, and weight fractions collapsed onto a single master curve. The simulated shear stress under both a magnetic field and shear rate sweep matched well with experiments.

Magnetorheology: a review

“…Moreover, hydrothermal methods have also been successful in the fabrication of hollow magnetic particles. 32 Other methods and syntheses modifications apart from hydro-and solvothermal ones have also been reported in the formulation of MRFs. For instance, Berasategi et al 33 used the electric explosion of a wire to fabricate iron nanoparticles with a saturation magnetization larger than that of CIPs and a high production rate.…”

Recent progress on the simulation technology of magnetic fluid

“…Parsegian [33] 指出, 两个 球形颗粒间的范德华力为 评 述 图 1 (网络版彩色)磁性液体剪切模式示意图. (a) 宏观示意图 [13] ; (b) 细观示意图 [20] Figure 1 (Color online) Schematic diagram of magnetic fluid under shear mode. (a) From macroscopic view [13] ; (b) from mesoscopic view [20] [34] 提出, 为了避免范德华力趋于 [35] 引入了颗粒间的指数排斥力:…”

“…(a) 分子动力学模拟, 其中小颗粒代表基体 [48] ; (b) 颗粒动力学模拟 [20] Figure 4 (Color online) Typical microstructures of magnetic fluid obtained from simulations. (a) Molecular dynamics simulation, small spheres represent the matrix [48] ; (b) particle-level dynamic simulation [20] (式(13)), 可以得到所需的宏观物理量和力学量. 分 子动力学适用于微观到细观尺度问题, 可像实验一 样实时观察, 许多实验中难以获得的微观细节, 在模 拟中都可以方便地观察到, 这一优点使其成为机理 研究的有效手段.…”

“…(a) Microstructures obtained from Monte Carlo simulation [18] ; (b) flow curves obtained from machine learning simulation [19] 评 述 表 1 磁性液体常用数值模拟方法的适用范围及优缺点 [20] ; (b) 流动曲线 [20] ; (c) 粒径、 壁厚、 质量分数对空心Fe 3 O 4 磁流变液表观黏度的影响 [20] ; (d) 体积分数、反磁颗粒比例对顺-反磁颗粒磁性液体正应力的影响 [80] Figure 7 (Color online) Simulation results of mechanical properties of novel magnetic fluid. (a) Shear stress versus magnetic flux density curves of hollow Fe 3 O 4 MR fluid [20] ; (b) flow curves [20] ; (c) influences of particle diameter, wall thickness, and weight fraction on the apparent viscosity of hollow Fe 3 O 4 MR fluid [20] ; (d) the magneto-induced normal stress of magnetic fluid with different volume fractions and ratios of diamagnetic particles [80] ( ) 图 8 (网络版彩色)传统磁性液体复杂力学行为的数值模拟结果. (a) 磁性液体沉降前后的内部结构图 [82] ; (b) 多分散磁性液体连通性随时间的 演化 [83] Figure 8 (Color online) Simulation results of complex mechanical behaviors of conventional magnetic fluid.…”

Shape-Controlled Syntheses of Magnetite Microparticles and Their Magnetorheology

“…In fact, ferrofluids, which are colloidal dispersions of magnetic nanoparticles approximately 10 nm in diameter, exhibit a weak MR effect because of predominant Brownian motion [8]. As another material for MR fluids, magnetite (Fe 3 O 4 ) particles have been studied because they exhibit better chemical stability against oxidation and are less prone to sedimentation than Fe particles [9,10,11].…”