We present an analytical model that explains the motion of finite-size diamagnetic particles in paramagnetic or diamagnetic fluid media. Our model problem is the magnetic field-assisted three-dimensional assembly of carboxylate microspheres in a gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) solution that is placed in a cuboid. The trajectory of each microparticle is determined through a time marching solution of its equation of motion. The effects of the (1) magnetic field distribution and (2) magnetic susceptibility of the paramagnetic solution, which depends on the Gd-DTPA concentration, on the dynamics of particle assembly are identified. Validation of the analytical model is provided through experimental measurements. For the first time, we demonstrate that it is possible to form structures of diamagnetic particles in diamagnetic fluid media, for which we select the assembly of graphene in water.

中文翻译：

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顺磁性和反磁性介质中反磁性微粒的三维打印

我们提出了一个分析模型，该模型解释了顺磁性或反磁性流体介质中有限尺寸反磁性粒子的运动。我们的模型问题是在放置在长方体中的钆-二亚乙基三胺五乙酸 (Gd-DTPA) 溶液中的羧酸盐微球的磁场辅助三维组装。每个微粒的轨迹是通过其运动方程的时间推进解来确定的。确定了顺磁性溶液的 (1) 磁场分布和 (2) 磁化率（取决于 Gd-DTPA 浓度）对粒子组装动力学的影响。分析模型的验证是通过实验测量提供的。首次，