Understanding the motion of particles on an air-liquid interface can impact a wide range of scientific fields and applications. Diamagnetic particles floating on an air–paramagnetic-liquid interface are previously known to have a repulsive motion from a magnet. Here, we show a motion mechanism where the diamagnetic particles floating on the air–paramagnetic-liquid interface are attracted and eventually trapped at an off-center distance from the magnet. The behavior of magnetic particles has been also studied and the motion mechanisms are theorized in a unified framework, revealing that the motion of particles on an air–paramagnetic-liquid interface is governed not only by magnetic energy, but as an interplay of the curvature of the interface deformation created by the nonuniform magnetic field, the gravitational potential, and the magnetic energy from the particle and the liquid. The attractive motion mechanism has been applied in directed self-assembly and robotic particle guiding.

中文翻译：

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气-顺磁-液界面上的微米和毫米大小颗粒的运动和捕获

了解颗粒在气液界面上的运动会影响广泛的科学领域和应用。先前已知漂浮在空气-顺磁性-液体界面上的反磁性粒子具有来自磁体的排斥运动。在这里，我们展示了一种运动机制，其中漂浮在空气-顺磁性-液体界面上的反磁性粒子被吸引，并最终以与磁铁偏离中心的距离被捕获。还研究了磁性粒子的行为，并在统一的框架中对运动机理进行了理论分析，结果表明，空气-顺磁-液界面上的粒子运动不仅受磁能支配，而且还受制于其曲率的相互作用。由非均匀磁场，引力引起的界面变形，以及来自粒子和液体的磁能。有吸引力的运动机制已应用于定向自组装和机器人粒子引导。