Magnetophoretic Control of Diamagnetic Particles Inside an Evaporating Droplet

The present study reports the magnetophoresis of diamagnetic particles in an evaporating ferrofluid droplet. Both solid and ring magnet arrangements are used to investigate the effect of magnetic field distribution. The distance of the magnet from the droplet is varied to study the effect of magnetic field strength. The magnetic field distribution is computed using COMSOL multiphysics software. Magnetometer measurements have been carried out to validate the simulation results. The motion of particles and the drying pattern of evaporating ferrofluid droplets are visualized using the confocal microscopy technique. Both bright-field and fluorescence imagings have been carried out to observe the differential deposition of the fluorescent particle (microparticle) and magnetic nanoparticles in the absence and presence of a magnetic field. The velocity of diamagnetic particles as a function of magnetic field distribution and strength has been studied using the micro-PIV technique. In the absence of the magnetic field, a ring-shaped deposition pattern is observed. The mixture of microparticles (diamagnetic) and nanoparticles (magnetic) is deposited between the outer and inner edges of the ring. The diamagnetic particles occupy the inner and outer edges of the ring. Magnetic particles travel toward the higher magnetic field zone and diamagnetic particles move toward the smaller magnetic field zone when a magnetic field is applied by a solid magnet placed over the droplet. This can be attributed to the negative magnetic force originating from the difference between the susceptibility of magnetic and nonmagnetic particles. The negative magnetic force on the microparticle increases as the magnetic field intensity increases, causing the microparticle to convect faster toward the contact line. The deposition behavior can be reversed or suppressed using a ring magnet in place of a solid magnet. In this case, the negative magnetic force is stronger at the contact line region of the droplet and decreases as it approaches the center region of the droplet. The deposition behavior of diamagnetic particle depends on the balance between the Marangoni force and the magnetophoretic force. Overall, the present study demonstrates the capability of the controlled deposition of diamagnetic polystyrene particles by suitable arrangement of the solid and ring magnet.本研究针对蒸发铁磁流体液滴（ferrofluid droplet）内抗磁粒子（diamagnetic particles）的磁泳（magnetophoresis）行为展开报道。研究采用固态磁体与环形磁体两种排布方式，探究磁场分布的影响；通过改变磁体与液滴的间距，分析磁场强度的作用效果。采用COMSOL多物理场（COMSOL Multiphysics）软件计算磁场分布，并通过磁强计测量验证了仿真结果的准确性。利用共聚焦显微镜（confocal microscopy）技术可视化粒子运动与蒸发铁磁流体液滴的干燥沉积形貌，同时开展明场成像与荧光成像，以观测有无磁场条件下荧光微粒（microparticle）与磁性纳米粒子的差异化沉积行为。采用显微粒子图像测速（micro-PIV）技术，研究了抗磁粒子的速度随磁场分布与强度的变化规律。无磁场条件下，可观测到环形沉积形貌：微米颗粒（抗磁性）与纳米颗粒（铁磁性）的混合物沉积于环的内外边缘之间，而抗磁粒子则分布于环的内外边缘处。当在液滴上方放置固态磁体施加磁场时，磁性粒子会向高磁场区域迁移，抗磁粒子则向低磁场区域移动，这可归因于磁性与非磁性粒子磁化率差异产生的负磁作用力。微米颗粒所受的负磁作用力随磁场强度升高而增强，使其更快地向接触线处对流迁移。若改用环形磁体替代固态磁体，则可逆转或抑制上述沉积行为；此时，液滴接触线区域的负磁作用力更强，随着向液滴中心区域靠近，该作用力逐渐减弱。抗磁粒子的沉积行为取决于马兰戈尼力（Marangoni force）与磁泳力之间的平衡。综上，本研究证明了通过合理排布固态磁体与环形磁体，可实现抗磁聚苯乙烯粒子（polystyrene particles）的可控沉积。