Motion and trapping of micro- and millimeter-sized particles on the air--paramagnetic-liquid interface

Letter

Motion and trapping of micro- and millimeter-sized particles on the air–paramagnetic-liquid interface

Zoran Cenev, Alois Würger, and Quan Zhou

Phys. Rev. E 103, L010601 – Published 25 January 2021

Abstract

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.

Received 20 August 2020
Accepted 30 November 2020
Corrected 23 February 2021

DOI:https://doi.org/10.1103/PhysRevE.103.L010601

Physics Subject Headings (PhySH)

Capillary interactions Magnetic interactions Surface & interfacial phenomena

Gas-liquid interfaces

Interdisciplinary PhysicsPolymers & Soft Matter

Corrections

23 February 2021

Correction: In the paragraph beginning “Further, the pulling motion ...” (after Figure 4), a value given for the diameter of the NdFeB magnet has been fixed.

Authors & Affiliations

Zoran Cenev ^1,2, Alois Würger ^3,*, and Quan Zhou ^1,†

¹Department of Electrical Engineering and Automation, Aalto University, 02150 Espoo, Finland
²Department of Applied Physics, Aalto University, 02150 Espoo, Finland
³Laboratoire Ondes et Matière d’Aquitaine, Université de Bordeaux and CNRS, 33405 Talence, France

^*alois.wurger@u-bordeaux.fr
^†quan.zhou@aalto.fi

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Issue

Vol. 103, Iss. 1 — January 2021

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Images

Figure 1
Different motion modes for particles on an air–paramagnetic-liquid interface. (a) and (b), (d) and (e), (g) and (h): Experimental observations (top and side views) with (c), (f), (i) corresponding illustrations (not to scale). Green arrows denote the direction of particle motion. In (a) and (b), (d) and (e), and (g) and (h) particle visibility was enhanced with white dots. (a)–(c) A diamagnetic waterlike density PE spherical particle on the air–holmium-based paramagnetic-liquid interface is pushed. (d)–(f) A diamagnetic low-density EPS particle is pulled (1) or pushed (2) and finally trapped at the base of the interface deformation created by the magnet. (g)–(i) Magnetic low-density HC particle on the air–manganese dichloride-based paramagnetic-liquid interface is pulled and finally trapped at the peak of the meniscus. (a), (b), and (h) are superimposed images of before and after interface formation; (d) shows the initial position (1) and the trapping location of the particle; (g) shows only the initial position of the particle; (e) is an image consisting of three superimposed images, two images of starting positions (1 and 2) and one image of the final trapping location. Schematic energy profiles of the particles are shown as insets in (c), (f), and (i) where the vertical axis corresponds to the centerline of the magnet.
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Figure 2
Definition of parameters and effects of the air–paramagnetic-liquid interface deformation. (a) Illustration (not to scale) of system configuration showing a magnet and a deformed interface. The meniscus deformation $u (ρ)$ has its maximum value at the center, thus yielding the maximum interface deformation $h_{L}$ . The magnet position is denoted with $h_{M}$ . $δ_{EPS}$ denotes the trapping location of an EPS particle with respect to the centerline of the magnet. (b) and (c) Experimental results on the $h_{L}$ and $δ_{EPS}$ as a function of $h_{M}$ for (b) manganese dichloride-based paramagnetic liquid and (c) holmium-based paramagnetic liquid.
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Figure 3
Comparison of the profiles of interface deformation for manganese dichloride-based paramagnetic liquid. (a) Numerical simulation and (b) experimental data of $u (ρ)$ for five different vertical positions of the magnet, i.e., 2.3, 2.4, 2.5, 2.6, and 2.7 mm.
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Figure 4
Numerical estimation of energy profiles and comparisons to experimental measurements for manganese dichloride-based paramagnetic liquid. Individual energy contributions for diamagnetic waterlike density particles: (a) a PE particle and (b) a PS particle, and (c) a magnetic low-density HC particle and (d) a diamagnetic low-density EPS particle. The numerical simulations consider a magnet position of 2.3 mm in (a)–(c) and 2.6 mm in (d) (e) Numerically estimated total energy minimum, i.e., trapping location of an EPS particle at five different magnet positions $h_{M}$ . (f) The theoretical estimation (e) compared with the experimental measurement of a trapping location of an EPS particle $δ_{EPS}$ at five different vertical positions of the magnet (2.3, 2.4, 2.5, 2.6, and 2.7 mm). The insets in the gray dashed boxes in (c) and (d) are magnified views for the close-in plots. The red “×” signs in (d) and (e) denote energy minima.
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Figure 5
Application cases of the pulling motion and trapping of the EPS particles on the air–paramagnetic-liquid interface. (a) Directed self-assembly of four EPS particles (Video S6): (i) Four EPS particles residing on the air–manganese dichloride-based paramagnetic-liquid interface. The magnet is perpendicular to the interface at a distance greater than 20 mm. (ii) The magnet approaches the liquid surface and forms an interface deformation which in turn pulls the particles into the trapping ring. (iii) The particles self-assembled into a line formation and after the magnet was removed the particles rearranged into a T-like structure formation. (b) Robotic particle guiding (Video S7): (i) Robotic guiding of EPS particle on the air–manganese dichloride-based paramagnetic-liquid interface. The trajectories of the magnet and the particle are shown in white and green, respectively. Red stars denote start positions and black stars denote end positions. The yellow arrow shows a local error of the magnet tracking algorithm. (ii) $X$ coordinate of the trajectories for the particle (red) and the magnet (blue). (iii) $Y$ coordinate of the trajectories for the particle (red) and the magnet (blue). For (ii) and (iii) the curves have missing data due to occlusion of the particle by the magnet or inadequate images for processing.
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