Macroscopic measurements

Some of the properties of magnetic soft colloids cannot be obtained from microscopic measurements (e.g. orientation of the particle, peculiarities of dynamics). But this can be overcome by scaling the experiment. Here we perform macroscopic measurements of the magnetic particle system. 

In the present work, we focus on the macroscopic measurements of hematite cubes [1,2] in rotating field. We use cubic magnet which is firmly positioned in the 3D printed cubic shell. The particles are placed in the glycerol-water mixture and magnetic field is generated using coil system. The camera is calibrated and the camera matrix is obtained using multiplane calibration via chessboard detection [3]. Each face of the cube has a unique ArUco marker [4], and it is possible to detect and recognise these markers in an image of the cube [5]. The relative positions between the markers and their corners are known, thus a 3D to 2D point correspondence can be constructed. A perspective-n-point algorithm is used to recover the position and rotation of the cube by minimising the reprojection error [6].

The described system allows us to obtain phase diagram of an individual hematite cube in a rotating magnetic field separating regions with rotation on face, edge or vertex 

Below is table to compare experiments with microscopic hematite cubes used in [1] and our experiments with macroscopic 3D printed cubes.

Dimensionless parameters in the table are computed by following formulas:

The direction of magnetic moment in hematite cube is in the diagonal cross-section and make 12° angle with main diagonal (picture below) [1]

Blueprint of one half of the (cubic) shell with place for the magnet (which is in the same direction as for hematite cube) and with deepening for the ArUco stickers.

Obtained phase diagram of a magnetic cube in a rotating magnetic field

Reconstruction of cube orientation from the experimental data

These results were presented in ICMF2023 as poster presentation [0].
Below is the presented poster.

[0] J. Cīmurs, J. Pudāns, D. Gorovojs, V. Spūlis, R. Lopatko, M. Brics, A. P. Stikuts, G. Kitenbergs "Macroscopic emulaton of microscopic magnetic particle system", 16th International Conference of Magnetic Fluids (ICMF2023), Granada, Spain, 2023.06.12.-16., P.166.
[1] M. Brics, V. Šints, G. Kitenbergs, A. Cēbers "Rotating hematite cube chains" (2023) arXiv
[2] M. Brics, V. Šints, G. Kitenbergs, A. Cēbers "Energetically favorable configurations of hematite cube chains" Physical Review E, 105, 024605 (2022) link, arXiv
[3] Z. Zhang. "A flexible new technique for camera calibration" IEEE Transactions on Pattern Analysis and Machine Intelligence. vol. 22(11), pp. 1330-1334 (2000) link

[4] O. Oda, S. Feiner "Goblin XNA: A Platform for 3D AR and VR Research and Education" Columbia University Computer Graphics & User Interfaces Lab link
[5] S. Garrido-Jurado, R. Mu noz Salinas, F.J. Madrid-Cuevas, M.J. Marín-Jiménez "Automatic generation and detection of highly reliable fiducial markers under occlusion" Pattern Recognition, 47, pp. 2280-2292 (2014) link

[6] Vincent Lepetit, Francesc Moreno-Noguer, and Pascal Fua. Epnp "An accurate o(n) solution to the pnp problem" International journal of computer vision, 81(2):155–166 (2009).