- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Size-Specific Transport of Colloidal Particles Using Magnetic Fields

Sebastian Wohlrab1, Lara Schelter1, Aneena Rinu Perayil1, Piotr Kuświk2, Maciej Urbaniak2, Feliks Stobiecki2, Arne J. Vereijken3, Arno Ehresmann3, Thomas M. Fischer1 et al.

Daniel de las Heras4,1,*

PDF

Phys. Rev. Lett. 136, 188201 – Published 6 May, 2026

DOI: https://doi.org/10.1103/nvxs-n1ml

Abstract

Using computer simulations and experiments, we demonstrate a mechanism for simultaneous size-specific control over the trajectories of isotropic colloidal particles. Magnetic microparticles of different diameters suspended above a periodic magnetic film are driven by loops traced by the orientation of a uniform external magnetic field. The uniform time-dependent magnetic field couples to the inhomogeneous static magnetic field of the pattern, generating a complex energy landscape for the microparticles. The energy landscape varies with height above the pattern, acting on particles of different sizes in distinct ways, as their centers are located at different elevations. At a specific elevation, distinct modulation loops exist that transport the particles to a neighboring unit cell of the pattern. The transport is topologically protected because it is determined only by a set of winding numbers of the modulation loop, which act as topological invariants. The set of winding numbers depends on the elevation, and hence, on the particle size, allowing simultaneous and independent driving of different-sized particles along arbitrarily complex and distinct trajectories.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (41)

  1. J. Loehr, M. Loenne, A. Ernst, D. de las Heras, and T. M. Fischer, Topological protection of multiparticle dissipative transport, Nat. Commun. 7, 11745 (2016).
  2. D. de las Heras, J. Loehr, M. Loenne, and T. M. Fischer, Topologically protected colloidal transport above a square magnetic lattice, New J. Phys. 18, 105009 (2016).
  3. J. Loehr, D. de las Heras, M. Loenne, J. Bugase, A. Jarosz, M. Urbaniak, F. Stobiecki, A. Tomita, R. Huhnstock, I. Koch, A. Ehresmann, D. Holzinger, and T. M. Fischer, Lattice symmetries and the topologically protected transport of colloidal particles, Soft Matter 13, 5044 (2017).
  4. M. Mirzaee-Kakhki, A. Ernst, D. de las Heras, M. Urbaniak, F. Stobiecki, J. Gördes, M. Reginka, A. Ehresmann, and T. M. Fischer, Simultaneous polydirectional transport of colloidal bipeds, Nat. Commun. 11, 4670 (2020).
  5. N. C. X. Stuhlmüller, F. Farrokhzad, P. Kuświk, F. Stobiecki, M. Urbaniak, S. Akhundzada, A. Ehresmann, T. M. Fischer, and D. de las Heras, Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes, Nat. Commun. 14, 7517 (2023).
  6. M. A. Witek, I. M. Freed, and S. A. Soper, Cell separations and sorting, Anal. Chem. 92, 105 (2019).
  7. S. A. Kulkarni and S.-S. Feng, Effects of particle size and surface modification on cellular uptake and biodistribution of polymeric nanoparticles for drug delivery, Pharm. Res. 30, 2512 (2013).
  8. M. Xu, Y. Qi, G. Liu, Y. Song, X. Jiang, and B. Du, Size-dependent in vivo transport of nanoparticles: Implications for delivery, targeting, and clearance, ACS Nano 17, 20825 (2023).
  9. Y. Zhao, L. Shang, Y. Cheng, and Z. Gu, Spherical colloidal photonic crystals, Acc. Chem. Res. 47, 3632 (2014).
  10. J. Huh, K. Kim, E. Im, J. Lee, Y. Cho, and S. Lee, Exploiting colloidal metamaterials for achieving unnatural optical refractions, Adv. Mater. 32, 2001806 (2020).
  11. D. Ha, S. Seo, K. Lee, and T. Kim, Dynamic transport control of colloidal particles by repeatable active switching of solute gradients, ACS Nano 13, 12939 (2019).
  12. S. Shin, Diffusiophoretic separation of colloids in microfluidic flows, Phys. Fluids 32, 101302 (2020).
  13. V. S. Doan, S. Chun, J. Feng, and S. Shin, Confinement-dependent diffusiophoretic transport of nanoparticles in collagen hydrogels, Nano Lett. 21, 7625 (2021).
  14. S. Shin, E. Um, B. Sabass, J. T. Ault, M. Rahimi, P. B. Warren, and H. A. Stone, Size-dependent control of colloid transport via solute gradients in dead-end channels, Proc. Natl. Acad. Sci. U.S.A. 113, 257 (2015).
  15. F. Alnaimat, S. Dagher, B. Mathew, A. Hilal-Alnqbi, and S. Khashan, Microfluidics based magnetophoresis: A review, Chem. Rec. 18, 1596 (2018).
  16. J. Jung and K.-H. Han, Lateral-driven continuous magnetophoretic separation of blood cells, Appl. Phys. Lett. 93, 223902 (2008).
  17. J. D. Adams, U. Kim, and H. T. Soh, Multitarget magnetic activated cell sorter, Proc. Natl. Acad. Sci. U.S.A. 105, 18165 (2008).
  18. Y. Zhou, Y. Wang, and Q. Lin, A microfluidic device for continuous-flow magnetically controlled capture and isolation of microparticles, J. Microelectromech. Syst. 19, 743 (2010).
  19. B. B. Yellen, R. M. Erb, H. S. Son, R. Hewlin, Jr, H. Shang, and G. U. Lee, Traveling wave magnetophoresis for high resolution chip based separations, Lab Chip 7, 1681 (2007).
  20. P. Tierno, S. V. Reddy, M. G. Roper, T. H. Johansen, and T. M. Fischer, Transport and separation of biomolecular cargo on paramagnetic colloidal particles in a magnetic ratchet, J. Phys. Chem. B 112, 3833 (2008).
  21. P. Tierno and A. V. Straube, Transport and selective chaining of bidisperse particles in a travelling wave potential, Eur. Phys. J. E 39, 54 (2016).
  22. B. Lim, V. Reddy, X. Hu, K. Kim, M. Jadhav, R. Abedini-Nassab, Y.-W. Noh, Y. T. Lim, B. B. Yellen, and C. Kim, Magnetophoretic circuits for digital control of single particles and cells, Nat. Commun. 5, 3846 (2014).
  23. J. Do and C. H. Ahn, A polymer lab-on-a-chip for magnetic immunoassay with on-chip sampling and detection capabilities, Lab Chip 8, 542 (2008).
  24. M. Hejazian, W. Li, and N.-T. Nguyen, Lab on a chip for continuous-flow magnetic cell separation, Lab Chip 15, 959 (2015).
  25. C. P. Moerland, L. J. van IJzendoorn, and M. W. J. Prins, Rotating magnetic particles for lab-on-chip applications—A comprehensive review, Lab Chip 19, 919 (2019).
  26. F. Soto, E. Karshalev, F. Zhang, B. Esteban Fernandez de Avila, A. Nourhani, and J. Wang, Smart materials for microrobots, Chem. Rev. 122, 5365 (2021).
  27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/nvxs-n1ml for details regarding the magnetic potential, allowed and forbidden regions, fences, gates, and ratchets, which includes Refs. [28–32].
  28. C. Chappert, H. Bernas, J. Ferré, V. Kottler, J.-P. Jamet, Y. Chen, E. Cambril, T. Devolder, F. Rousseaux, V. Mathet, and H. Launois, Planar patterned magnetic media obtained by ion irradiation, Science 280, 1919 (1998).
  29. B. Yellen, G. Friedman, and A. Feinerman, Analysis of interactions for magnetic particles assembling on magnetic templates, J. Appl. Phys. 91, 8552 (2002).
  30. M. Urbaniak, P. Kuświk, Z. Kurant, M. Tekielak, D. Engel, D. Lengemann, B. Szymański, M. Schmidt, J. Aleksiejew, A. Maziewski, A. Ehresmann, and F. Stobiecki, Domain-wall movement control in Co/Au multilayers by He+-ion-bombardment-induced lateral coercivity gradients, Phys. Rev. Lett. 105, 067202 (2010).
  31. M. Urbaniak, D. Holzinger, A. Ehresmann, and F. Stobiecki, Magnetophoretic lensing by concentric topographic cylinders of perpendicular magnetic anisotropy multilayers, Biomicrofluidics 12, 044117 (2018).
  32. P. Kuświk, A. Ehresmann, M. Tekielak, B. Szymański, I. Sveklo, P. Mazalski, D. Engel, J. Kisielewski, D. Lengemann, M. Urbaniak, C. Schmidt, A. Maziewski, and F. Stobiecki, Colloidal domain lithography for regularly arranged artificial magnetic out-of-plane monodomains in Au/Co/Au layers, Nanotechnology 22, 095302 (2011).
  33. H. Butt, K. Graf, and M. Kappl, Physics and Chemistry of Interfaces (Wiley, New York, 2003).
  34. N. Zingsem, F. Ahrend, S. Vock, D. Gottlob, I. Krug, H. Doganay, D. Holzinger, V. Neu, and A. Ehresmann, Magnetic charge distribution and stray field landscape of asymmetric néel walls in a magnetically patterned exchange bias layer system, J. Phys. D 50, 495006 (2017).
  35. J. Takagi, M. Yamada, M. Yasuda, and M. Seki, Continuous particle separation in a microchannel having asymmetrically arranged multiple branches, Lab Chip 5, 778 (2005).
  36. J. Shi, H. Huang, Z. Stratton, Y. Huang, and T. J. Huang, Continuous particle separation in a microfluidic channel via standing surface acoustic waves (SSAW), Lab Chip 9, 3354 (2009).
  37. X. Wang and I. Papautsky, Size-based microfluidic multimodal microparticle sorter, Lab Chip 15, 1350 (2015).
  38. F. Klingbeil, F. Block, U. Sajjad, R. B. Holländer, S. Deshpande, and J. McCord, Evaluating and forecasting movement patterns of magnetically driven microbeads in complex geometries, Sci. Rep. 10, 8761 (2020).
  39. R. Huhnstock, M. Reginka, C. Sonntag, M. Merkel, K. Dingel, B. Sick, M. Vogel, and A. Ehresmann, Three-dimensional close-to-substrate trajectories of magnetic microparticles in dynamically changing magnetic field landscapes, Sci. Rep. 12, 20890 (2022).
  40. M. Urbaniak, D. Kiphart, M. Matczak, F. Stobiecki, G. D. Chaves-O’Flynn, and P. Kuświk, Ferrimagnetic Tb/Co multilayers patterned by ion bombardment as substrates for magnetophoresis, Sci. Rep. 14, 23771 (2024).
  41. M. Urbaniak, D. Kiphart, M. Matczak, and P. Kuświk, Reconfigurable ferrimagnetic Tb/Co based substrates for magnetophoresis, J. Magn. Magn. Mater. 629, 173312 (2025).

Outline

Information

Phys. Rev. Lett. 136, 188201– Published 6 May, 2026
  • Received 9 December 2025
  • Revised 9 March 2026
  • Accepted 10 April 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation