When Shear Cannot Break the Cluster: Off-Center Dipoles Under Flow

Dark liquid metal swirling under flow
Photo: Rick Rothenberg / Unsplash

A magnetic colloid that assembles beautifully at rest is not necessarily useful. Almost every application people have in mind for field-directed assembly — magnetorheological fluids, targeted delivery, microfluidic sorting — puts the suspension into flow, and flow is exactly what tears assembled structures apart. The practical question is therefore not what does this suspension build but what does it keep when you shear it.

Our 2025 paper in Soft Matter, led by Joysy R. Tafur-Ushiñahua with Ronal A. DeLaCruz-Araujo, takes that question to a specific and underexplored geometry: magnetic Janus particles whose dipole has been displaced laterally from the particle center.

The gap

Most models of magnetic colloids place a point dipole at the center of a sphere. That is a strong simplification. In real synthesized particles the magnetic material is a cap or an inclusion, not a centered point, and the offset changes which contacts are energetically favorable — it decides whether particles prefer to meet head-to-tail, head-to-side, or antiparallel. Displacing the dipole radially is one way to break that symmetry, and we mapped that case in a companion study on radially shifted dipoles under an external field. Displacing it laterally is a different symmetry break, and until this work its behavior under flow had not been mapped.

What we did

We used Brownian dynamics simulations of dilute suspensions in simple shear, and varied three quantities independently:

  • the dipolar shift s, the displacement of the dipole from the geometric center;
  • the Péclet number Pe, which sets the strength of the flow relative to Brownian motion — the same dimensionless group we discussed in an earlier post on particle transport;
  • the dipolar coupling constant λ, which sets the strength of magnetic interactions relative to thermal energy.

Sweeping this space produces distinct aggregation regimes, and the boundaries between them are where the physics is.

What we found

At small shifts (s ≤ 0.1) and low Pe, shear-enhanced diffusion actually helps: it drives particles into each other more often, so aggregation is faster, and the particles form loop-like clusters that align with the flow. Raise Pe and those loops fragment into smaller aggregates, then disperse entirely into a gas-like state.

At medium shifts (s ≥ 0.2) the picture inverts. The clusters that form are compact, vesicle- and micelle-like, and they resist shear-induced breakup even at high Pe — provided λ is large enough. The critical Péclet number needed to break a cluster rises with both s and λ. Moving the dipole off-center is, in this regime, a stabilization mechanism.

The orientational analysis explains why. Particles maintain head-to-tail, head-to-side and antiparallel alignments depending on s and Pe, and the lateral offset makes the compact configurations reachable and hard to unwind. The breakup criterion itself is a torque balance: dispersion sets in when the hydrodynamic and Brownian torques acting on a particle exceed the torques arising from interparticle magnetic interactions. That is a clean statement, and it is the kind that transfers — it tells you what to measure, not just what was observed.

Where this fits

Read alongside our earlier work on size ratio in bidisperse magnetic suspensions and on radial dipole shifts, a pattern emerges across the group’s magnetic-colloid program: small, physically realizable asymmetries in a particle — where the dipole sits, how big the neighbor is — produce large, categorical changes in what the suspension does. These are parameters a synthetic chemist can actually control, which is what makes a structure diagram worth computing.

The immediate implication is a design statement. If you need magnetic clusters that hold together in a flowing device, do not simply raise the field: displace the dipole. A laterally shifted particle at moderate λ withstands shear that a centered one at the same coupling strength does not.

Reference: Tafur-Ushiñahua, J. R., DeLaCruz-Araujo, R. A., & Córdova-Figueroa, U. M. “Shear-induced assembly and breakup in suspensions of magnetic Janus particles with laterally shifted dipoles.” Soft Matter, 21, 6516, 2025. DOI: 10.1039/D5SM00457H

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