We introduce a phenomenological model for the dipolar interaction of polarizable particles under an external field, where the relative radial and rotational components of a particle pair interaction can be tuned. We show that the relative strengths of these two components govern the microstructure and dynamics of a suspension of such particles. Notably, dominant radial interactions give rise to the formation of zigzag band patterns, which were previously only thought to occur in systems where hydrodynamic interactions dominate. Through this phenomenological model, we show that dipolar interactions can be used to access an array of patterns in suspensions of polarizable particles, from chains to bands, which would dramatically affect suspension shear rheology, for instance.

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