From hydrodynamics to dipolar colloids: modeling complex interactions and self-organization with generalized potentials

When spherical particles are submerged in a viscous fluid and subjected to oscillations, they align themselves in one-particle-thick chains or multiple-particle-wide bands. Both are oriented perpendicular to the oscillation direction with a regular spacing between them, which depends on the oscillatory forcing.



This self-organization is a nonlinear effect, driven by vortices in the period-averaged flow, or steady streaming flow. These vortices vary in size, position, and magnitude with flow conditions, resulting in complex particle-fluid interactions. Overall, the hydrodynamic interactions between two neighboring chains can be divided into short-range attraction, mid-range repulsion, and long-range attraction.



To capture the essential aspects of the self-organization, we introduce simplified model potentials that incorporate the aforementioned interactions. Using Monte Carlo simulations, we explore the parameter space and successfully replicate the patterns observed in the hydrodynamic system.



Furthermore, we apply our models to electrorheological fluids, consisting of colloidal particles with parallel dipole moments. We highlight the similarities between the systems, effectively bridging interdisciplinary gaps and enhancing the understanding of self-organization processes.