A boundary integral simulation of ferrofluid droplet emulsion in shear flow: Cluster formation, deformation, and specific viscosity

Recent numerical studies have focused on the deformation, breakup, and rheological behavior of single ferrofluid droplets under shear flow. However, research on ferrofluid droplet emulsions remains limited due to computational challenges involved. In this study, a fully graphics processing unit-accelerated boundary integral method framework is developed for simulating ferrofluid droplet emulsions in a triply periodic domain under simple shear flow with a uniform magnetic field. The method combines Ewald summation, multipole expansion for fast far-field evaluation, and near-field regularization to stably resolve close interactions. A magnetic field imposed perpendicular to the shear plane promotes chain-like clustering through coupled magnetic and hydrodynamic interactions. Clusters are only found in the presence of a magnetic field, but the cluster length decreases as the shear rate increases. Therefore, the balance between magnetic and hydrodynamic interactions is crucial for cluster formation. In addition, droplet deformation decreases owing to the reduced cross-sectional radius in the shear plane; rescaling, guided by the small deformation theory, organizes the data across volume fractions. The orientation trends are consistent with the deformation–orientation relation, with dense emulsions exhibiting smaller angles than dilute emulsions. The specific viscosity is reduced under the magnetic field across volume fractions, with a larger relative decrease at low flow strengths, where the clusters are most pronounced. Collectively, these findings establish a relationship among field-driven alignment, deformation control, and macroscopic rheology, suggesting practical routes to control the structure–property relationships in ferrofluid droplet emulsions.