Numerical analysis of geometrical effect on drop deformation and breakup between rotating cylinders

Abstract

This study numerically investigates the effects of geometrical curvature on drop deformation and breakup in shear flow between counter-rotating concentric cylinders. Simulations were performed using a geometric Volume-of-Fluid (VOF) method incorporating plicRDF interface reconstruction and isoAdvector interface advection, combined with adaptive mesh refinement. Three circular geometries with different values of the non-dimensional geometrical curvature, $κ_{\mathrm F}$, were considered and compared with a planar shear flow system. At fixed Reynolds and Capillary numbers ($Re$ and $Ca$), the breakup morphology differed substantially between the planar and circular systems. In the planar system, the drop underwent relatively symmetric neck thinning, whereas in the circular systems, the drop exhibited asymmetric deformation and pronounced azimuthal elongation. At higher curvature, the drop formed a thin filament that subsequently fragmented, producing multiple satellite drops. Analysis of the internal velocity field and the magnitude of the rate-of-deformation tensor revealed distinct flow and deformation structures associated with these breakup behaviors. Furthermore, the critical $Re$ for breakup, $Re_{\mathrm{cr}}$, decreased with increasing $κ_{\mathrm F}$ at nvestigated $Ca$ values. In contrast, the maximum dimensionless elongation length immediately before breakup at $Re=Re_{\mathrm{cr}}$ increased with $κ_{\mathrm F}$. These findings suggest that geometrical curvature affects not only the breakup threshold but also the deformation process leading to breakup, providing insights into drop breakup in curved shear flows.