A Theoretical Investigation of Flow Topologies in Bubble- and Droplet-Affected Flows

Abstract

A local flow topology analysis was conducted for laminar particle-affected flows. Based on the invariants of the velocity gradient tensor, all possible flow structures can be categorized into two focal and two nodal topologies for incompressible flows. The underlying field descriptions for bubble- and droplet-affected flows in the creeping flow regime were determined analytically for two different boundary conditions. A nodal-to-focal-to-nodal transition can be observed in both phases and the focal topologies are predominant in the interior phase. It was also found that the topology distribution in the interior phase is independent of the dynamic viscosity ratio and the boundary conditions, which is not the case in the exterior phase. The focal region in the exterior phase extends to infinity for the far-field boundary condition, whereas it is bounded to a tire-like zone attached to the bubble or droplet for the near-field boundary condition. Furthermore, the existence of a narrow band of intermediate nodal topologies was demonstrated analytically, which raises the question on the origin of this behavior. To complement the findings about the flow topology classification, the strengths of the underlying vorticity and invariant fields are discussed, including their dependency on the considered phase and boundary condition.

Keywords

• topological fluid dynamics
• creeping flow
• bubbles and droplets