Next Article in Journal
Geophysical Equatorial Edge Wave with Underlying Currents in the f-Plane Approximation
Previous Article in Journal
Retraction: Ahmed, A. et al. Dual Solutions in a Boundary Layer Flow of a Power Law Fluid over a Moving Permeable Flat Plate with Thermal Radiation, Viscous Dissipation, and Heat Generation/Absorption. Fluids 2018, 3, 6, doi:10.3390/fluids3010006
Article Menu

Export Article

Open AccessArticle

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

Institute of Applied Mathematics and Scientific Computing, Bundeswehr University Munich, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany
Department of Physics, University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
Author to whom correspondence should be addressed.
Fluids 2019, 4(3), 117;
Received: 7 March 2019 / Revised: 13 June 2019 / Accepted: 23 June 2019 / Published: 28 June 2019
PDF [1905 KB, uploaded 3 July 2019]


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. View Full-Text
Keywords: topological fluid dynamics; creeping flow; bubbles and droplets topological fluid dynamics; creeping flow; bubbles and droplets

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Hasslberger, J.; Marten, S.; Klein, M. A Theoretical Investigation of Flow Topologies in Bubble- and Droplet-Affected Flows. Fluids 2019, 4, 117.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics



[Return to top]
Fluids EISSN 2311-5521 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top