Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session AA04: V: Fluids I
5:00 AM–7:00 AM,
Monday, March 20, 2023
Room: Virtual Room 4
Sponsoring
Unit:
DFD
Chair: Simon Huynh, Brandeis University
Abstract: AA04.00006 : Applications of the image method in low-Reynolds-number hydrodynamics and linear elasticity to right-angled edges and corners*
6:00 AM–6:12 AM
Presenter:
Lukas Fischer
(Institut für Physik, Otto-von-Guericke Universität Magdeburg)
Authors:
Lukas Fischer
(Institut für Physik, Otto-von-Guericke Universität Magdeburg)
Tyler Lutz
(Institut für Physik, Otto-von-Guericke Universität Magdeburg)
Andreas M Menzel
(Institut für Physik, Otto-von-Guericke Universität Magdeburg)
We start with the well-known solutions in the case of planar interfaces. Afterwards, we extend this work to orthogonal edges where two boundaries meet and finally to corners with three mutually orthogonal boundaries [1]. We find that the applicability of the image method crucially depends on the type of boundary condition: We consider cases where the boundaries are (stress-)free, free-slip boundaries (only sliding along the surface is allowed) as well as no-slip boundary conditions (vanishing fluid velocities/displacements at the boundary) and all possible combinations thereof. Interestingly, we find that the image method can only be applied if all but one boundary are of free-slip type. In those cases, we also explicitly list the resulting solutions and illustrate them.
*Support by the German Research Foundation (DFG) through the Heisenberg Grant No. ME 3571/4-1 and the Research Grant No. Me 3571/5-1 is gratefully acknowledged.
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