Using the singularity method, the primary fundamental solution (stokeslet) associated with a point force is obtained. The particle mobility for a spherical particle can be found after integrating the stokeslet over the surface of the particle. I would like to know please whether integrating the stokeslet over the surface of an anisotropic particle e.g. an oblate ellipsoid would also lead to the desired mobility. In fact, I tried this approach and compared with the analytically known solutions from Kim and Karrila textbook [Microhydrodynamics: Principles and Selected Applications] but it turns out that they are different. Does actually this integration procedure holds as well for anisotropic particles? Thank you!
Dear Abdallah,
I think that you are looking for analytical solutions of Laplace equation with the surface of oblate ellipsoid. Laplace equation emerges in hydrodynamics of in-viscous and in-compressible fluid. There exist several coordinate systems where variables can be separated, and one of them can fit your problem: http://mathworld.wolfram.com/OblateSpheroidalCoordinates.html
Please read the following paper:
https://www.researchgate.net/publication/281620595_Hydrodynamics_of_orthotropic_shapes_utilizing_ellipsoidal_harmonics
Article Hydrodynamics of orthotropic shapes utilizing ellipsoidal harmonics
You can also read the following paper for spheroidal bodies:
https://www.researchgate.net/publication/260292315_The_hydrodynamics_of_submerged_spheroidal_bodies_in_infinite_water_depth
Conference Paper The hydrodynamics of submerged spheroidal bodies in infinite...
- Badges
- Science topic
- Similar topics
- Engineering
- Thermal Engineering
- Thermofluid
- Fluid Mechanics
- Fluid Dynamics