Summary
Creeping axisymmetric slip flow past a spheroid whose shape deviates slightly from that of a sphere is investigated. An exact solution is obtained to the first order in the small parameter characterizing the deformation. As an application, the case of flow past an oblate spheroid is considered and the drag experienced by it is evaluated. Special well-known cases are deduced and some observations made.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- A n, Bn, Cn, Dn, En, Fn, b2, d2 :
-
Constants
- a, b :
-
radii of spheres
- β:
-
coefficient of sliding fraction
- D :
-
drag
- ε, α m :
-
parameters characterizing the deformation of the sphere
- c :
-
a(1+ε)
- μ:
-
viscosity coefficient
- θ:
-
\(\frac{{\mu \beta }}{a}\)
- σ:
-
dimensionless coordinate\(\frac{r}{a}\)
- I n :
-
Gegenbauer function
- P n :
-
Legendre function
- ψ:
-
Stream function
- U :
-
stream velocity at infinity
References
Sampson, R. A.: On Stokes current function. Phil. Trans. Roy. Soc. A182, 449–518 (1891).
Brenner, H.: The Stokes resistance of a slightly deformed sphere. Chem. Eng. Sci.19, 519–539 (1964)
Acrivos, A., Taylor, T. D.: The Stokes flow past an arbitrary particle, the slightly deformed sphere. Chem. Eng. Sci.19, 445–451 (1964).
Basset, A. B.: A treatise on hydrodynamics, Vol. 2. New York: Dover 1961.
Happel, J., Brenner, H.: Low Reynolds number hydrodynamics. London: Prentice Hall 1965.
Payne, L. E., Pell, W. H.: The Stokes flow problem for a class of axially symmetric bodies. J. Fluid Mech.7, 529–549 (1960).
Ramkissoon, H.: Stokes flow past a slightly deformed sphere. Z. angew. Math. Phys.37, 859–866 (1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ramkissoon, H. Slip flow past an approximate spheroid. Acta Mechanica 123, 227–233 (1997). https://doi.org/10.1007/BF01178412
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01178412