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.
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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
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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).
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Ramkissoon, H. Slip flow past an approximate spheroid. Acta Mechanica 123, 227–233 (1997). https://doi.org/10.1007/BF01178412
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DOI: https://doi.org/10.1007/BF01178412