Stokes flow with slip and Kuwabara boundary conditions. (English) Zbl 1042.35054
The steady Stokes flow of a fluid volume bounded by two parallel surfaces is considered. The boundary conditions are:
i) vanishing of the normal component of velocity and slip condition on the inner (solid) surface,
ii) continuity of the normal component of velocity and vanishing of vorticity on the outer (cell) surface.
The authors obtain expressions for the stream function in the cases of coaxial cylinders, concentric spheres, deformed spheres (in particular oblate spheroid). The drag forces are calculated for all cases above.
i) vanishing of the normal component of velocity and slip condition on the inner (solid) surface,
ii) continuity of the normal component of velocity and vanishing of vorticity on the outer (cell) surface.
The authors obtain expressions for the stream function in the cases of coaxial cylinders, concentric spheres, deformed spheres (in particular oblate spheroid). The drag forces are calculated for all cases above.
Reviewer: Il’ya Sh. Mogilevskij (Tver)
References:
| [1] | Dassios, G., Stokes flow in spheroidal particle-in-cell models with Happel and Kuwabara boundary conditions, Int. J. Engg. Sci., 33, 10, 1465-1490 (1995) · Zbl 0899.76118 · doi:10.1016/0020-7225(95)00010-U |
| [2] | Happel, J.; Brenner, H., Low Reynolds Number Hydrodynamics (1965), NJ: Prentice Hall, Englewood Cliff, NJ |
| [3] | Kuwabara, S., The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds number, J. Phys. Soc. Jpn., 14, 527-532 (1959) · doi:10.1143/JPSJ.14.527 |
| [4] | Palaniappan, D., Creeping flow about a slightly deformed sphere, Zeit. angew. Math. Phys., 45, 832-838 (1994) · Zbl 0810.76014 · doi:10.1007/BF00942756 |
| [5] | Rainville, E. D., Special Functions (1971), New York: Chelsea, New York · Zbl 0231.33001 |
| [6] | Stokes, G. G., On the effects of internal friction of fluids on pendulums, J. Trans. Camb. Philos. Soc., 9, 8-106 (1851) |
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