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Stokes flow of a micropolar fluid exterior to several non‐intersecting closed surfaces, but contained by an exterior contour
Author(s) -
Power Henry,
Ramkissoon Harold
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670171403
Subject(s) - mathematics , mathematical analysis , stokes flow , flow (mathematics) , fredholm integral equation , integral equation , gravitational singularity , boundary (topology) , surface (topology) , geometry
The problem of determining the Stokes flow of a micropolar fluid exterior to several closed surfaces but contained by an exterior contour that encloses all the interior surfaces, is formulated as a system of linear Fredholm integral equations of the second kind. These integral equations are obtained when the velocity and microrotation vector fields are represented by a double‐layer potential with unknown density, and certain singular solutions of the Stokes' micropolar equations. This double‐layer potential is defined over the union of all the surfaces involved including the exterior contour. The singularities, corresponding to a concentrated force and concentrated couple located within each interior surface, give rise to force and torque whose magnitudes are linearly dependent on the unknown density of the double layer. It is shown that the system possesses a unique continuous solution when the boundaries are Lyapunov surfaces and the boundary data is continuous.