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Low-Reynolds-number resistance functions for two spheres. (English) Zbl 0689.76014

Summary: If two equal spheres translate or rotate in an ambient linear flow field at low Reynolds number, the forces, couples and stresslets that the spheres exert on the surrounding fluid can be described by a set of resistance functions. The method of twin multipole expansions is used to calculate these resistance functions as power series in a/r, where a is the radius of one of the spheres and r is the distance between the spheres’ centres. The leading terms of the series are given explicitly, for use when the spheres are far apart. When the spheres are close together, the series converge slowly because of singularities in the forces, couples and stresslets. Thus, asymptotic forms must be found for the resistance functions when the spheres are close to touching. This is done by obtaining recurrence relations that allow many terms of the series expansion for each function to be calculated. The coefficients in the series are then examined for large powers of a/r and the asymptotic form of the function inferred.

MSC:

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M99 Basic methods in fluid mechanics
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