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Volume 8,     Number 2,     Summer 2000

 

AN ANALYSIS OF A STOKES FLOW IN AN ANNULAR REGION
W.W. HACKBORN

Abstract. A study is made of the steady two-dimensional Stokes flow stirred by an infinitesimal rotating cylinder (a line rotlet) in the annular region between two fixed concentric cylindrical walls. It is shown that this simple flow exhibits a rich diversity of possible flow structures. Generally, one component of the flow is associated with a net flux through the annular region in either a clockwise or anticlockwise direction depending on whether the radial distance between the rotlet and the center axis of the bounding cylinders is greater or less than a unique value at which this flow component vanishes. The remaining components of the flow are either eddies attached to the boundary or free eddies in the interior of the flow. Owing to some of the dynamical features of this flow, the results obtained here may be applicable in engineering settings where mixing by the chaotic advection of fluid particles is desirable.

 

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