Flow in a differentially rotated cylindrical drop at low Reynolds number

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Abstract
A liquid drop held captive between parallel disks that are differentially rotated is a model for the swirling flows induced by crystal rotation in the floating-zone process for growing semiconductor materials. An asymptotic analysis for a cylindrical drop is presented that elucidates the structure of the axisymmetric cellular motions caused by disk rotation at low Reynolds number. Variations of meniscus shape induced by these flows are described in the limit of small capillary number. Most cellular flow fields break the bifurcation point that corresponds to the Plateau–Rayleigh limit for the length of a static drop into two disjoint shape families and lower the maximum stable drop length. This effect is studied by a singular bifurcation analysis.

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