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The Quarterly Journal of Mechanics and Applied Mathematics 2002 55(2):273-296; doi:10.1093/qjmam/55.2.273
© 2002 by Oxford University Press
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Flow Patterns in a Two-Roll Mill

Christopher P. Hills1

( 1 Lincoln College, Oxford, OX1 3DR )

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of a two-roll mill is also given. Photographs confirm the salient features predicted by our theoretical study.

Received 5 January 2001. Revised 28 June and 17 August 2001.


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