Document Type



This item is available under a Creative Commons License for non-commercial use only


Applied mathematics, Fluids and plasma physics, Applied mechanics

Publication Details

Quarterly Journal of Mechanics and Applied Mathematics. Vol. 55, Part 2, 2002, pp. 273-296. Available from


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.