Flow Patterns in a Two‐Roll Mill

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.