Three‐dimensional viscous flow over rotating periodic structures

Abstract

SUMMARYThe three-dimensional Stokes ow in a periodic domain is examined in this study. The problem corresponds closely to the ow inside internal mixers, where the ow is driven by the movement of a rotating screw; the outer barrel remaining at rest. A hybrid spectral=ÿnite-di erence approach is proposed for the general expansion of the ow ÿeld and the solution of the expansion coe cients. The method is used to determine the ow ÿeld between the screw and barrel. The regions of elongation and shear are closely examined. These are the two mechanisms responsible for mixing. Besides its practical importance, the study also allows the assessment of the validity of the various assumptions usually adopted in mixing and lubrication problems.