Study of low Reynolds number hydrodynamics generated by symmetric corotating two-roll mills

A Closed-form analytical solution for the creeping flow equations in bipola r cylindrical coordinates is presented and used to study the flow generated by a corotating symmetric two-roll mill. The flow field has:a stagnation p oint where elongational flow conditions exist. The geometric characteristic s of the mill define the ratio of vorticity to rate of deformation that exi sts at the stagnation point. The solution is based upon Jeffery's solution of the biharmonic equation obtained for the stresses on a plate [Proc. Roy Sec. London A 101 (1922) 169]. The streamlines, the velocity field, the mag nitude of the velocity gradient and other properties of the flow are obtain ed for the complete flow domain. For the region around the stagnation point , the calculated results show good agreement with the numerical predictions of Singh and Leal [J. Rheology 38 (1994) 485] and the experimental measure ments of Wang ct al. [Phys. Fluids 6 (1994) 3519]. This solution should be useful for investigations of the dynamics of drops, elastic capsules, or st udies of chaotic advection, where exact solutions are necessary benchmarks.