A corotating two-roll mill for studies of two-dimensional elongational flows with vorticity

Abstract

A closed-form analytical solution for the Stokes flow generated by a corotating two-roll mill is used to generate two-dimensional elongational flows with well-defined amounts of vorticity. These flow devices can generate conditions found between simple shear and purely elongational flows, and are among the few systems that can take into account the presence of nearby boundaries. In the laboratory, these devices have been used for studies of the microstructural dynamics of complex fluids such as polymeric solutions, colloids, bubbles and drops, etc., and allow pointwise optical studies of the flow parameters. Hence, a comparison is presented of available experimental and numerical results for the stagnation point versus the analytical solution presented here. Based upon this solution, a new design for the two-roll mill is presented for the purpose of minimizing the disadvantages of current mills.