The kinematics of the four-roll mill

Numerical computations are employed to study the flow field produced by a four-roll mill. The radius of the cylinders a, the cylinder spacing 2b, and the size 2l of the square container are varied to assess the effects on the kinematics of the flow field. It is found that a ratio of a/b=0.625 with l/b≥3.0 produces the best approximation to a pure extensional flow. With these parameter values, the extension rate remains constant with an error of less than 1% over an axial region x/b≤0.5. By contrast, the commonly accepted design a/b=0.772 suggested by Fuller and Leal [J. Polym. Sci. Polym. Phys. 19, 557 (1981)] produces a variation in extension rate of 50% over the same region. Streamline patterns and velocity gradient error contours are presented for these two designs.