A new representative measure of chaotic mixing in a chaos single-screw extruder

It has been reported recently that mixing in a single-screw extrusion process can be greatly enhanced due to the chaotic flow induced by spatially periodic barriers inserted in the screw channel. This new screw was named the "chaos screw," because mixing produced by this new screw is chaotic in nature. It is of great importance to establish a systematic method in designing such a chaos screw, with the objective of achieving a uniform and efficient mixing. In this study, we numerically studied the effects of design variables on chaotic flow by means of a Poincare section and attempted to quantify the mixing in terms of a mixing measure proposed in the literature, namely the Lyapunov exponent. It is well known that Lyapunov exponents have a spatial, Gaussian distribution for systems without islands. As a measure of mixing, however, a "distribution" does not seem to be adequate for use in industrial engineering applications. Thus, we propose two new types of representative deformation measures as new chaotic mixing measures: sigma(z) and sigma(t),which are termed modified Lyapunov exponents, representing the exponential stretch rate of a relatively long material Line along the downchannel direction and with respect to time, respectively. It was found that the modified Lyapunov exponents are almost identical to the material line chosen for their computation, and are thus reliable measures to represent the overall mixing as a kind of domain-averaged Lyapunov exponent. (C) 1999 John Wiley & Sons, Inc.