A New Complex Mixing Index Based on Entropy for Polymer Process Control and Optimization

混合是大多数加工操作的重要组成部分。混合和复合在新材料的开发中也起着重要作用。因此，更好地理解混合现象和发展新的标准来评估混合质量是至关重要的。在以前的工作中，我们已经定义了用于过程控制和优化以及机器放大的分散和分布混合标准。然而，我们期望通过定义一个新的基于熵的复杂混合指数来获得额外的基本见解和增强的适用性，该指数综合了分散和分布混合成分。熵是在统计力学和信息论等科学中使用的一种对无序性或系统同质性的严格度量。这一新指标可应用于包括纳米复合材料制造在内的多种聚合物加工技术。此外，通过流动特征与新的复杂混合指数之间的相关性来理解机器几何形状和加工条件对混合的影响，可以为设备设计指明新的方向。所提出的混合表征方法可以应用于聚合物加工工业以外的其他工程过程。这项研究是一项跨学科的努力，涉及一位化学工程师，他的专长在于聚合物加工和一位物理学家，他的专长是统计力学。凯斯西储大学和克利夫兰州立大学之间的合作将使理论物理概念应用于与制造工程社区相关的问题。此外，这种合作努力还具有教育影响，有可能引起学生对处理复杂问题的跨学科研究项目的兴趣。研究生和本科生都将从这个合作研究项目中受益。

Mixing is an important component of most processing operations. Blending and compounding also play a major role in the development of new materials. Thus better understanding of mixing phenomena and development of new criteria to assess mixing quality are of paramount importance. In previous work we have defined dispersive and distributive mixing criteria for process control and optimization and for machine scale-up. However, we expect additional fundamental insight and enhanced applicability can be gained by defining a new complex mixing index based on entropy, which synthesizes both dispersive and distributive mixing components. Entropy is a rigorous measure of disorder or system homogeneity used in several sciences such as statistical mechanics and information theory. This new index can be applied in a variety of technologies in polymer processing including fabrication of nanocomposite materials. Furthermore, understanding the influence of machine geometry and processing conditions on mixing as reflected through correlations between flow features and the new complex mixing index can point out to new directions in equipment design. The proposed mixing characterization methodology can be applied in other engineering processes beyond the polymer processing industry. This research is an interdisciplinary effort involving a chemical engineer whose expertise lies in polymer processing and a physicist with expertise on statistical mechanics. This collaboration between Case Western Reserve University and Cleveland State University will enable application of concepts from theoretical physics to problems relevant to the manufacturing engineering community. Moreover, such collaborative efforts have also an educational impact with the potential of inducing student interest for interdisciplinary research projects dealing with complex problems. Students at both the graduate and undergraduate levels will benefit from this collaborative research project.