**1. Introduction**

Plasticating extruders abound in the polymer industry. Due to their great versatility, they are used in many polymer-shaping operations, producing semi-finished plastic products such as films, pipes, profiles, sheets, and fibers. In addition, they are frequently found in compounding and recycling operations. Although plasticating extruders come in various designs, the elementary processing steps are generally the same: (i) transport and (ii) melting of particulate solids, followed by (iii) mixing and (iv) pumping of the polymer melt.

Numerous theoretical studies have modeled the extrusion process to increase the understanding of the transport mechanisms governing physical operation. The fundamentals of extrusion modeling were summarized in various books: Tadmor and Klein [1], White and Potente [2], Tadmor and Gogos [3], Campbell and Spalding [4], Rauwendaal [5], Agassant et al. [6], and others. Recently, Wilczy ´nski et al. [7] presented a thorough review of global extrusion modeling.

The assessment of leakage flow and its prediction has been of interest since the earliest theories for the metering zone. Over the past decades, many analyses have modeled polymer-melt flows in single-screw extruders. Most of these, however, ignored the effect of flight clearance.
