Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers

The problem of isothermal flow of a shear-thinning (pseudoplastic) fluid in the gap between two concentric cylinders is considered. A pump provides an axial pressure gradient which causes flow down the device. The outer cylinder is fixed and has ‘scrapers’ attached to it to cause flow mixing, whilst the inner cylinder rotates about its axis to provide shear and thus thin the fluid. The goal is to determine the optimal distribution of power between rotation and pumping. Although ostensibly the flow is nonlinear and three-dimensional we show that judicious use of fairly straightforward asymptotic methods can yield a great deal of information about the device, including cross-sectional flow predictions and throughput results. Furthermore, these results are derived for a variety of different flow conditions. Some numerical calculations are carried out using a commercial CFD code. These show good agreement with the asymptotic analysis.