# Leakage flow of an isothermal power law fluid

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Leakage flow of an isothermal power law fluid Leakage Flow of an Isothermal Power Law Fluid Chris Rauwendaal Raychem Corporation Menlo Park, California 94025 J.F. Ingen Housz University of Technology of Twente Enschede, The Netherlands INTRODUCTION One of the first analyses of leakage flow in single screw extruders was perfonned by Rowel1 and Fin- layson, who considered the leakage flow to be a pres- sure flow only. They approximated the annular space between the flight tip and the barrel as two parallel plates. Their expression for the leakage flow can be written as follows: . ‘rrDij3AP& v, = 12vb where AP, is the pressure drop per turn. J$ is an eccen- tricity factor; when the screw is centered, J$ = 1, and, when the screw is in contact with the barrel, Ef = 2.5. The same approach was used later by Carley and Strub.’ This approach is flawed by the fact that it neglects the drag flow contribution to the leakage flow, as well as the pressure flow due to the cross channel pressure gra- dient. These two contributions will often be larger than the leakage flow described by Eq. (1). Advances in Polymer Technology, Vol. 8, No. 3, 290-316 (1988) 0 1988 by John Wiley & Sons, Inc. A much improved analysis of leakage flow was developed by Mohr and M a l l ~ u k , ~ including the drag flow contribution and the pressure flow due to the cross channel pressure gradient. B00y4 carried out a modified analysis following the procedure developed by Mohr and Mallouk. A detailed description of the complete analysis for a Newtonian fluid was given by T a d m ~ r , ~ who writes the leakage flow as ij3WpH3(W + w) g, + (pij3W + prH3w) 12 It is well known that the flow behavior of polymer melts in screw extruders is strongly dependent on the pseudoplastic behavior of the melt. Therefore, it is to be expected that the same will be true for the leakage CCC 0730-6679/88/0302%26$04.~ LEAKAGE FLOW FIGURE 1 Coordinate system. flow. In the

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