Derivation and correction of polyethylene melt strength equation

The following equation for the determination of polyethylene melt strength (MS) has been derived: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm MS}({\rm poise}) = {{1.492 \times 10^7 (\Delta l)^2 r_0^2} \mathord{\left/ {\vphantom {{1.492 \times 10^7 (\Delta l)^2 r_0^2} {({\rm MF})}}} \right. \kern-\nulldelimiterspace} {({\rm MF})}} $$\end{document} where Δl is the length (inches) of extruded polymer cord required for 50% decrease in diameter of the cord, r0 is the radius (inches) of the molten polymer cord as it first emerges from the melt indexer die, and MF is melt flow rate in grams/10 min. The required measurements are made on the initially extruded 0.5‐in. portion of the polymer cord from a conventional melt indexer using the standard 0.0825‐in.‐diameter die and 2160‐g. load and a temperature of 230°C. This melt strength equation was derived by using the assumption that the melt strength can be expressed as melt viscosity at low shear rates. Melt strengths of polyethylenes having similar melt indices have been shown to have over a 37‐fold difference.