| Abstract: | In high shear rate capillary rheometry the combined effect of pressure dependent viscosity and dissipative heating becomes significant. Analytical expressions are derived to treat curved Bagley plots and throttle experiments. End effects are taken into account by using an effective length over radius ratio. The non-adiabatic case is described using a lump heat transfer coefficient ? following Hay et al. (1999). The latter enters into the dissipative heating coefficient % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakeaacqaH1oqzdaWgaaWcbaGaemiCaahabeaakiabg2da % 9iabeg8aYnaaCaaaleqabaGaeyOeI0IaeGymaedaaOWaaeWaaeaacq % WGJbWydaWgaaWcbaGaemiCaahabeaakiabgUcaRmaalyaabaGaeu4M % dWeabaGafmyBa0MbaiaaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacq % GHsislcqaIXaqmaaaaaa!4D6C! ep = r - 1 ( cp + L \mathord | / | \vphantom L (m)\dot] (m)\dot] ) - 1 \varepsilon _p = \rho ^{ - 1} \left( {c_p + {\Lambda \mathord{\left/ {\vphantom {\Lambda {\dot m}}} \right. \kern-\nulldelimiterspace} {\dot m}}} \right)^{ - 1} ( ? density, c p heat capacity, % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBam % XvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2DaeHbuLwB % Lnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFf % euY-Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9 % q8aq0-yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqaba % WaaqaafaaakeaacuWGTbqBgaGaaaaa!3C5E! (m)\dot] \dot m mass flow rate). A rigorous treatment is possible for incompressible melts, assuming a flat radial temperature profile. For compressible melts, the downstream density variation reduces the effective temperature and pressure coefficients of viscosity. In addition, it causes less dissipative heating. The applicability of the treatment was carefully checked for a well characterised LDPE melt and consistent results from throttle experiments and the Bagley plot curvature are found. The pure dissipation effect was treated by a viscous FEM simulation. A fit of the expected analytical expression to the simulated axial pressure profile allows to extract ?. Throttle experiments allow a reliable determination of the pressure coefficient of viscosity ß ? from a fit of the analytical prediction for the measured pressure loss ? p as function of the die inlet pressure P i, provided the dissipation coefficient from the FEM simulation is used. An analytical solution for the Bagley plot was derived for the pure dissipation or pressure effect, respectively. In the parabola approximation, however, the two contributions may be superimposed. Whereas dissipative heating increases the curvature of the axial pressure profile in a die in the same direction as the pressure effect, it operates in the opposite direction for the Bagley plot curvature. Pressure coefficients solely determined from Bagley plots are not reliable. The effect of variable melt density on the temperature and pressure coefficients of the LDPE remains below 5%. |
