Slit die viscometry at shear rates up to 5 � 106s?1: An analytical correction for small viscous heating errors

Abstract

If the viscosity can be expressed in the form rl = a ( T ) f ( a ) , the walls are at a constant temperature To, and the extra stress, velocity and temperature fields are fully developed, then the wall shear rate ~)w can be calculated by applying the Weissenberg-Rabinowitsch operator to F~Q instead of to the flow rate Q, where Fc is a correction factor which differs from 1 when the temperature field is non-uniform; the isothermal equation relating the wall shear stress and pressure gradient is still valid. For the case in whcih ~7 = ~0lal n/(1 + fl(T-To)), where n, ~/0, and fl are independent of shear stress a and temperature T, an exact analytical expression for F c in terms of the NahmeGriffith number N a and n is obtained. Use of this expression gives agreement with data obtained for degassed decalin (r/= 2.5 mPa s) from a new miniature slit-die viscometer at shear rates # up to 5× 10 6 S-l; here, the correction is only 7070, Na is 1.3, and Gz, the Graetz number at the die exit, is 119. For a Cannon standard liquid $6 (~/=9mPas), agreement extends up to 5×105s-1; at 2× 106 s -~ (where Na = 7.2 and Gz = 231), the corrections are 1107o (measured) and 3607o (calculated).

Geometry and heat loss in channel flow of a fluid with temperature‐dependent density

“…In general, material properties depend on both thermal and mechanical state variables. In many polymer processes the mechanical dependence of density, specific heat, viscosity, and thermal conductivity is weak, due to the low to moderate pressure levels encountered in these processes (Cox and Macosko, 1974;Lodge and KO, 1989;Spencer and Gilmore, 1950;Winter, 1977), and can be neglected. In contrast, temperatures are high enough and the temperature changes and gradients are sufficiently large that the temperature dependence of material properties must be incorporated.…”

Measurements of first and second normal stress differences in a polymer melt

“…This causes the pressure, P 2 , measured by a transducer in the bottom of the hole to be lower than the pressure, P 1 , measured by a flush mounted transducer on the opposite wall. In literature there is sufficient proof for the pressure hole effect, especially Lodge has made a substantial amount of work, see [3,14,15,18]. Reviews on this topic are found in Refs.…”

Retrieving Equivalent Shear Viscosity for Molten Polymers from 3-D Nonisothermal Capillary Flow Simulation

“…To address viscous heating in capillary or slit flows, it is possible to measure the temperature rise of the fluid in the flow channels by means of various experimental techniques [ 4 , 15 , 16 , 17 , 18 , 19 , 21 , 22 , 23 ]. The effects of viscous heating can also be analyzed by means of theoretical calculations of temperature profiles [ 1 , 3 , 4 , 7 , 8 , 9 , 13 , 14 , 16 , 17 , 20 , 21 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. In principle, the temperature rises obtained from either of the two approaches can be combined with a viscous heating correction method to retrieve the equivalent viscosity for isothermal flow [ 7 , 15 , 33 ].…”