Slit Die Viscometry at Shear Rates Up to 5 x 10 to the 6th power/s-1 : An Analytical Correction for Small Viscous Heating Errors.

摘要

If the viscosity can be expressed in the form eta = alpha(T) f(sigma), the walls are at a constant temperature T sub 0, and the extra stress, velocity and temperature fields are fully developed, then the wall shear rate gamma sub w can be calculated by applying the Weissenberg-Rabinowitsch operator to F sub c Q instead of the flow rate Q, where F sub c 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 which eta = eta sub 0 (ab. val. sigma) to the nth power/(1 + beta(T-T sub O)), where eta, eta sub 0, and beta are independent of shear stress sigma and temperature T, an exact analytical expression of F sub c in terms of the Nahme-Griffith number Na and n is obtained. Use of this expression gives agreement with data obtained for degassed decalin (eta = 2.5 mPa s) for a new miniature slit-die viscometer at shear rates gamma up to 5,000,000/s; here, the correction is only 7%, Na is 1.3, and Gz, the Graetz number at the die exit, is 119. For a Cannon standard liquid S6 (eta = 9 mPa s), agreement extends up to 500,000/s; at 2,000,000/s (where Na = 7.2 and Gz = 231), the corrections are 11% (measured) and 36% (calculated). Keywords: Slit die viscometer; Viscous heating correction; Weissenberg Rabinowitsch operator; Time temperature superposition principle; Reprints. (jhd)