Geometrical effects in the measurements of mechanical properties in parallel superposed flows

The shear-dependent complex viscosity η^*₁₂, which governs the linear time-dependent stresses in a viscoelastic fluid undergoing infinitesimal shearing oscillations in-line with a viscometric motion, has been investigated. Formulas relating η^*₁₂ to measured quantities have been derived for the cone-and-plate and parallel-plate geometries. In the former case, the formula has the same form as that found when there is no steady shearing present. For the parallel-plate geometry, the formula is different because of the radial variation in the viscometric shear rate. In order to determine the empirical significance of this formula, η^*₁₂ data were obtained for two fluids, NBS nonlinear sample No. 1 and a 4.3 g/dl aqueous polyethylene oxide (molecular weight, 5 X 10⁶) solution using a Weissenberg rheogoniometer Model R-18. Data were acquired and analyzed using a minicomputer on-line with the rheogoniometer. The obtained data indicate that good agreement between the η^*₁₂ measured using the two geometries is obtained only if the derived formulas are used. Also, it is shown that theoretical results of simple-fluid theory are valid for these data.