The role of the mathematical mean value theorem (MVT) in rheometry: an easy way to convert apparent flow curves into correct ones |
| |
Authors: | Peter O Brunn Thomas Wunderlich |
| |
Institution: | Universit?t Erlangen-Nürnberg Lehrstuhl für Str?mungsmechanik Cauerstra?e 4, 91058 Erlangen, Germany, DE
|
| |
Abstract: | The mean value theorem of integral calculus guarantees that the apparent viscosity η
a
can easily be converted into the correct viscosity η. For ordinary liquids there is a direct identity between η
a
and η but the apparent shear rate (or apparent shear stress) has to be shifted to the representative shear rate γ˙^ (or representative shear stress τ^). A model free approximation scheme is introduced which implies a constant shift factor. The corresponding approximation
for η is acceptable for liquids most commonly encountered. For plastic fluids the relation between η and η
a
is more complex since it involves a function depending upon α; the yield stress relative to the maximum stress within the
viscometer. Using the same approximation scheme as before the shift factor will involve α as well. The corresponding approximation
of η is shown to be acceptable for the whole range of α.
Received: 7 February 2000/Accepted: 15 February 2000 |
| |
Keywords: | Mean value theorem Apparent shear rate/shear stress Representative shear rate/shear stress Viscometry Shift factor |
本文献已被 SpringerLink 等数据库收录! |