The role of the mathematical mean value theorem (MVT) in rheometry: an easy way to convert apparent flow curves into correct ones

The mean value theorem of integral calculus guarantees that the apparent viscosity eta(a), can easily be converted into the correct viscosity eta. For ordinary liquids there is a direct identity between eta(a), and eta but the apparent shear rate (or apparent shear stress) has to be shifted to the representative shear rate (gamma) over dot (or representative shear stress <(tau)over cap>). A model free approximation scheme is introduced which implies a constant shift factor. The corresponding approximation for eta is acceptable for liquids most commonly encountered. For plastic fluids the relation between eta and eta(a) is more complex since it involves a function depending upon alpha; the yield stress relative to the maximum stress within the viscometer. Using the same approximation scheme as before the shift factor will involve alpha as well. The corresponding approximation of eta is shown to be acceptable for the whale range of alpha.