Rheology, rheometers, and matching models to experiments

We consider the general problem of matching rheological models to experiments. We introduce the concept of identifiability of models from a given set of experiments. To illustrate this in detail, we study two rheology models, the grade-two and Oldroyd 3-parameter models, and consider two hypothetical rheometers to see if the coefficients of the rheology models are identifiable from experimental measurements or not. For the Oldroyd models, we show that the coefficients can be estimated from experiments from the two rheometers. But for the grade-two model, it is not possible to distinguish the two nonNewtonian parameters, only their sum can be estimated, and thus the grade-two model is not identifiable by the two hypothetical rheometers. However, our results imply that a different rheometer may be able to do that.