The Deborah and Weissenberg numbers

摘要

Since their introduction to the literature nearly fifty years ago the Deborah and Weissenberg numbers have proved invaluable for rheologists in quantifying viscoelastic effects. Despite their different origins, and the fact that they quantify different effects, they are frequently used as synonyms. This situation is perhaps partly explainable given that in a wide range of flows of complex fluids characterised by a relaxation time (λ) the use of simple single characteristic length (L) and velocity scales (U) does indeed result in identical definitions! In this short article we return to the original papers to highlight the different effects that the Deborah and Weissenberg numbers measure.