The Weissenberg number: the prince of dimensionless numbers in fluids

This talk was presented on 9th November 2016 at the Department of Mathematics of UCL as part of the postgraduate seminars programme. I also gave this talk in the conference UCL-ICL day 2017, an event organised by students from University College London and Imperial College London.


“The mountains flowed before the lord”, proclaimed the Prophetess Deborah,  who has given her name to an important non-dimensional number in rheology, the science of deformation. The basic idea is that everything will flow (even the mountains) if we wait long enough.

In this talk I will mention the historical/poetic origins of the Deborah number, which gave birth to a more important non-dimensional number: the Weissenberg number.  I will show the importance of this number in the mathematical modelling of materials that exhibit memory effects. Time permitting, I will also describe how these numbers are useful to explain why some fluid-like materials (under certain conditions) might behave as elastic solids (and viceversa).

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