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.

Abstract:

“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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