Dr. Rafi Blumenfeld 

Cavendish Lab, Cambridge
&
Imperial College London 

Date: Dec. 26, 2010

Title: Da Vinci Fluid - a minimal model for flow of dense
granular materials

Abstract:

The flow of dense granular materials is a long-standing fundamental
scientific problem with a wide range of relevance to engineering
fields, to technological applications and to natural phenomena that
affect human society. In spite of hundreds (!) of years of research
into it, this state of matter is still poorly understood.

A minimal model for such fluids is introduced and discussed  - the da
Vinci Fluid - whose dissipation is dominated by solid friction. The
flow rheology is first analysed for insight in discrete systems and it
is then coarse-grained to the continuum. The model explains
quantitatively nucleation and growth of plug flow - a phenomenon that
has been notoriously difficult to model until now.

It is found that internally formed plugs generically expand and the
expansion rate is calculated analytically. In systems whose internal
effective dynamic and static friction coefficients are relatively
uniform the linear size of internally formed plug regions is found to
grow initially as 1/3 power of time.    Time permitting, recent
results will be presented on cylindrical Couette flows, which shed
much needed light on recent experiments.