Eur. Phys. J. E (2010) 32: 333-338
https://doi.org/10.1140/epje/i2010-10628-9

Regular Article

da Vinci fluids, catch-up dynamics and dense granular flow

¹ Earth Science and Engineering, and Institute of Shock Physics, Imperial College, SW7 2AZ, London, UK
² Cavendish Laboratory, JJ Thomson Avenue, CB3 0HE, Cambridge, UK
³ Beverly and Sackler School of Physics and Astronomy, Tel Aviv University, 69934, Ramat Aviv, Israel

^* e-mail: rbb11@cam.ac.uk

Received: 19 February 2010
Accepted: 24 June 2010
Published online: 29 July 2010

Abstract

We introduce and study a da Vinci fluid, a fluid whose dissipation is dominated by solid friction. We analyse the flow rheology of a discrete model and then coarse-grain it to the continuum. We find that the model gives rise to behaviour that is characteristic of dense granular fluids. In particular, it leads to plug flow. We analyse the nucleation mechanism of plugs and their development. We find that plug boundaries generically expand and we calculate the growth rate of plug regions. In systems whose internal effective dynamic and static friction coefficients are relatively uniform we find that the linear size of plug regions grows as (time)^1/3 . The suitability of the model to granular materials is discussed.