Da Vinci Fluids, catch-up dynamics and dense granular flow

TL;DR

This paper introduces a da Vinci Fluid model dominated by solid friction, analyzing dense granular flow behavior, including plug formation and growth, through discrete and continuum approaches.

Contribution

It presents a novel fluid model capturing dense granular flow rheology and plug dynamics, bridging discrete and continuum descriptions.

Findings

Plug regions expand over time with size ~ t^{1/3}

Model reproduces characteristic dense granular flow behavior

Analyzes nucleation and growth of plugs in granular materials

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 friction coefficient is 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.