Jamming and growth of dynamical heterogeneities versus depth for granular heap flow

TL;DR

This study investigates how grain dynamics and heterogeneities evolve with depth in a granular heap flow, revealing exponential growth of dynamical heterogeneities near jamming without structural change, and confirming a universal scaling law.

Contribution

It introduces a novel image-based order parameter and demonstrates the exponential growth of dynamical heterogeneities with depth, linking experimental results to simulation predictions.

Findings

Velocity fluctuations increase near jamming.

Dynamical heterogeneity scales with inertia number to the -1/3 power.

Heterogeneity size grows exponentially with depth.

Abstract

We report on grain dynamics versus depth for steady-state gravity-driven flow of grains along a heap formed between two parallel sidewalls. Near the surface the flow is steady and fast, while far below there is no flow whatsoever; therefore, a jamming transition occurs where depth is an effective control parameter for setting the distance from the transition. As seen previously, the time-averaged velocity profile along the sidewall exhibits a nearly exponential decay vs depth. Using speckle-visiblility spectroscopy (SVS), we find that velocity fluctuations grow relative to the average on approach to jamming. Introducing an image-based order parameter and the variance in its temporal decay at a given depth, we also characterize the spatially heterogeneous nature of the dynamics and find that it increases on approach to jamming. In particular, the important time and length scales for dynamical heterogeneities are found to grow almost exponentially as a function of depth. These dynamical changes occur without noticeable change in structure, and are compared to behavior found by experiment and simulation elsewhere in order to test the universality of the jamming concept. In particular we find that the size of the heterogeneities scales as the inertia number raised to the -1/3 power, in agreement with two recent simulations.