What Is a Fluid? — Question 8

Question 8

A pile that pours but also stands

Dry grains can pour from a hopper, yet form a stationary sloping pile. A sample of the grains is confined in a shear cell. Below a threshold tangential load it deforms slightly and then stops; above the threshold it rearranges continuously. An ordinary liquid, tested without interfacial pinning, continues to deform under every sustained nonzero shear load in the idealization.

1. Explain why the ability to pour does not make the resting grain assembly an ordinary fluid in the same mechanical sense as the liquid.

2. A student attributes the distinction solely to whether the material consists of particles. Correct the argument and propose a load protocol that exposes the difference.

Question 8 - Solution

A pile that pours but also stands

(a) Derivation and calculation

Let $F_y$ denote the stated grain-yield threshold and $\gamma$ the internal shear strain. The observed distinction is$$0<|F|<F_y:\quad\gamma_{\mathrm{grains}}\to\gamma_\infty,\quad\dot\gamma_{\mathrm{grains}}\to0;$$$$|F|>F_y:\quad\text{grains continue deforming}.$$The ordinary liquid continues deforming for every sustained nonzero shear load in the idealization.

(b) Result and interpretation

A discriminating protocol maintains loads$$0<F_1<F_2<F_y<F_3$$$$\text{and records }\gamma(t),\quad\dot\gamma(t),\quad\text{boundary slip}.$$Bounded low-load deformation followed by yielding identifies the specified grain response. Both materials consist of particles; the static contact network and its response to shear are what matter.

Physical check

Pouring demonstrates a flowing regime, not the inability to support an arbitrarily small static shear load.