Janssen's Experiment in small silos

Devontae Baxter, Michael Tennenbaum, and Alberto Fernandez-Nieves

Janssen's experiment is a classic grannular matter expeiment originally performed in the 1800s. It aims to describe the difference between filling a silo with a liquid and a grannular material, originally corn in silos. We are working on understanding in narrow silos. Since Janssen showed that the force in a granular silo saturates with height, we know that the interaction with the wall is important. We are looking at narrow silos to see if the wall effects are amplified.

Fig. 1: Beans loaded into a narrow silo. The silo is supported from the side and a scale is used as the base to measeure the weight felt at the bottom of the silo. The silo in the image has 200g of beans in it.

The idea behind Janssen's theory is that in a grannular system the walls are able to support some of the weigt of the column through frction between the walls and the particles. This leads to a non-linear relationship between the mass added to the silo, $$M_{total}$$, and the measured mass at the bottom of the silo, $$M_{apparent}$$. $$M_{apparent} \simeq \frac{\pi}{2} D^3 \rho (1-e^{-M_{total}/(\rho \pi D^3/8)})$$ where $$\rho$$ is density of the ganular media and $$D$$ is the diameter of the silo.

Fig. 2: Plot of the mass measured by the scale and the total mass added to the silo. The solid line is liquid behavior, $$M_{apparent}=M_{total}$$, and the dashed line is a fit to Janssen's model.

References:
[1] H. Janssen Zeitschr. d. Vereines deutscher Ingenieure 39, 1045-1049 (1895).
[2] M. Sperl Granular Matter 8, 59-65 (2006).

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
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alberto.fernandez [at] physics.gatech.edu