Matthias Schröter, Home

In 1989 Sam Edwards and Coworkers suggested a statistical mechanics approach to static granular media. A central postulate of this theory is the existence of temperature-like state variable called compactivity X = dV / dS. The entropy S is defined in analogy to classical statistical mechanics as S(V,N) = λ ln Ω, where Ω is the number of mechanically stable configurations of N particles in the volume V, and λ is an unknown analog to the Boltzmann constant. The assumption that X is a relevant control parameter in granular systems has found support in simulations of segregation in binary mixtures, compaction under vertical tapping, and shearing. However, no previous measurements of X have been reported.

Figure 1
Experimental setup. The inset shows the correlation between the height changes Δh during a flow pulse to the fluidized bed, as seen by the two cameras (800 flow pulses, Q = 60,mL/min, d is particle diameter).

Figure 2
Photograph of the fluidized bed in its thermally insulating housing. The orange LED arrays are used to illuminate the sand-water interface, in the back is a window for one of the two CCD cameras.

Results

Figure 3
Steady state: in a series of flow pulses the volume fraction Φ of the sedimented bed reaches a steady state that depends only on the flow rate Q of the pulses. The volume fraction fluctuations around the steady states are Gaussian distributed with a standard deviation σ_Φ.

Figure 4
The standard deviation σ_Φ of the volume fraction fluctuation fit a parabolic curve.

Figure 5
Knowing the dependency of σ_Φ on Φ enables us to determine for the first time Edward's compactivity X using a granular version of the fluctuation dissipation theorem derived by Nowak et al.

Conclusion

We have shown that the phase space of mechanically stable, granular configurations can be explored by using flow pulses in a liquid-fluidized bed. The configurational temperature X can be determined from the volume fraction fluctuations; hence X is a well-defined parameter representative of the material. This opens the door for new experiments that will, for example, investigate the use of compactivity as a control parameter for segregation in binary mixtures.

Publication

• Matthias Schröter, Dan Goldman, and Harry L. Swinney
  Stationary state volume fluctuations in a granular medium
  Physical Review E 71, 030301(R) (2005)
  [Journal URL], [pdf], [arxiv]
  
  

In collaboration with

Dan I. Goldman Georgia Institute of Technology

Harry L. Swinney University of Texas at Austin

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