Fluctuation-Induced Casimir Forces in Granular Fluids

We numerically investigate the behavior of driven noncohesive granular media and find that two fixed large intruder particles, immersed in a sea of small particles, experience, in addition to a short-range depletion force, a long-range repulsive force. The observed long-range interaction is fluctuation-induced and we propose a mechanism similar to the Casimir effect that generates it: The hydrodynamic fluctuations are geometrically confined between the intruders, producing an unbalanced renormalized pressure. An estimation based on computing the possible Fourier modes explains the repulsive force and is in qualitative agreement with the simulations.

Figure 1

Relative effective dimensionless force $FD/T_0$ between the intruders as a function of the distance $R$ between their centers. We plot simulations results for $L=60d$ (solid circles) and for $L=80d$ (open triangles), together with theoretical predictions (solid lines). Inset: Short-range region showing the depletion forces. Note the difference in the vertical scale, compared with the long-range part. Error bars in the inset are smaller than the symbols.

Figure 2

Probability distribution of the fluctuating force $F_{12}$ at $R=20d$, for $L=80d$. The net effective force is obtained as the average of this histogram. The average value is $F=0.223T_0/D$ and the standard deviation is ${\sigma }_F=4.83T_0/D$, which is about 20 times larger than the average value.

Figure 3

Sketch of the hydrodynamic fluctuations leading to the Casimir-like force. In the gap between the intruders, only fluctuations of wavelength smaller than $R-D$ are allowed, while in the outer space the wavelengths can be larger.