Vibrated grains

Many interesting observations can be done when the granular medium is subject to periodic vibration. As already discussed (see paragraph 1.1.2) the effect of slow vibration under of the bottom of a container filled of grains induces a very slow compaction of the material. When the amplitude of vibration is strong enough, i.e. when

$$\Gamma= \frac{a_{max}}{g} > 1$$ (1.14)

(where $a_{max}$ is the maximum acceleration of the vibrating plate, e.g. $a_{max}=A\omega^2$ if the plate is harmonically vibrating with $A$ amplitude and $\omega$ frequency), then the granular shows several new phenomena.

• Convection and segregation: A large literature [87] exists on the convection and segregation phenomena observed in granular media contained in a box shaken from the bottom (or from the sides). Faraday [88] was perhaps the first to observe such a phenomenon. The geometry of the container can change dramatically the quality of the convection (e.g. in a cylinder may happen that the grains near the walls move downwards and the ones in the bulk move upwards, while inside an inverted cone the convection occurs in the opposite direction). Usually the larger grains (independent of their density) tend to move upwards (see Fig. fig_coffee), so that the material segregate (see for example [127,79,135,125,124]).

  Figure 1.10: Segregation and convection in a vibrated mixture of grains of different sizes

  

• Pattern formation in surface waves: another problem that has been extensively studied in recent years is the formation of patterns on the surface of vibrated layers of grains. Depending on the whole set of parameters (amplitude and frequency of the vibration, shapes and sizes of the grains, size of the container, depth of the bed and so on) different qualities of standing waves can be observed, leading to unexpected and fascinating textures [161,162,209,163] (see Fig. fig_patterns and Fig. fig_oscillon).

  Figure 1.11: Different surface patterns obtained by vertical vibration of granular layers

  

  Figure 1.12: The oscillon: a two-dimensional solitary standing wave on the surface of a granular monolayer

  

• Validations of kinetic theory: a part of the experimental effort [147,224,223,222] has also devoted to the study of hydrodynamic and kinetics fields (i.e. packing fraction profiles, granular temperature profiles, self-diffusion, velocity statistics) in vertically vibrated boxes (or vertical slices, that is 2d setups). The interest has also focused on the difficulties of imposing boundary conditions to the existing kinetics model, due to the existence of non-hydrodynamic boundary layers. This has also led to the formulation of hypothesis of scaling for the granular temperature as a function of the amplitude of vibration  [134,204]. For more recent experiments see [225].

• Clustering: the formation of high density clusters has also been studied in the same previous simple setup, i.e. in a vibrated cylindrical piston [84,86,85]. A transition has been observed with the increasing number of particles in the cylinder, from a gas-like behavior to a collective solid-like behavior. Such a transition has been also observed in the framework of fluidized beds [172], i.e. vertically shaken granular monolayers: the authors have observed a transition (with reducing the vibration amplitude) from a gas-like motion to a coexistence between a crystallized state (a pack of particles arranged in an ordered way) surrounded by gas.

• Velocity distributions: after the recent progresses in the numerical study of granular rapid dynamics, almost in the investigation of the limits of existing granular kinetic theories [42,39,211], the question of the true form of the velocity distributions has arisen and has induced many new experiments in order to give a realistic answer to it. The experiment of Olafsen and Urbach [172,173] with a horizontal granular monolayer subject to a vertical vibration (and measuring horizontal velocities) has proven that, in the presence of clustering, the distributions are non-Gaussian, showing nearly exponential tails. The experiment of Losert et al. [144] on a similar monolayer with vertical vibration verify that both the predictions of van Noije and Ernst [211] on the high energy tails for cooling and driven granular gases are correct, measuring exponential tails for the former and $\exp(-v^{3/2})$ for the latter. Very recently Rouyer and Menon [189] have again measured the velocity fluctuations in a vertically vibrated vertical monolayer of grains, obtaining again a velocity distribution with $\exp(-v^{3/2})$ tails.