Acoustic Fluidization : What It Is , and Is Not

Acoustic Fluidization: I introduced the concept of acoustic fluidization in 1979 to explain the astonishingly low strength and viscosity exhibited by the collapse of impact craters and the formation of central peaks in lunar craters [1]. The name I gave to this process was not well chosen for the geologic community—“vibrational fluidization” might have been more apt--but that name was already in use in another context and would have proven confusing [2]. The principal motivation for introducing this process was to explain the transition from simple to complex craters on the Moon. Mechanical analysis of the collapse of simple craters indicates that the strength of the underlying material is only about 3 MPa [3]. Furthermore, the rise of central peaks in craters larger than about 15 km diameter on the Moon suggests that the post-impact debris can flow as a fluid with a viscosity in the vicinity of about 10 Pa-sec [4], implying a Bingham rheology for the material surrounding the crater. How could dry, broken rock debris on the surface of a planet lacking water, air or even clay minerals flow like a liquid? My solution was to invoke the action of strong vibrations in the rock debris broken by the shock from the impact, which I proposed could briefly fluidize the debris. The reality of such strong vibrations near an impact is supported by ground motion measurements near large explosions on Earth [5], and the nonlinear dependence of strain rate on stress predicted by the theoretical model is consistent with the phenomenological Bingham rheology [6]. Moreover, the predicted relation between stress and strain rate as a function of the amplitude of vibrations was verified by measurements with a rotational viscometer [7], as shown in Figure 1. The acoustic fluidization model has been widely applied to hydrocode modeling of impact crater collapse through the approximate scheme of the “Block Model” [8], with great success, although at the cost of introducing three empirical parameters; one that relates the amplitude of the vibrations to the strength of the initial shock wave, another that specifies an effective viscosity (it essentially chooses an effective frequency or wavelength of the vibrations) and one that specifies the decay rate of the vibrational energy. The full acoustic fluidization model also envisions a feedback between flow and the vibrational energy field [9,10], which is not captured by the Block Model. A recent study has finally begun to lift this restriction [11] and provides a more accurate model of how craters collapse. Figure 1. Strain rate vs. stress in sand fluidized by strong vibrations at a frequency of about 300 Hz. Σ is the ratio between the rms vibration amplitude and the overburden pressure, and the yield stress is measured in the absence of vibrations. The solid theoretical curves are fit to the data with no free parameters.