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Soft Impact Cratering

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Physics of Soft Impact and Cratering

Part of the book series: Lecture Notes in Physics ((LNP,volume 910))

Abstract

In this chapter, various experiments of impact cratering performed at a laboratory scale will be reviewed. As discussed in Chap. 5, natural planetary craters have a wide variety of shapes. Very high-speed and large-scale impact events must be reproduced to fully mimic the actual planetary craters, which is evidently impossible to accomplish. Instead, low-velocity soft matter impact experiments might be helpful for understanding the morphology and fundamental processes of actual cratering on the basis of scaling concept written in Chap. 2 Moreover, a basic understanding of the cratering mechanics brings crucial and primordial knowledge to soft matter physics itself. Therefore, phenomenological studies of soft matter impacts and some of their tentative relations to the actual cratering will be exemplified in this chapter.

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Notes

  1. 1.

    This assumption is called Schröter’s rule .

  2. 2.

    This is natural because the lunar craters could also roughly satisfy the volume conservation. Note that, however, the lunar crater cavity is not spherical. The relation of the rim height and the cavity radius should be different in actual lunar craters.

  3. 3.

    Since both terms in Eq. (6.8) diverge at z cra = 0 (\(x = \infty \)), these values must be numerically evaluated.

  4. 4.

    Note that the sheet is very thin, and its potential energy is negligible.

  5. 5.

    Specifically, 2E target∕ρ t can be computed as \(\int _{V }(\nabla \varPhi _{f})^{2}dV =\int _{V }[\nabla \cdot (\varPhi _{f}\nabla \varPhi _{f}) -\varPhi _{f}\nabla ^{2}\varPhi _{f}]dV =\int _{S}\varPhi _{f}\nabla \varPhi _{f} \cdot \boldsymbol{ n}dS =\int _{S}\varPhi _{f}v_{n}dS\), where v n is the outward normal component of velocity at the surface S. Here, we use Gauss’ theorem and irrotational condition ∇2 Φ f  = 0.

  6. 6.

    This jetting is different from the jet induced by the cavity collapse. The jet by cavity collapse is discussed in the next section.

  7. 7.

    Indeed, the range of container diameter varies within a relatively narrow regime (D con ≤ 6D i ).

  8. 8.

    Water saturation indicates the fraction of water in the pore space expressed by volume ratio (Eq. (4.36)).

  9. 9.

    \(\varTheta (x) = 0\) for (x < 0) and 1 for (x > 0).

  10. 10.

    This assumption is important for the scaling. Another scaling relation can be obtained by a different definition of viscous dissipation. This point will be discussed later in the next section (see Eqs. (6.78) and (6.79)).

  11. 11.

    The typical initial packing fraction is ϕ 0 = 0. 44. Furthermore, the target is considerably compressed by the impact.

  12. 12.

    Note that the axes in the phase diagram of Fig. 6.13 are on logarithmic scales.

  13. 13.

    Because the capillary effect becomes dominant in the small-scale regime (Sect. 2.8.5), its effect is pronounced in a small-bead bed.

  14. 14.

    See Eq. (3.28). Note that the kinematic viscosity η∕ρ i corresponds to the diffusion coefficient K d .

  15. 15.

    The radius of curvature is defined by \(R_{c} = ds/d\theta\), where \(ds = \sqrt{(dx)^{2 } + (dz)^{2}}\) is an arc length and \(d\theta\) is the corresponding arc angle. The relation \(d\theta = (d^{2}z/dx^{2})dx/[1 + (dz/dx)^{2}]\) is obtained from the geometrical condition \(\tan (\theta +d\theta ) = dz/dx + (d/dx)(dz/dx)dx\) (using \(d\theta \ll 1\), \(\tan \theta = dz/dx\) and \(\tan (\theta +d\theta ) = (\tan \theta +\tan d\theta )/(1 -\tan \theta \tan d\theta )\)). Equation (6.71) is computed from these relations.

  16. 16.

    This criterion is equivalent to the condition that the viscosity is negligible.

  17. 17.

    The assumption \(D_{c} \simeq 2D_{i}\) is not actually very evident in astronomical impacts. While we assume this approximation herein, another constraint is necessary to obtain the truly closed form.

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    Hiroaki Katsuragi

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Katsuragi, H. (2016). Soft Impact Cratering. In: Physics of Soft Impact and Cratering. Lecture Notes in Physics, vol 910. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55648-0_6

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