Abstract. As a droplet impacts on a granular substrate, both the intruder and the target deform, during which the liquid may penetrate into the substrate. These three aspects together distinguish it from other impact phenomena in the literature. We perform high-speed, double-laser profilometry measurements and disentangle the dynamics into three aspects: the deformation of the substrate during the impact, the maximum spreading diameter of the droplet, and the penetration of the liquid into the substrate. By systematically varying the impact speed and the packing fraction of the substrate, (i) the substrate deformation indicates a critical packing fraction φ * ≈ 0.585; (ii) the maximum droplet spreading diameter is found to scale with a Weber number corrected by the substrate deformation; and (iii) a model about the liquid penetration is established and is used to explain the observed crater morphology transition.Liquid droplet impact on a granular layer is very common in nature, industry, and agriculture, ranging from raindrops falling onto desert or soil to granulation in the production process of many pharmaceuticals. In spite of its commonness, the physical mechanisms involved in the impact of a droplet on sand did not attract much attention until recently [1][2][3][4][5][6][7][8][9][10][11][12], and the underlying physics is still largely unexplored. In contrast, droplet impact on a solid surface or a liquid pool has been studied extensively [13][14][15]. However, a granular substrate can act both solidlike and fluid-like [16] and many experiments have been conducted to reveal the response of a granular packing to a solid object impact [17][18][19][20][21][22][23], where the intruder does not deform. Droplet impact on a granular substrate adds new challenges to the above: First, both the intruder and the target, not merely one of the two, deform during impact; second, the liquid composing the droplet may penetrate into the substrate during the impact and may, in the end, completely merge with the grains. These complex interactions between the droplet intruder and the granular target create various crater morphologies as reported in the literature [1,2,4,9,12] [see Fig. 1 for examples] . An appealing and natural question is by what mechanism craters are formed and how this leads to the observed rich morphological variation. This is the main focus of the present work. Quantitative dynamic details, e.g., on the deformation of droplet and substrate in response to the impact, are necessary to gain insight about this issue. Previous dynamic measurements only regard the

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Jammed packings of granular materials differ from systems normally described by statistical mechanics in that they are athermal. In recent years a statistical mechanics of static granular media has emerged where the thermodynamic temperature is replaced by a configurational temperature X which describes how the number of mechanically stable configurations depends on the volume. Four different methods have been suggested to measure X. Three of them are computed from properties of the Voronoi volume distribution, the fourth takes into account the contact number and the global volume fraction. This paper answers two questions using experimental binary disc packings: first we test if the four methods to measure compactivity provide identical results when applied to the same dataset. We find that only two of the methods agree quantitatively. This implies that at least two of the four methods are wrong. Secondly, we test if X is indeed an intensive variable; this becomes true only for samples larger than roughly 200 particles. This result is shown to be due to recently measured correlations between the particle volumes [Zhao et al., Europhys. Lett., 2012, 97, 34004].