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. 2017 Sep 8;3(9):e1701558. doi: 10.1126/sciadv.1701558

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Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

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Fig. 2 — (A) Dependence of the cavity-to-sphere volume ratio V_C/V_S on the sphere-to-liquid density ratio ρ_S/ρ. Data are for 10-mm (blue circles), 15-mm (green triangles), and 20-mm (red squares) steel (ρ_S = 7.7 g/cm³) or tungsten carbide (TC) (ρ_S = 14.9 g/cm³) spheres falling in PP1 (ρ = 1.7 g/cm³) and 95°C water (ρ = 0.96 g/cm³). The dotted line corresponds to neutral buoyancy of the sphere-in-cavity structure. (B) Cavity volume, as a function of (LD²), cavity diameter D, and length L, for the same sphere sizes and liquid combination as in (A). The dotted line is the best linear fit to the data that gives the relation V_C ≈ 0.45 LD².