How far can a person sink downwards in quicksand? Experience would seem to suggest that there is low risk of submerging completely, but it is not easy to demonstrate this because of the complex rheology of granular suspensions. We study several mathematical models for the sinking of a vertical cylinder downwards into quicksand, finding that an approach with a buoyancy equation modified by drag force gives an unphysical answer. We instead argue that our proposed conclusion is supported by considering the dynamics of vibration-induced compactification of liquid-saturated granular suspensions. We compare quicksand with other non-Newtonian fluids, emphasising that in this case the same model does not apply and that the risk of drowning could be much more significant. We finish by suggesting some relevant experiments that can be performed in a classroom setting.

中文翻译：

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最大程度地浸没在致密颗粒悬浮液中

人在流沙中能下沉多深？经验似乎表明完全浸没的风险较低，但由于颗粒悬浮液的流变学复杂，要证明这一点并不容易。我们研究了垂直圆柱体向下沉入流沙的几种数学模型，发现采用阻力修正的浮力方程的方法给出了非物理答案。相反，我们认为，我们提出的结论是通过考虑液体饱和颗粒悬浮液振动引起的致密化动力学来支持的。我们将流沙与其他非牛顿流体进行比较，强调在这种情况下，相同的模型不适用，并且溺水的风险可能要大得多。最后，我们建议一些可以在课堂环境中进行的相关实验。