Escape of a granular chain from a pore in a wall in the presence of diffusing granular particles on one side of the wall is studied experimentally. The escape time shows power-law behavior as a function of the chain length (τ ∝ N^α). A Langevin dynamics simulation of a polymer chain in a similar geometry is also performed and similar results to those for a granular system are obtained. A simple scaling argument and an energetic argument (based on the Onsager principle) are introduced which explain our results very well. Experiments (simulations) show that by increasing the number of particles on one side of the wall from zero, the exponent α decreases from 2.6 ± 0.1 (3.1 ± 0.1) to about 2. Both scaling and the Onsager principle argument predict α = 2 at high particle concentration, in agreement with the experiments and simulations. In the absence of particles, the scaling predicts τ = N^2.5 (in agreement with the experimental result for the granular chain) and the Onsager principle predictsτ = N³ ln N, supporting the simulation result for the polymer chain. Experiments, simulations, scaling, and the Onsager principle confirm an inverse relation between τ and the density of particles on one side of the wall.

中文翻译：

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在一侧存在颗粒的情况下，颗粒链从壁上的孔中逸出：与聚合物易位的比较†

实验研究了在壁的一侧上存在扩散的颗粒的情况下从壁中的孔中逃逸出的颗粒链。逃逸时间显示幂律行为作为链长度的函数（τ α Ñ ^α）。还对相似几何形状的聚合物链进行了Langevin动力学模拟，并获得了与粒状系统相似的结果。介绍了一个简单的缩放参数和一个有力的参数（基于Onsager原理），它们很好地解释了我们的结果。实验（模拟）表明，通过将壁的一侧的粒子数量从零增加，指数α从2.6±0.1（3.1±0.1）减小到大约2。缩放和Onsager原理参数都可以预测与实验和模拟一致，在高颗粒浓度下，α = 2。在没有颗粒的情况下，结垢可预测τ = N ^2.5（与颗粒链的实验结果一致），Onsager原理可预测τ = N ³  ln  N，从而支持聚合物链的模拟结果。实验，模拟，缩放和Onsager原理证实了τ与壁的一侧上的粒子密度之间的反比关系。