Using index matching and particle tracking, we measure the three-dimensional velocity field in an isotropic porous medium composed of randomly packed solid spheres. This high-resolution experimental dataset provides new insights into the dynamics of dispersion and stretching in porous media. Dynamic-range velocity measurements indicate that the distribution of the velocity magnitude, , is flat at low velocity (probability density function ). While such a distribution should lead to a persistent anomalous dispersion process for advected non-diffusive point particles, we show that the dispersion of non-diffusive tracers nonetheless becomes Fickian beyond a time set by the smallest effective velocity of the tracers. We derive expressions for the onset time of the Fickian regime and the longitudinal and transverse dispersion coefficients as a function of the velocity field properties. The experimental velocity field is also used to study, by numerical advection, the stretching histories of fluid material lines. The mean and the variance of the line elongations are found to grow exponentially in time and the distribution of elongation is log-normal. These results confirm the chaotic nature of advection within three-dimensional porous media. By providing the laws of dispersion and stretching, the present study opens the way to a complete description of mixing in porous media.

中文翻译：

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三维多孔介质中的速度分布、色散和拉伸

使用指数匹配和粒子跟踪，我们测量了由随机填充的固体球体组成的各向同性多孔介质中的三维速度场。这个高分辨率的实验数据集为多孔介质中的分散和拉伸动力学提供了新的见解。动态范围速度测量表明速度幅度 的分布在低速时是平坦的（概率密度函数 ）。虽然这种分布应该导致对流非扩散点粒子的持续异常弥散过程，但我们表明，非扩散示踪剂的弥散在超过示踪剂最小有效速度设定的时间后变为 Fickian。我们推导出 Fickian 状态的开始时间和纵向和横向色散系数的表达式，作为速度场特性的函数。实验速度场还用于通过数值平流研究流体物质线的拉伸历史。发现线伸长的平均值和方差随时间呈指数增长，伸长的分布是对数正态的。这些结果证实了三维多孔介质内平流的混沌性质。通过提供分散和拉伸定律，本研究为全面描述多孔介质中的混合开辟了道路。发现线伸长的平均值和方差随时间呈指数增长，伸长的分布是对数正态的。这些结果证实了三维多孔介质内平流的混沌性质。通过提供分散和拉伸定律，本研究为全面描述多孔介质中的混合开辟了道路。发现线伸长的平均值和方差随时间呈指数增长，伸长的分布是对数正态的。这些结果证实了三维多孔介质内平流的混沌性质。通过提供分散和拉伸定律，本研究为全面描述多孔介质中的混合开辟了道路。