Arrested shear dispersion and other models of anomalous diffusion
Arrested shear dispersion and other models of anomalous diffusion
复制标题
受阻剪切色散和反常扩散的其他模型
DOI：
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发表时间：
1988
影响因子：
3.7
通讯作者：
W. Young
中科院分区：
文献类型：
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作者：
W. Young
在微观无序流体流动中，示踪剂的宏观弥散最终在很大程度上可以用平流-扩散方程来描述。但在达到这个渐近状态之前，有一个中间状态，其中分布的第一和第二空间矩与t成比例。传统的平流扩散（适用于大时间）ν = 1，但在中间区域ν < 1。这种现象被称为“反常扩散”，本文详细讨论了ν = 1 / 2的特殊情况。这个特殊的ν值是由示踪剂在中心管道中的色散产生的，中心管道有许多停滞的侧分支通向远离它的地方。当示踪剂漫游到侧分支时，它被“阻挡”或“阻止”，因此在中央管道中的分散比传统的平流扩散更缓慢（即ν = 1 / 2 < 1）。这个特殊的例子可以作为一个入口点，进入更一般的一类模型，这些模型用积分微分方程描述了示踪剂在再循环闭合口袋中的滞留，可渗透颗粒等。在这种观点中，追踪者被逮捕，并在一个特定的地点被拘留一段随机的时间。在建立这种中断随机行走的连续体模型时，一个基本的重要量是在一个地点停止时间的分布。慢尾衰减分布（长逗留时间）产生异常扩散，而传统模型是由短尾分布产生的。
The macroscopic dispersion of tracer in microscopically disordered fluid flow can ultimately, at large times, be described by an advection-diffusion equation. But before this asymptotic regime is reached there is an intermediate regime in which first and second spatial moments of the distribution are proportional to tν. Conventional advection-diffusion (which applies at large times) has ν = 1 but in the intermediate regime ν < 1. This phenomenon is referred to as ‘anomalous diffusion’ and this article discusses the special case ν = ½ in detail. This particular value of ν results from tracer dispersion in a central pipe with many stagnant side branches leading away from it. The tracer is “held up” or ‘arrested’ when it wanders into the side branches and so the dispersion in the central duct is more gradual than in conventional advection-diffusion (i.e. ν = ½ < 1). This particular example serves as an entry point into a more general class of models which describe tracer arrest in closed pockets of recirculation, permeable particles, etc. with an integro-differential equation. In this view tracer is arrested and detained at a particular site for a random period. A quantity of fundamental importance in formulating a continuum model of this interrupted random walk is the distribution of stopping times at a site. Distributions with slowly decaying tails (long sojourns) produce anomalous diffusion while the conventional model results from distributions with short tails.