Quantifying fluid mixing with the Shannon entropy
Quantifying fluid mixing with the Shannon entropy
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DOI：
10.1002/mats.200600037
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发表时间：
2006-10-11
影响因子：
1.4
通讯作者：
Manas-Zloczower, Ica
中科院分区：
文献类型：
--
作者：
Camesasca, Marco;Kaufman, Miron;Manas-Zloczower, Ica
我们介绍了一种方法来量化的质量混合在各种系统中，包括聚合物的，通过适应香农信息熵。为了说明的目的，我们使用两个物种在二维空腔流的粒子平流。我们通过使用在给定位置找到给定种类的粒子的合适的选择组/复合体的概率来计算熵。通过选择与混合物中组分的总浓度成正比的组的大小，我们确保了对于完全混合的情况，即当在每个位置处组分浓度等于相应的总组分浓度时，熵测度最大化。利用熵方法分析了观测在混合评价中的作用尺度。我们还说明了在层流系统中混合的初始条件的影响，典型的涉及聚合物的操作。
We introduce a methodology to quantify the quality of mixing in various systems, including polymeric ones, by adapting the Shannon information entropy. For illustrative purposes we use particle advection of two species in a two-dimensional cavity flow. We compute the entropy by using the probability of finding a suitable chosen group/complex of particles of a given species, at a given location. By choosing the size of the group to be in direct proportion to the overall concentration of the components in the mixture we ensure that the entropic measure is maximized for the case of perfect mixing, that is, when at each location the component concentration is equal to the corresponding overall component concentrations. The scale of observation role in evaluating mixing is analyzed using the entropic methodology. We also illustrate the effect of initial conditions on mixing in a laminar system, typical in operations involving polymers.