CSIRO Division of Materials Science and Engineering, Box 56 Graham Road, Highett Victoria 3190, Australia.
Philos Trans A Math Phys Eng Sci. 2010 Jan 13;368(1910):217-30. doi: 10.1098/rsta.2009.0198.
In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.
在自然界中，流体、热和/或反应物质的耗散通量相互耦合，并且也可能与周围多孔基质的变形耦合。我们使用众所周知的Hele-Shaw 流对达西流的类比来制作一个具有与局部单元高度成比例的孔隙率的模型多孔介质。通过多个源/汇井进行随时间和空间变化的流体注入，使我们能够创建许多不同类型的混沌流动和化学浓度模式。初始时变势流模型的结果表明，这是一种部分开放的流动，其中部分通过流动输送的材料永远留在单元中，而部分则通过具有自相似特征的停留时间和出口时间分布通过，其在搅拌的控制参数空间中具有自相似特征。我们从理论上推导出在搅拌控制参数空间中，存在一个边界，在这个边界上，孤立的流体区域可以或不能永远留在开放流动中。实验证实了这些预测。
