论文标题
达西的屈服压力定律在特鲁利等网络上
Darcy's law of yield stress fluids on a treelike network
论文作者
论文摘要
了解多孔培养基中屈服应力流体的流动是一个主要挑战。特别是，实验和广泛的数值模拟报告了一种非线性Darcy定律作为压力梯度的函数。在这封信中，我们考虑了一种类似树状的多孔结构，可以通过对定向聚合物（DP）的映射来解决该流的问题，并在Cayley树上具有无序的键键能。我们的结果证实了流动的非线性行为，并通过限于消失重叠的DP的低能路径的密度来表达其全压依赖性。这些通用预测通过广泛的数值模拟证实。
Understanding the flow of yield stress fluids in porous media is a major challenge. In particular, experiments and extensive numerical simulations report a non-linear Darcy law as a function of the pressure gradient. In this letter, we consider a tree-like porous structure for which the problem of the flow can be resolved exactly thanks to a mapping with the directed polymer (DP) with disordered bond energies on the Cayley tree. Our results confirm the non-linear behavior of the flow and expresses its full pressure-dependence via the density of low-energy paths of DP restricted to vanishing overlap. These universal predictions are confirmed by extensive numerical simulations.
