Institut de Physique du Globe de Strasbourg, Université de Strasbourg, EOST, Centre National de la Recherche Scientifique, 67084 Strasbourg, France.
PoreLab, Department of Physics, University of Oslo, P.O. Box 1074 Blindern, 0316 Oslo, Norway.
Phys Rev E. 2018 Jan;97(1-1):012908. doi: 10.1103/PhysRevE.97.012908.
By means of digital image correlation, we experimentally characterize the deformation of a dry granular medium confined inside a Hele-Shaw cell due to air injection at a constant overpressure high enough to deform it (from 50 to 250 kPa). Air injection at these overpressures leads to the formation of so-called pneumatic fractures, i.e., channels empty of beads, and we discuss the typical deformations of the medium surrounding these structures. In addition we simulate the diffusion of the fluid overpressure into the medium, comparing it with the Laplacian solution over time and relating pressure gradients with corresponding granular displacements. In the compacting medium we show that the diffusing pressure field becomes similar to the Laplace solution on the order of a characteristic time given by the properties of the pore fluid, the granular medium, and the system size. However, before the diffusing pressure approaches the Laplace solution on the system scale, we find that it resembles the Laplacian field near the channels, with the highest pressure gradients on the most advanced channel tips and a screened pressure gradient behind them. We show that the granular displacements more or less always move in the direction against the local pressure gradients, and when comparing granular velocities with pressure gradients in the zone ahead of channels, we observe a Bingham type of rheology for the granular paste (the mix of air and beads), with an effective viscosity μ_{B} and displacement thresholds ∇[over ⃗]P_{c} evolving during mobilization and compaction of the medium. Such a rheology, with disorder in the displacement thresholds, could be responsible for placing the pattern growth at moderate injection pressures in a universality class like the dielectric breakdown model with η=2, where fractal dimensions are found between 1.5 and 1.6 for the patterns.
通过数字图像相关技术，我们实验表征了在足够高的恒定超压下（从 50kPa 到 250kPa）注入空气，导致内部的干燥颗粒介质变形的情况。在这些超压下注入空气会导致形成所谓的气动裂缝，即没有珠子的通道，我们讨论了介质围绕这些结构的典型变形。此外，我们模拟了流体超压向介质中的扩散，将其与随时间变化的拉普拉斯解进行比较，并将压力梯度与相应的颗粒位移相关联。在压实介质中，我们表明，扩散压力场在由孔隙流体、颗粒介质和系统尺寸的特性给出的特征时间量级上变得类似于拉普拉斯解。然而，在扩散压力在系统尺度上接近拉普拉斯解之前，我们发现它类似于通道附近的拉普拉斯场，在最先进的通道尖端处存在最高的压力梯度，而在它们后面存在屏蔽的压力梯度。我们表明，颗粒位移或多或少总是沿着与局部压力梯度相反的方向移动，并且当将颗粒速度与通道前方区域的压力梯度进行比较时，我们观察到空气和珠子混合的颗粒糊状物具有宾汉型流变学，有效粘度 μ_B 和位移阈值 ∇[over ⃗]P_c 在介质的动员和压实过程中不断演变。这种流变学，具有位移阈值的无序性，可能是导致在中等注入压力下放置图案生长的原因，类似于具有 η=2 的介电击穿模型的普适类，其中图案的分形维数在 1.5 和 1.6 之间。
