Oliveira Rafael S, Andrade José S, Andrade Roberto F S
Instituto de Física, Universidade Federal da Bahia, 40210-210 Salvador, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Apr;81(4 Pt 2):047302. doi: 10.1103/PhysRevE.81.047302. Epub 2010 Apr 7.
This work considers the flow of a Newtonian fluid in a two-dimensional channel filled with an array of obstacles of distinct sizes that models an inhomogeneous medium. Obstacle sizes and positions are defined by the geometry of an Apollonian packing (AP). The radii of the circles are uniformly reduced by a factor s<1 for assemblies corresponding to the five first AP generations. The region of validity of Darcy's law as a function of the channel Reynolds number is investigated for different values of s and the dependency of the flow pattern and permeability with respect to porosity is established. Our results show that the semiempirical Kozeny-Carman scaling relation is satisfied provided the effects of the apparent porosity and s-dependent formation factor are properly considered.
这项工作考虑了牛顿流体在充满不同尺寸障碍物阵列的二维通道中的流动，该通道模拟了非均匀介质。障碍物的尺寸和位置由阿波罗尼斯填充（AP）的几何形状定义。对于对应于前五代AP的组件，圆的半径统一缩小了s<1倍。针对不同的s值，研究了达西定律作为通道雷诺数函数的有效区域，并建立了流动模式和渗透率与孔隙率的相关性。我们的结果表明，只要适当考虑表观孔隙率和与s相关的地层因数的影响，半经验的柯曾尼-卡曼标度关系就能得到满足。
