Yan Yiguang, Koplik Joel
Benjamin Levich Institute, City College of the City University of New York, New York, NY 10031, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Mar;77(3 Pt 2):036315. doi: 10.1103/PhysRevE.77.036315. Epub 2008 Mar 24.
The two-dimensional pressure driven flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds number is calculated. The channels have constant mean aperture and two values zeta=0.5 and 0.8 of the Hurst exponent are considered. The calculation is based on the lattice-Boltzmann method, using a different technique to obtain a power-law variation in viscosity, and the behavior of shear-thinning, Newtonian, and shear-thickening liquids is compared. Local aspects of the flow fields, such as maximum velocity and pressure fluctuations, are studied, and the non-Newtonian fluids are compared to the (previously studied) Newtonian case. We find a scaling relation between permeability and mean aperture in the low Reynolds number regime, generalizing an earlier result for Newtonian fluids. As the Reynolds number increases, we observe the same sequence of transitions to nonlinearity found in intergranular porous media. Furthermore, the permeability results may be collapsed into a master curve of friction factor vs Reynolds number, using a scaling similar to that employed for power-law fluids in porous media.
计算了有限雷诺数下非牛顿幂律流体在自仿射断裂通道中的二维压力驱动流动。通道具有恒定的平均孔径，并考虑了赫斯特指数的两个值ζ = 0.5和0.8。计算基于格子玻尔兹曼方法，采用不同技术获得粘度的幂律变化，并比较了剪切稀化、牛顿和剪切增稠液体的行为。研究了流场的局部特征，如最大速度和压力波动，并将非牛顿流体与（先前研究的）牛顿情况进行了比较。我们在低雷诺数区域发现了渗透率与平均孔径之间的标度关系，推广了牛顿流体的早期结果。随着雷诺数的增加，我们观察到在粒间多孔介质中发现的向非线性转变的相同序列。此外，使用类似于多孔介质中幂律流体的标度，渗透率结果可以合并为摩擦系数与雷诺数的主曲线。
