The effective slip length at the interface between pure fluid flow and porous media composed of packed spheres has been accurately characterized. In this study, as the first part of a two-part series, the slip length is obtained by matching the flow rate over the actual packed spheres from a direct simulation with that over an effective smooth surface using the Navier-slip boundary condition from analytic solution. Three classical packing structures, e.g., simple cubic (SC), face-centered cubic (FCC), and body-centered cubic (BCC), are employed. The accuracy of the slip length is validated by comparing the velocity field of flow over the actual porous architecture and over the effective smooth surface. We report that the slip length is best described as a function of the free slip area, rather than conventional variables such as solid volume fraction and packing structure, with the error less than 7.5%. Then, the effective smooth surface with the slip length is applied to describe two flow problems: a stick–slip–stick flow and channel flow. The slip velocity as well as its slope at the interface and the velocity profile within the pure fluid channel is accurately reproduced. In Part 2, effective slip length will be employed to characterize optimal effective viscosity and stress jump coefficient in the Stokes–Brinkman approach, which can be applied for industrial and natural flows in dual-scale porous media in predicting flow solutions inside and outside the porous media.

中文翻译：

---

在由填充球组成的多孔介质上的界面流动：第 1 部分 - 有效滑移长度的确定

已准确表征纯流体流和由填充球组成的多孔介质之间界面处的有效滑移长度。在这项研究中，作为两部分系列的第一部分，滑移长度是通过使用 Navier-slip 边界条件将直接模拟中的实际填充球体上的流速与有效光滑表面上的流速相匹配来获得的。解决方案。采用三种经典的堆积结构，例如简单立方（SC）、面心立方（FCC）和体心立方（BCC）。通过比较实际多孔结构和有效光滑表面上的流动速度场来验证滑移长度的准确性。我们报告说滑移长度最好被描述为自由滑移面积的函数，而不是固体体积分数和填料结构等常规变量，误差小于7.5%。然后，使用具有滑移长度的有效光滑表面来描述两个流动问题：粘-滑-粘流和通道流。滑移速度及其在界面处的斜率和纯流体通道内的速度分布被准确再现。在第 2 部分中，将使用有效滑移长度来表征 Stokes-Brinkman 方法中的最佳有效粘度和应力跳跃系数，该方法可应用于双尺度多孔介质中的工业和自然流动，以预测多孔内外的流动解媒体。粘滑粘流和通道流。滑移速度及其在界面处的斜率和纯流体通道内的速度分布被准确再现。在第 2 部分中，将使用有效滑移长度来表征 Stokes-Brinkman 方法中的最佳有效粘度和应力跳跃系数，该方法可应用于双尺度多孔介质中的工业和自然流动，以预测多孔内外的流动解媒体。粘滑粘流和通道流。滑移速度及其在界面处的斜率和纯流体通道内的速度分布被准确再现。在第 2 部分中，将使用有效滑移长度来表征 Stokes-Brinkman 方法中的最佳有效粘度和应力跳跃系数，该方法可应用于双尺度多孔介质中的工业和自然流动，以预测多孔内外的流动解媒体。