On the Interfacial Flow Over Porous Media Composed of Packed Spheres: Part 1-Identification of the Effective Slip Length

Abstract

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.