FRACTAL ANALYSIS OF STOKES FLOW IN TORTUOUS MICROCHANNELS WITH HYDRAULICALLY ROUGH SURFACES

Abstract

Previous studies have shown that the flow in porous media can be affected by the structure of microchannels. In this paper, the capillary bundle model is used to simplify the complex and irregular structure of porous media, which is assumed to be comprised of tortuous capillaries covered with statistical self-similar conical rough elements. Considering the boundary layer effect, a fractal geometry-based quantitative model has been proposed to investigate the relationship between the hydraulic roughness of capillaries and the micro-flow properties. According to the proposed model, the influence of roughened surfaces on the tortuosity of Stokes flow can be considered as the combination of every individual rough element in 2D flow fields, which is extended to 3D flow fields based on a series of assumptions and approximations. Analytical expressions of tortuosity and permeability of Stokes flow through roughened capillaries are derived. According to the results, the tortuosity of capillary flow increases with a higher relative roughness, while the permeability is inversely proportional to it. Predictions of permeability by the present model are compared with the previous models and experiment data, which show good agreement.