Based on the statistical self-similar fractal characteristics of the microstructure of porous media, the total flow rate and permeability of Newtonian fluids in the rough fracture network and rough matrix pores are derived, respectively. According to the connection structure between fractures and pores, the permeability analysis model of fluids in a matrix-embedded fracture network is established. The comparison between the predicted values of the model and the experimental data shows that the predicted values of the permeability of the rough fracture network and the rough matrix pores decrease with the increase in the relative roughness of the fractures and matrix pores, and are lower than the experimental data. Meanwhile, the predicted total flow rate of a rough fractured dual porous media is lower than that of a smooth fractal model and experimental data. In addition, it is also found that the larger the average inclination angle and the relative roughness of the fracture network, the smaller the permeability of the fractured dual porous media, and the relative roughness of the fracture network has a far greater influence on fluid permeability in the fractured dual porous media than the relative roughness of the matrix pores.

To better understand the application of droplet impingement in industry and agriculture, in this paper, the coupled level set and volume of fluid ($CLSVOF$) method is applied to study droplet oblique impact on a dynamic liquid film. The conclusions are the following: the downstream crown height increases and then decreases as the impact angle increases, whereas upstream crown height and spreading length decrease significantly; moreover, the spreading length and upstream crown height increase with the increase of film velocity, while the downstream crown height decreases instead. The increase of gas density inhibits both upstream and downstream crowns. When the fluid viscosity decreases or the impact velocity increases, the crown height increases significantly, which easily leads to crown rupture or droplet splash. The increase in impact velocity leads to an increase in spreading length; however, viscosity has almost no effect on the spreading length.