Effect of Capillary Number on Drainage from Microscale Sinusoidal Pores

Understanding the dynamics of fluid transport and trapping within micro-scale pores is important for a range of environmental, industrial, and research applications. Prior work has used porous media micromodels containing 2D or 3D networks of obstacles to investigate drainage of a trapped phase being displaced by another immiscible fluid. Here, we explore liquid drainage/entrapment in microscale pores in a quasi-1D system at a range of capillary numbers with water as a displacing fluid, fluorinated oil as the (wetting) trapped phase, and PDMS microfluidics patterned with sinusoidal pores as the solid matrix. We find that higher velocity flow leads to a greater amount of oil trapped within each pore. This is in contrast with findings from 2D and 3D micromodels in which the availability of multiple flow pathways leads to less drainage at lower flow rates. We also discuss the role of geometry and aspect ratio on oil drainage, and show two limiting behaviors. At lower flow rates and greater aspect ratio between pore wavelength to amplitude, oil is completely displaced. At larger flow rates, there is a geometry-dependent critical flow rate at which the trapped oil phase forms a continuous thin film across the geometry rather than snapping-off into discrete pockets within the pores.