Abstract
We present analytical solutions to the capillary rise of a wetting liquid in a closed column packed with small solid particles, including hydrostatic effects and the non-linear dependence of the pressure differential on the penetration height of the liquid. The solutions describe the evolution of both the penetration height (and mass) of the liquid and the pressure differential that develops in the closed column. Using closed column systems provides versatility to characterize different liquid-solid systems, covering a broad range of capillary pressures, by directly, and independently measuring both liquid mass and pressure differential. We identify the two non-dimensional parameters governing the evolution of the system, that is the capillary pressure and the initial pressure in the closed column, both made non-dimensional with the effective column height of the system. These results provide the means to improve and possibly optimize the experimental setup and conditions for any given liquid-solid system under consideration. For example, we show how modifying the effective column height and the initial pressure in the closed column could significantly reduce the duration of capillary rise experiments.