Droplet spreading and capillary imbibition in a porous medium: A coupled IB-VOF method based numerical study

Abstract

We investigate the dynamics of a liquid droplet in contact with a surface of a porous structure by means of the pore-scale level, fully resolved numerical simulations. The geometrical details of the solid porous matrix are resolved by a sharp interface immersed boundary method on a Cartesian computational grid, whereas the motion of the gas-liquid interface is tracked by a mass conservative volume of fluid method. The numerical simulations are performed considering a model porous structure that is approximated by a 3D cubical scaffold with cylindrical struts. The effect of the porosity and the equilibrium contact angle (between the gas-liquid interface and the solid struts) on the spreading behavior, liquid imbibition, and apparent contact angle (between the gas-liquid interface and the porous base) are studied. We also perform several simulations for droplet spreading on a flat surface as a reference case. Gas-liquid systems of the Laplace number, La = 45 and La = 144 × 10³ are considered neglecting the effect of gravity. We report the time exponent (n) and pre-factor (C) of the power law describing the evolution of the spreading diameter (S = Ctⁿ) for different equilibrium contact angles and porosity. Our simulations reveal that the apparent or macroscopic contact angle varies linearly with the equilibrium contact angle and increases with porosity. Not necessarily for all the wetting porous structures, a continuous capillary drainage occurs, and we find that the rate of the capillary drainage very much depends on the fluid inertia. At La = 144 × 10³, numerically we capture the capillary wave induced pinch-off and daughter droplet ejection. We observe that on the porous structure the pinch-off is weak compared to that on a flat plate.