The inertial regime of drop impact on an anisotropic porous substrate

Axisymmetric droplet impact on a hydrophilic substrate with one pore of relatively large radius is numerically studied using diffuse-interface methods. The flows above the substrate and in the capillary are fully resolved by a Navier–Stokes solver that accounts for contact-angle hysteresis. Upon impact, the infiltration of the drop into the capillary is seen to follow one or more of the three regimes identified in recent experiments (Delbos, Lorenceau & Pitois, J. Colloid Interface Sci., vol. 341, 2010, p. 171): complete penetration, partial penetration as a slug, and re-entry with bubble entrapment. The agreement on experimentally measured quantities, such as transition criteria and slug lengths, is quantitative. On this basis we reveal previously unidentified flow phenomena, investigate flow details that are not accessible experimentally, expand the parameter space considered previously, identify the key asymptotic regimes in the penetration transient, generalize the results in terms of relevant dimensionless groups, and provide a further step (using a multi-capillary arrangement as an idealization of a porous substrate) towards the ultimate purpose of such work, which is the understanding of inertial effects with porous substrates, including eccentric impacts. The significant effect of impact inertia is revealed as a spatial anchoring of a stagnation region, formed and persisting for most of the transient. As a consequence, fluid within an upright cylinder is destined to enter the capillary, and this is in agreement with the hypothesis of Delbos et al. in interpreting the amounts of liquid found inside the capillary, except that the radius of the cylinder is 30 % greater than the capillary radius. The remainder of the liquid spreads laterally on the substrate surface, and the slug regime is a consequence of this partition. Numerical experiments also indicate that after reaching the maximum-spread area, the lamella on the substrate tends to refill the capillary and entrap a bubble, unless contact-angle hysteresis hinders the radially inward motion of the lamella.