Infiltration and dimensional scaling of inkjet droplets on thick isotropic porous materials

We study the imbibition of picoliter (pL)-sized inkjet droplets on controlled pore glass membranes (CPG), as a suitable model for isotropic three-dimensional porous materials. We do so using a variety of liquids, i.e., water, formamide and diiodomethane, and measure the evolution of the imbibition process using high-speed digital imaging. Here, experiments were conducted on 2-280 nm CPG membranes with drops with initial volumes ranging from 100 to 600 pL. We derive scaling laws for imbibition through dimensional analysis and advance the argument that the rate of absorption is related to two-dimensionless groups where v(t) is the imbibed volume, as determined from experiments, t is the time, v (tot) the total liquid volume, the porosity, mu the liquid viscosity, k the permeability, and p (c) the Laplace capillary pressure. We show this scaling to well describe the system at intermediate T values and report that V alpha T-0.8.