Spreading on and penetration into thin, permeable print media: application to ink-jet printing.

This paper examines spreading and penetration of surfactant-laden drops on thin-permeable media with reference to ink-jet printing. A detailed review of the interaction of both pure liquids and surfactant containing solutions with porous substrates is given for individual spreading and penetration and for the combined processes. A new model based on energy arguments is derived and compared to current hydrodynamic equations used to describe simultaneous spreading and penetration. Three studies of how surfactant solutions interact with thin commercial ink-jet photographic quality papers are presented. Here, two relevant systems are examined: Tergitol 15-S-5 and 1,2-octanediol. The first study examines the spreading and penetration profiles for surfactant solutions over a range of concentrations spanning their critical micelle concentration. As expected, these profiles depend on the concentration of surfactant and the chemistry of the medium with which it interacts. In many cases, partial vertical penetration of the region directly beneath the drop dominates at low interaction times and will be significant in ink-jet applications. The second study consists of a parametric investigation of the energy-based model derived herein. It shows that the model can capture all of the behaviors observed in the first study. In the final study, the ability of the energy-based model to fully predict the spreading behavior of Tergitol 15-S-5 solutions is tested. It is found that the model produces good quantitative agreement at the highest concentrations and, as such, will be useful in screening spreading dynamics concentrated systems like ink-jet inks. Agreement at low to intermediate concentrations is often limited by finite induction periods prior to significant spreading and penetration. Possible corrections that could improve the agreement for weakly concentrated solutions are discussed, and directions for future studies of simultaneous spreading and penetration are proposed.