Movement of a liquid droplet within a fibrous layer: Direct pore-scale modeling and experimental observations

In this study, the spreading of a liquid droplet on the surface of a fibrous paper and its penetration into the paper is studied. The spreading of the droplet was visualized using confocal microscopy and the penetration depth was quantified using Automatic Scanning Absorptiometry (ASA) measurements. The three-dimensional structure of the paper was obtained through micro-tomography imaging with a resolution of 0.9 µm. The obtained images were used to reconstruct the pore space, which was in turn used in direct numerical simulations of penetration of a droplet into paper. Simulations were performed using open source code OpenFOAM, which solves equations of two-phase flow (in our case air and water) in pores based on the Volume of Fluid Method. Simulation results showed a good agreement with the experimental observations. In particular, the dimensions of spreading area of a droplet and the depth of penetration were simulated reasonably well. Then, we used the model to investigate effects of changes in various liquid properties on spreading and penetration of a droplet liquid. We made calculations for three different values of contact angle (CA): 0°, 60°, and 120°. We found the largest penetration depth for CA = 0. For CA = 60 and CA = 120, we found that the liquid droplet moved sideways from the jetted location, which is not favorable in inkjet printing. We also made simulations with larger values for viscosity and density, based on properties of an ink-based liquid used in inkjet printing. The results have shown a slower spreading and penetration compared with water. The model can be used to study effects of changes in either ink physical properties or paper layer microstructure on final spreading/penetration extent.