Droplet Imbibition into Paper Coating Layer: Pore-Network Modeling Simulation

Abstract

Liquid penetration into thin porous media such as paper is often simulated using continuum-scale single-phase Darcy’s law. The underlying assumption was that a sharp invasion front percolates through the layer. To explore this ambiguous assumption and to understand the controlling pore-scale mechanisms, we have developed a dynamic pore-network model to simulate imbibition of a wetting phase from a droplet into a paper coating layer. The realistic pore structures are obtained using the FIB-SEM imaging of the coating material with a minimum resolution of 3.5 nm. Pore network was extracted from FIB-SEM images using Avizo software. Data of extracted pore network are used for statistically generating pore network. Droplet sizes are chosen in the range of those applicable in inkjet printing. Our simulations show no sharp invasion front exists and there is the presence of residual non-wetting phase. In addition, penetration of different sizes of droplets of different material properties into the pore network with different pore body and pore throat sizes are performed. We have found an approximately linear decrease in droplet volume with time. This contradicts the expected -behavior in vertical imbibition that is obtained using macroscopic single-phase Darcy’s law. With increase in flow rate, transition of imbibition invasion front from percolation-like pattern to a more sharper one with less trapping of non-wetting phase is also reported. Our simulations suggest that the single-phase Darcy’s law does not adequately describe liquid penetration into materials such as paper coating layer. Instead Richards equation would be a better choice.

Numerical Simulation Using Finite-Difference Schemes with Continuous Symmetries for Processes of Gas Flow in Porous Media

“…For example, problems of CO 2 geological storage [18] or, in particular, problems of CO 2 injection on macroscales of porous media [19] can be studied using the results obtained from this study. There are several results for microscales that can be studied using results of this article for some specific cases of initial and boundary conditions, forms of pore network models and methods for calculating conductivities: suggested models for gas flow in [20], one-phase flow in [21], multiphase flow in [22], and modeling of films in gas-liquid-capillary systems in [23].…”

“…The explicit difference scheme (21) and (23) were chosen for the sake of application demonstrations of the obtained invariant necessary conditions for stability. Figure 1 shows a comparison of numerical solutions for the difference scheme (21) and (23) and the difference scheme (22) and (23) (with the constant time step and with the time step choosing) and the exact solution, which is from [24]. The exact solution can be written as…”

“…This section is intended to present results of generations of numerical solutions for the difference scheme (22) and (23) of differential Equation (5) of gas flow in porous media. There are results of numerical solution generations [25] for the Rapoport-Leas equation [26], which is a generalization of the Buckley-Leverett problem.…”

“…The groups of transformations are t = e 2a t, x = e a x, P = P, t = e −a t, x = x, P = (P + K 2 )e a − K 2 (24) for X 3 and X 4 , respectively. In Figure 2, actions of (24) for the numerical solution from Figure 1 (the implicit scheme (22) and (23) with the continuous symmetry groups (24)) are used to show the concept of the solution generation method.…”

“…It would be more interesting for the generation to consider operators for 3 X and 4 X , respectively. In Figure 2, actions of (24) for the numerical solution from Figure 1 (the implicit scheme (22) and 23 (Figure 1) obtained using the implicit scheme with the time step choice. Plots (a,b) show generations using dilations for time and spatial variables (infinitesimal operator 3 X ) with certain values of the group parameter a ; plots (c,d) show the applications of 4 X , which defines dilations of time and the combination of dilations and translations for pressure (the set initial left boundary pressures define group parameters for generations, where k is the factor for left P ).…”