Adhesive penetration in Beech wood Part II: Penetration Model

We propose an analytical model to predict the adhesives penetration into hard wood. Penetration of hard wood is dominated by the vessel network which prohibits porous medium approximations. Our model considers two scales: a one dimensional capillary fluid transport of a hardening adhesive through a single, straight vessel with diffusion of solvent through its walls and a mesoscopic scale based on topological characteristics of the vessel network, where results from the single vessel scale are mapped onto a periodic network. Given an initial amount of adhesive and applied bonding pressure, we calculate the portion of the filled structure. The model is applied to beech wood samples joined with three different types of adhesive (PUR, UF, PVAC) under various growth ring angles. We evaluate adhesive properties and bond line morphologies described in part I of this work. The model contains one free parameter that can be adjusted in order to fit the experimental data.