Adhesive penetration in Beech wood Part II: Penetration Model

TL;DR

This paper introduces an analytical model to predict adhesive penetration in beech wood, considering vessel network topology and fluid transport, validated with experiments using different adhesives and growth ring angles.

Contribution

The paper presents a novel multi-scale analytical model for adhesive penetration in hard wood, incorporating vessel network topology and solvent diffusion, validated with experimental data.

Findings

Model accurately predicts adhesive penetration depth.

Adhesive type and growth ring angle significantly influence penetration.

One adjustable parameter allows fitting the model to experimental data.

Abstract

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.