Empirical mathematical model for absorption and evaporation phenomena of organic solvent in electrically-sensitive wood

Wood, an anisotropic and hygroscopic material, is often exposed to organic solvents as well as moisture, accompanying absorption and evaporation phenomena. Although different dynamics are expected at the uptake and evaporation of solvents mathematically with respect to time, exploring an empirical mathematical model to describe the absorption and evaporation of organic solvents simultaneously within wood remains unexplored relatively. This study proposes a mathematical model to explain empirically observed absorption and evaporation behaviors, including a novel method for qualitative analysis. To measure solvent uptake and evaporation, we employed electrical current as an indicator, making the wood electrically conductive through the incorporation of carbon nanotubes. The electric signals produced during the absorption and evaporation of acetone, ethanol, isopropyl alcohol, water, benzene, and toluene were measured in electrically sensitive wood. As a result, our mathematical model approximated absorption and evaporation data with few deviations in all cases, leading to an adjusted R² greater than 0.95. Furthermore, the novel qualitative analysis, the second derivative versus the first derivative of electrical current with respect to time, revealed a subtle change in the absorption dynamics that were not observable in the time domain. Especially, it has been revealed that polar and non-polar organic solvents with a low boiling point exhibited a large closed curve in the derivative plot, compared with other solvents. By introducing a comprehensive mathematical model and utilizing electrical current-based signals, this study opens doors to improved insights into how organic solvents interact with wood.