# Estimation of the apparent anisotropic water diffusivity on spruce evaluated with a simplified derivative approach and as a function of the flow rate

## TL;DR

The study estimates water diffusivity in spruce wood using a simplified method and compares it with other fitting approaches.

## Contribution

A simplified derivative method is shown to effectively estimate anisotropic water diffusivity in spruce with minimal deviation.

## Key findings

- The DER method produced diffusivity values comparable to the DSE method with up to 10% deviation.
- Apparent diffusivity values were determined for longitudinal, radial, and tangential directions of spruce.
- The DER method simplifies the estimation process while maintaining accuracy.

## Abstract

The anisotropic apparent diffusivity as a function of the flow rate was determined in a series of Dynamic Vapor Sorption (DVS) experiments on spruce samples in the three orthotropic directions. Four different fitting procedures were applied for the evaluation of the time-sorption isotherms, i.e., the double-stretched exponential (DSE), the Ritger-Peppas (RP), and the Fickian and double-Fickian (SUM/DSUM) fitting methods, together with a derivative (DER) method for the determination of the apparent diffusivity. The results confirm that the DER method delivers similar results to the DSE fitting procedure, i.e., 1.98·10− 10, 0.94·10− 10 and 1.00·10− 10 m2/s for the longitudinal, radial and tangential direction, respectively, with a maximum of 10% deviation, in a much simpler manner.

The online version contains supplementary material available at 10.1038/s41598-026-38932-7.