Analytical and numerical investigation of water diffusion through Raffia vinifera pith

Abstract

This work aims to develop analytical and numerical approaches for predicting the water diffusion through raffia vinifera pith using Fick’s law. A representative elementary volume consisting of a fiber surrounded by a layer of natural matrix is considered. Assuming that the physical properties of fiber and matrix are constant, the resulting equations are solved analytically by the separation of variables method and numerically by finite difference method. A constant water concentration is imposed at the external surface of material while the continuity of the moisture and flux is applied at the fiber/matrix interface. To test the computational results, physical properties of the two layers are set equal. The experimental solutions in this case are used as the reference results, and the present computational method results are compared. Results demonstrate that the maximum value of the relative error is less than 6.5% for numerical and 11% for analytical methods. The case of two layers with different physical properties is examined. Results indicate that the heterogeneity of raffia vinifera pith reduces considerably the water absorption in the fiber. This study can be applied to composite materials where the polymers are combined to natural fibers to achieve high mechanical properties of materials.