Tailored saturation functions and its application to liquid uptake processes in fibrous composite reinforcements

Saturation processes occur in almost every theoretical and practical field, e.g. liquid uptake within fibrous composite reinforcements. These processes require appropriate mathematical functions to model them and use them for design purposes. This includes assessing the saturation level, especially in microfluidic processes of fibrous composite reinforcements. This paper proposes a mathematical approach that uses a simple and well-known saturation function with modification through variable transformations and/or linear combinations. When the initial asymptotic behaviour is numerically known, this modified function provides a tailored and robust approximation of the measured saturation process and makes it possible to assess the asymptotic saturation level as well. A saturation function based on micro-tensiometer measurements and a simple exponential function was applied to validate this method. The mathematical approach was validated by test results based on distilled water uptake in polyester yarns and unsaturated polyester (UP) resin absorption within fibreglass chopped strand mats. In both cases, a good correlation was found between the experimental results and the applied mathematical approach, where the determination coefficients were higher than 0.989.