Development of mathematical model to predict vertical wicking behaviour. Part I : flow through yarn

Theoretical models have been proposed in this article (Parts I and II) to predict the vertical wicking behaviour of yarns and fabrics based on different fibre, yarn and fabric parameters. The first part of this article deals with the modelling of flow through yarn during vertical wicking, whereas the second part deals with the modelling of vertical wicking through the fabric. The yarn model has been developed based on the Laplace equation and the Hagen– Poiseuille’s equation on fluid flow; pore geometry has been determined as per the yarn structure. Factors such as fibre contact angle, number of filaments in a yarn, fibre denier, fibre cross-sectional shape, yarn denier and twist level in the yarn have been taken into account for development of the model. Lambertw, a mathematical function, has been incorporated, which helps to predict vertical wicking height at any given time, considering the gravitational effects. Experimental verification of the model has been carried out using polyester yarns. The model was found to predict the wicking height with time through the yarns with reasonable accuracy. Based on the proposed yarn model, a mathematical model has been developed to predict the vertical wicking through plain woven fabric in the second part of this article