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.     

Mathematical model to predict vertical wicking profile of single weft knitted structure

Mathematical models has been proposed to predict the vertical wicking height in single weft knitted fabric considering two scales of capillary flow; macroscale capillary flow through capillaries formed between yarns in the fabric, and microscale capillary flow through capillaries formed with in yarn. Macroscale model has been developed based on the sinusoidal irregular capillary to predict wicking profile along the wale and course directions. Microscale capillary model was developed considering capillaries as tortuous stream tubes along the wale and along the course. Another model based on inclined tube capillary has been developed to predict the wicking along wale. Lambert function has been used to calculate wicking height at different intervals of time. Validation of theoretical results has been done with experimental results taking fabric knitted from polyester yarns. Three different levels of tightness and three different shape factors of filament have been taken in the experimental study and the significance of their effect has been evaluated using ANOVA. A good correlation has been found between theoretical and experimental results.     

Geometry of plain weave fabric under shear deformation. Part II: 3D model of plain weave fabric before deformation

The main attempt of this investigation is to establish a model for evaluating internal geometry of woven fabric. A new concept about packing density of yarns inside of fabric is putted in forward and then internal geometry of fabric before deformation is predicted by common data of a fabric. A numerical analysis has been performed for two kinds of actual plain weave fabric on the basis of proposed model. The geometrical specifications of these fabrics are successfully evaluated. This model is to be expanded for predicting shear deformation of fabric in subsequent Part III (Kamali Dolatabadi &; Kova?, 2009b Kamali Dolatabadi, M. and Kova?, R. 2009b. Geometry of plain weave fabric under shear deformation. Part III: 3D model of plain weave fabric under shear deformation. Journal of Textile Institute, 100: 387–399.  [Google Scholar]).