Mathematical Model of Size Penetration into the Yarn in the Warp Sizing

This study discusses the capillary model of the space formed between the fibers in the yarn. Transfer of solution into yarn is one of the important factors affecting the processes and in application of textiles. The solution that flows into the space between fibers can cause changes in dimensions which have a direct effect on the structure of space between fibers in the yarn. Furthermore, in this study, an analysis of the geometry model of fiber bonds in the yarn suggested by Schwartz was used to determine the capillary diameter of the yarn and in the determining the area. This study also considered the nature of fibers which are swelling while absorbing water molecules. The results of the discussion of this model were used to understand the effects of geometric parameters and materials in fluid transfer in the application of warp sizing using Poison law. The theoretical calculation resulted differently compared to the results of research on cotton yarn which are assumed to be that the fibers are considered perfectly round, uniform twist. The absence of fiber migration greatly affects the cavity between fibers in the yarn. In addition, other problems were found in the covenant process such as viscosity stability during the process, as well as the quality of the size recipe used