Core bulk of wool fibres as a function of their curvature and diameter

Abstract

The compressibility of a fibre mass affects processing and end-product performance. The compressibility of wool can be measured by compressing a sample of clean fibre in a cylinder with a standard weight. The specific volume of the sample after compression is termed its bulk, or core bulk if a short core bored sample is used. Prediction of core bulk from the standard simultaneous measures of fibre diameter and fibre curvature would reduce testing costs. This applies to all types of fibre assemblies, but the potential for highest industrial influence is with natural fibres (wool, hairs, etc.) as the key characteristic of bulk is controlled by relatively few genes, and the ability is available to increase the bulkiness of a fibre from animals by carefully selective breeding procedures. A first approach to the problem is to model the wool sample as a collection of flexible rings. The Euler strut equation is then used to describe the rings and compute their linear deformation in response to the applied load. The resulting formula reveals that the core bulk depends on the fibre diameter and the fibre curvature only through their product. This agrees with an expression for the core bulk derived from van Wyk's formula (van Wyk, 1946) in one limit.