Fibre migration

Key words hbre, yarn, woven fabric, knitted fabric, non-wovens, design of experiment, hypothesis testing, analysis of variance (ANOVA), regression analysis, geometrical models, structural models, fibre migration, unit cell, knot invariants, textile mechanics, physical properties of textiles, homogenization, optimization. 

It is assumed that the distances between the leading ends of the fibres are distributed exponentially with parameter Xfr and the fibre length follows a normal distribution. Fibre remains in the VL(f, r) for a migration distance, which is distributed exponentially with parameter and after that it either migrates to a neighbouring VL(/,s) with probability pjf.p or terminates with probability p The process of fibre migration thus can be regarded as a... 

Fibre migration model (a) VLs in the yarn cross-section (b) an open network of queuing systems. 

Non-linear methods are used not only for the optimization as illustrated above but also in regression analysis when fitting functions which are nonlinear with respect to their coefficients. For example, an application of the least squares method for the estimation of coefficients a and b of the function y = a(l-exp(-bx)) leads to NLP. In Section 1.4.3 NLP has been used for the estimation of unknown parameters of a fibre migration model. 

El-Sheikh A and Backer S (1972), The mechanics of fibre migration. Part I Theoretical analysis . Text Res J, 42(3), 137-146. 

Grishanov S, Siewe F and Cassidy T (2011), An apphcation of queuing theory to modelling of melange yarns. Part II A method of estimating the fibre migration probabUities and a yarn structure simulation algorithm , Text Res /, 81(8), 798-818. 

Grishanov S A, Harwood R J and Bradshaw M S (1999), A model of fibre migration in staple fibre yarn , / Text Inst, 1999,90,298-321. 

Multi-layer construction is also employed using different filter media, e.g. an inner layer of rather more open form for dust retention, an intermediate layer for fine filtration and an even closer outer layer to prevent fibre migration. Synthetic fabrics are proving to have some advantages over spun glass fibre materials although glass fibre media have proven to be very efficient. 

The medium is a thin (110 am) microporous nylon membrane, having a controlled pore size. Its homogeneous cast polymer structure cannot release fibres, and no fibrous medium is used downstream of the nylon membrane (to prevent fibre migration). The only materials used in these cartridges are nylon and polypropylene, and because of this construction the cartridges can be autoclaved. 

---