Combing carbon fibre arrays - P.D. Howell; H. Ockendon; J.R. Ockendon; J. Roberts (Partial Differential Equations in Applied Mathematics)
Before they can be reused, recycled carbon fibres are combed using a carding machine which is a technology widely used in the textile industry. We revisit the carding model of Lee and Ockendon (2005) to develop a continuum model for the alignment of an initially random ‘web’ of carbon fibres passing between two toothed cylinders in a carding machine. The web is modelled as a compressible viscous fluid with density-dependent viscosity coefficients. The model reveals how the ultimate alignment of the fibres depends on key control parameters, including the gap between the cylinders and their relative velocities. We also find a small region of parameter space where solutions may exhibit singularities.