Many processes in the textile industry are just starting to be modelled mathematically. Typical configurations involve may thousands of fibres interacting with each other and with external forces.
The novel mathematics that can arise will be exemplified by two situations involving man-made fibres. The first concerns the dynamics of a wet tow modelled as an anisotropic deformable porous medium and the second involves the crimping of dry fibres, which leads to a delay integral equation.
Traditional processes involving carding and spinning of natural fibres seem to be especially hard to model mathematically, and some of the challenges will be discussed.