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A mathematical model for washing a tow of fibres: Part 1

A mathematical model is presented for the washing of a band, or tow, of fibres which is pulled past a submerged obstacle. A lubrication flow between the obstacle and the tow is coupled to a flow through the tow, which is modelled as a porous medium. Coupled first-order ordinary differential equations for the fluid pressure and volume flux are solved numerically and the results are analysed. The washing of the tow induced by the reversal of the viscous boundary layers lying above and below the tow is discussed briefly. In Part 2, the model is extending to allow for fibre bending. The numerical solution of the resulting differential equation shows that at a critical value of the tow porosity, the tow touches the obstacle. An existence proof for a family of touching solutions is obtained. Using the existence of these solutions, a method for constructing a solution with a rubbing region, where the gap width is zero, is outlined. The numerical solutions for these solutions are also given.