A theoretical analysis of the flow stability in roll forming of paper

This paper deals with the fundamental mechanisms that control partial roll dewatering in papermaking. The flow around the forming cylinder is modelled in a cylindrical coordinate system and the wire is assumed to be impermeable. The governing equations are reduced based on a discussion where the magnitude of the different terms is estimated. Given this reduced set of equations a non-linear equation for the position of the wire is deduced. This clearly shows that one of the most important parameters is the Weber number, We, which is the non-dimensional number that can be obtained by comparing the effect of wire tension in relation to the momentum of the incoming headbox jet. The characteristics of the non-linear equation are discussed and the equation is linearized around the trivial solution to the equations, which gives that the wire is displaced a constant distance from the roll along the whole wrap. The linear equation has a standing wave solution with a specific wavelength that scales with We. This solution is compared to previously measured profiles regarding the wavelength of the waves.
QC 20100525