A Two-dimensional Viscous Model of a Wet Paper Forming Process

The variations of nal mat thickness (basis weight) in the machine direction (MD) and cross machine direction (CD) on a crescent former are examined using a two-dimensional dynamic model. This two-dimensional model is extended from a previous one-dimensional model by including viscosity and a cross ow in the CD. The uid velocity pro les are parabolic in the MD and CD with no-slip conditions on the ber mat and the surface of the roll former. In addition, a periodic boundary condition in the CD is applied. This study examines the CD variations due to the in uences of major classes of steady disturbances, and the coupled MD and CD variations due to dynamic process disturbances in the uid jet. Among the steady disturbances, the nonuniform uid velocity in the CD generated at the entrance of a forming region signi cantly ampli es the CD variations in the nal mat thickness. Unsteady disturbances lead to coupled MD and CD variations that are magni ed near the fundamental natural frequency of a translating wire, and particularly so for disturbances with long wavelengths.