An estimate of the in-plane velocity difference between the fibres and water during wet pressing: The saturated case

An analysis is presented to estimate the velocity difference between the fi bres and water passing through the compression phase of an idealized press nip. The model considers the fibrous solid network and water as a saturated compressible porous medium under an externally applied spatially varying l oad. A partial differential equation is derived to estimate the solidity of the web and used to estimate the flow of water in the machine direction us ing a force balance; temperature effects due to a hot roll have been consid ered. Analytical solutions are derived for a number of limiting cases and e stimates of the relative in-plane flow are reported as expressions normaliz ed to the transversal dewatering velocity. The results indicate that, if th e transversal dewatering velocity is of the order UHo/R smaller than the ma chine speed U, where H-o is the original thickness of the paper web and R i s the radius of the roll, and if H-o/R<<1, then the in-plane velocity will not affect the solidity of the sheet. The ratio of the relative in-plane fl ow to transversal velocity was found to be very small throughout the pressi ng event for both the cold and hot pressing situations examined. We found s imilarity between platen and roll presses under these conditions.