The J-Box Problem

Abstract

The study group was presented with the problem of determining the behaviour of a web of wet cellulose fibres - called a tow - as it passes through part of the manufacturing process. The name of the problem derives from the fact that on its passage down the production line the tow passes through a J-shaped box, whose purpose is to provide a buffer where the tow is stored long enough and hot enough for certain chemical reactions to take place, mainly concerned with giving the right quality to the fibre surface. (The production line in fact involves two J-boxes, one containing wet tow, the other dry, and we are here entirely concerned with the first of these, the wet J-box.)

Three aspects of the tow behaviour were proposed for investigation:
1. What is the mechanical behaviour of the tow within the J-box ? Specifically, how do the time spent within the J-box and the shape of the tow outlet column depend on the J- box geometry, tow density and compressibility, flow rate, friction coefficients etc.
2. What is the temperature history, and hence the chemical history, of the tow within the J-box?
3. Why do dislocations and loops occur within the tow?

We first give typical parameters and other details of the process, and then further details of these three questions.