Modeling the Diffusive Transport of Bulk Fiber Mass in a Card

Abstract

A probabilistic model for the behavior of bulk fiber mass in a card is developed. This model is based on a random-walk description of fiber motion in the interface regions between rotating cylinders. The description incorporates the likelihood of fiber-surface interactions resulting in fibers traveling with one surface or the other, the speeds of the surfaces, the typical distances traveled between such interactions, and the lengths of time spent in the interfaces. These parameters depend, in turn, on the geometry of the card and the characteristics of both the surfaces and the fibers. The model is implemented in a computational simulation of a basic card consisting of a main cylinder and a worker/stripper pair; this includes not only the transport of mass through each interface, but the propagation of the mass around the cylinder surface and transfer from one surface to another at each time step of the numerical computations. Given certain data representing the density of input fiber mass versus time, the corresponding output fiber mass density is calculated, along with the fiber mass density at all points on the card at each time step. These results are then analyzed to determine the amount of smoothing of bulk fiber mass effectively performed by the card.