A model of the formation of a porous fibrous cake
A continuous physical cake made up of porous fibrous media can be formed by using air to draw the fibers to a moving screen. A numerical model of the formation of this cake has been formulated and solved. The numerical model is based on solving Darcy’s law, the Bernoulli equation, and two-material related experimental correlations at discrete points along the screen. A permeability measurement test apparatus was designed and built, and experiments were run to determine the experimental relations for two different materials. A computer code was then written to solve the system of equations at each point on the screen and give a density distribution of the resulting cake. Tests were then run to see the effects of various density anomalies in the material at different points along the screen.
The results of the experiments show that the first material was more permeable and more compressible than the second material. This lead to distinct differences in the cake that the two formed in the numerical model. The first material formed a fairly constant density cake that was not greatly affected by the density anomalies. The second material had a large variation in density across the final cake height and was affected more by the different density anomalies.