Probabilistic Modeling of Fiber Length Segments within a Bounded Area of Two-Dimensional Fiber Webs

Statistical and probabilistic behaviors of fibers forming fiber webs of all kinds are of great significance in the determination of the uniformity and physical properties of the webs commonly found in many industrial products such as filters, membranes and non-woven fabrics. However, in studying the spatial geometry of the webs the observations must be theoretically as well as experimentally confined within a specified unit area. This paper provides a general theory and framework for computer simulation for quantifying the fiber segments bounded by the unit area in consideration of the "edge effects" resulting from the truncated length segments within the boundary. The probability density function and the first and second moments of the length segments found within the counting region were derived by properly defining the seeding region and counting region.