Maximum Fiber-Packing Density in Electrostatic Flocking

The maximum fiber-packing density expected in electrostatic flocking or any process involving random impingement of fibers onto a substrate has been calculated using a Monte Carlo technique. This value was determined by generating random numbers to select the coordinates of points representing the location of fiber centers on a circular target, subject to the restriction that no two fibers overlap. The process was terminated after a specified number of trials failed to locate an unoccupied space large enough to accommodate an additional fiber. The fiber-packing density was then computed in terms of the number of fibers per unit area n and the fraction of total available space on the target occupied by fibers F. It is found that F is independent of fiber diameter and has a value of 0.531 with a standard deviation of 0.0038. This value (∼53% of available space occupied) is considerably less than the value of 90.7% expected for close-packed circles but much greater than those reported experimen tally.