The Fractal Nature of Dendrites Formed by the Collection of Particles on Fibers

Abstract Aerosols or particles suspended in air are often filtered by pads of fibers. The particles collect on the surface of the fibers in chain‐like structures called dendrites. An example scanning electron micrograph of 4.1 μm diameter particles captured on a 25‐m̈m fiber was analyzed by a Richardson plot. The Richardson plot is the measured perimeter of an image as a function of the length of measure or stride length. Three distinct regions were identified. For long and short stride lengths, the linear fiber and spherical particles were Euclidean. In the intermediate stride length region, the dendrite was fractal with a dimension of 1.36. The fractal nature of dendrites results from the random position of particles approaching the fiber and the shadowing effect of collected particles. Fractal geometry is potentially a useful approach for describing the morphology of the dendritic structures.