ABSTRACT
Inflation pressure loss in tires degrades performance, raises rolling resistance, and reduces fuel economy. The incorporation of solid fillers, such as carbon black, at relatively high loadings in tire innerliners helps minimize these pressure losses by reducing innerliner permeability due to increases in average gas molecule diffusion path lengths (tortuosity), as well as reductions in diffusion pathway density (capacity). The effects of filler morphology and loading on diffusion path tortuosity can be explored by modeling biased random-walk diffusion through impermeable sphere-filled matrices. Modeled diffusion rate was found to decrease with increased filler loading, reduced filler sphere sizes, increased random-walk step sizes, and the aggregation of filler spheres. Initial correlations with limited empirical permeability measurements are used to validate the model approach.
A Markov chain model for the search time for max degree nodes in a graph using a biased random walk
