Diffusion of pieces from a shattered object in a single-file arrangement

We explore the time required for a densely packed, single-file diffusion system, originating from the fragmentation of an object, to expand to a point where each particle can be distinctly identified. We use Monte Carlo methods to investigate this class of problems and define the time taken to reach the required final state as a relative first-passage spreading time. Our results show that the stochastic nature of the diffusion process is as important as the details of the particle size distribution when it comes to determining the spreading time. Nevertheless, we introduce a distribution randomness parameter, Z, which is linearly correlated with the final spreading time. By studying the correlation between the time required for particles to disperse and the final space they cover, we identify the fundamental length scale that governs this phenomenon. Finally, we show that the distribution function of spreading times follows a well-known form for first-passage time problems, and that its variance decreases linearly with the number of particles.