Particle size distributions and the sequential fragmentation/transport theory applied to volcanic ash

The assumption that distributions of mass versus size interval for fragmented materials fit the log normal distribution is empirically based and has historical roots in the late 19th century. Often other used distributions (eg Rosin-Rammler, Weibull) are also empirical and have the general form for mass per size interval: n(l) = kl^αexp(-l^β), where n(l) represents the number of particles of diameter l l is the normalized particle diameter, and k, α, and β are constants. We describe and extend the sequential fragmentation distribution to include transport effects upon observed volcanic ash size distributions. The sequential fragmentation/transport (SFT) distribution is also of the above mathematical form, but it has a physical basis rather than empirical. The SFT model applies to a particle-mass distribution formed by a sequence of fragmentation (comminution) and transport (size sorting) events acting upon an initial mass m′:n(x,m) = C ∫∫ n(x′,m′)p(ξ)dx′ dm′, where x′ denotes spatial location along a linear axis, C is a constant, and integration is performed over distance from an origin to the sample location and mass limits from 0 to m. -from Authors