A stochastic model of ice particle multiplication by drop splintering

Abstract

AbstractA stochastic model is developed which describes the increase in ice particle concentrations resulting from the splintering of supercooled drops on freezing. Analysis of the experimental evidence suggests that significant splintering occurs at least for drops with diameters in the range 50 to 200 μm. At time t = 0 one such drop freezes and ejects r ice splinters. Each of these splinters may be captured by another water drop in the same size range at any subsequent time, which in turn will freeze and eject a further r splinters, and so on. Consideration of the probability that a particular capture will take place at a particular time yields an expression for m(t), the estimated number of particles existing at time t,m(t) = (r2e(r‐1)t/τ − 1)/(r − 1),Where τ is the mean lifetime of an ice splinter. It is stressed that by considering the probability of a collision occurring at any time after the birth of a splinter, far higher estimates of the population are obtained than from a non‐stochastic model.Calculations show that the largest ice particle multiplication factors measured by Mossop et al. (1972), of order 104, can be produced in the available time if the value of r for the splintering size range is 5 or 6. Analysis of the experimental evidence suggests that such a value for r is possible.