Vertical air classification is widely used in waste separation processes, where the separation curves, i.e. the recovered percentages of the lighter and heavier fractions plotted against air velocity, determine the characteristics of separation. Although several different models of separation curve equations exist, the common mechanism underlying them is unknown. Here, a meta-model based on the stochastic process of particle separation is presented. Through mathematical and numerical analyses, the following findings are obtained. 1) Three typical separation curve models, i.e. a cumulative Weibull model, a Lynch-Rao model, and a cumulative normal model, are described as the different realizations of the meta-model with different settings. 2) The three separation curve models give almost identical curve-fitting results with sufficient accuracy, while the flexibility of fit slightly but distinctively differs: the best is the Lynch-Rao model, followed in order by the Weibull CDF model and the normal CDF model. (c) 2020 Elsevier B.V. All rights reserved.