Probabilistic-statistical investigation of the evolution processes of particle distributions in oil dispersed systems in the maple software environment

Abstract The paper presents statistical studies on the features of the evolution of oil disprsed systems in various technological processes in the Maple-2020 software package. Experimental distributions of oil particle concentrations by size, measured by dynamic light scattering (DLS), were used. These distributions were obtained for various types of oils and their mixtures at different temperatures, as well as under the influence of surface-active substances (surfactants). For each statistical set of oil dispersed system (ODS) particles, regression models in the form of eighth-order polynomial equations were built based on values averaged over three parallel measurements. These approximations reflect the corresponding particle distributions with high adequacy. Using Garasu oil as an example, polynomial dependencies for temperatures of 30 and 40 °C were investigated, as well as the influence of surfactants on ODS. For this same Garasu oil sample, statistical characteristics of distributions evolving over time were studied: Mean, Variance (Std Dev), Skewness, and Excess Kurtosis. The nature of their behavior corresponds to the physical meaning of fragmentation and destruction of oil particles under the influence of surfactants. Based on the results of kinetic modeling of aggregation and fragmentation processes of a mixture of two normal particle distributions, and based on the probabilistic-statistical justification of distribution evolution and the Edgeworth formula, approximating expressions for the densities of time sections of distribution evolution and their density functions were obtained. These confirmed the fulfillment of normality conditions for a bimodal distribution, which is consistent with the nature of oil particle aggregation and may be related to the hydrocarbon composition of the oil.