A mathematical model of the dynamic viscosity dependence of motor oils on temperature, soot concentration, and its morphology

Objectives. A quick cold start of emergency and auxiliary power units based on diesel engines should be possible at any time without problems and in the shortest possible time. The condition of the engine oil is one of the most important factors influencing the smooth start-up of power plants. During diesel engine operation, engine oil accumulates soot in its composition, negatively affecting its rheological properties. The aim of this research is to develop a mathematical model to describe changes in the dynamic viscosity of motor oils as a function of temperature. This model will account for the concentration of soot and its morphology, based on the results of experimental studies.
Methods. Standardly used motor oils for diesel engines M-14D₂SE and M-5z/14D₂SE were used as oil samples in the preparation of model mixtures. The dispersed phase of the suspensions comprised carbon black of the N110, N220, N330, and N220 grades, characterized by a dusty (nongranular) texture. The rheological properties of the samples were determined using a TA Instruments DHR-2 rotational rheometer. The experimental data was subjected to mathematical statistical processing, in order to obtain approximating dependencies.
Results. The paper presents an analysis of the various approaches to the description of the rheology of suspensions and the results of experimental studies of the viscosity-temperature characteristics (VTCs) of model samples of oils containing soot. The extant models of the dependence of the dynamic viscosity of suspensions on temperature, volume concentration of the dispersed phase, particle size and shape are demonstrated to be inadequate for the description of the VTCs of motor oils containing soot. A model of the rheological properties of soot-oil suspensions is proposed in the form of a mathematical dependence of their dynamic viscosity on temperature, mass concentration of soot, material density and size of soot particles, characteristics of the shape and structure of primary aggregates and the ratio of the sizes of aggregates and molecules of the dispersion medium.
Conclusions. It was demonstrated that a comprehensive description of the VTCs of engine oils containing soot necessitates the consideration of the structural characteristics of the primary aggregates of soot particles. A mathematical model of the VTCs of oils was developed. This model is based on the dependence of the dynamic viscosity of oils on temperature, mass concentration of soot, density of the particle material, degree of non-sphericity of aggregates, the ratio of the particle sizes of the dispersed phase (either aggregates orsingle particles of non-aggregated soot) and oil molecules, and on the structure ofsoot, characterized by adsorption of dibutyl phthalate.

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