Analysis and construction of an exponential-power model of the dependence of the viscosity of a liquid on temperature

Abstract

Information technologies are widely used in the management of technological processes, in particular, processes related to Newtonian fluid. It is known that a liquid is used as a working fluid, for example, in hydraulic drives, solutions, medicines, as well as as a cooling, separating reagent, etc. One of the main physical quantities characterizing the most important properties of a liquid for both nature and industry is its viscosity (or internal friction). Unfortunately, due to the current lack of a general mathematical theory of liquid state, it is not possible to develop accurate, theoretically sound methods for calculating the dependence of the viscosity coefficient of both Newtonian and non-Newtonian liquids on temperature. This leads to the fact that when solving problems of both theoretical and applied nature, problems arise with experimentally observed results. The article deals with the problem of mathematical modeling of the dependence of the viscosity of a liquid on temperature. An exponential-power model of the viscosity-temperature dependence for Newtonian liquids is proposed. Despite the fact that various semi-empirical formulas are used in the scientific literature to take into account the dependence of viscosity on temperature based on experimental data, verification of the proposed exponential-power model has shown the relevance of this choice, or at least in the absence of obvious contradictions compared with known experimental data. The least squares method (sum of squares of deviations of experimental viscosity values from model values) was used as an objective function to identify the proposed mathematical model. Taking into account the developed generalized algorithm (linear and nonlinear programming), numerical modeling in the Java programming language was carried out. The numerical results for Newtonian liquids have shown that the proposed mathematical model allows calculating the change in the coefficient of dynamic viscosity in a wide temperature range with a certain pre-set relative error.