Determination of Individual Parameters for the Model Mapping of a Boundary Curve in the Phase Diagram of a Stratifying Liquid Mixture

Abstract

The properties of a model based on the analogy between binary stratifying liquid mixtures and coupled self-oscillating systems is studied. In this paper, an expression representing a curve mapping in the phase diagram of a binary system is derived. The mapping of a boundary curve is presented in the form of the dependence between the ratio of characteristic frequencies assigned to pure components and the mixture concentration. In the framework of this model, the temperature dependence of the squared ratio of frequencies $$({\nu}_{a}/{\nu}_{b})^{2}$$ is also determined. One important aspect of this model is that the temperature-dependent characteristic frequencies $$\nu_{a}$$ and $$\nu_{b}$$ reflect the properties of pure components (instead of solutions). The problem is posed of investigating the physical aspects of the model proposed in this paper in more detail. In the present study, it has been shown that the use of Pade approximants makes it possible to determine the character of the temperature dependence of each characteristic frequency separately on the basis of the temperature dependence derived by linking to experimental data for the ratio $$({\nu}_{a}/{\nu}_{b})^{2}$$ .