Selection and Verification of Phenomenological Suspension-Viscosity Models

Abstract

An analysis of the accuracy of the existing phenomenological suspension-viscosity models has been made. A procedure for approximating the viscosity curve by three one-parametric models but identifying only two empirical parameters has been proposed. Phenomenological models most accurately describing experimental data for suspensions of different compositions in the entire range of concentrations of a dispersed phase have been established.Introduction. Numerous empirical and semiempirical equations have been proposed for quantitative description of the viscosity of suspensions in the entire range of concentrations of a dispersed phase. With nearly identical degree of accuracy, one can describe, with one and the same equation, systems different in physicochemical nature, and with different rheological equations, one and the same disperse system [1]. Therefore, a rheological equation for approximation of experimental data is selected subjectively from the researcher′s own experience. Equations with the smallest number of empirical constants are preferred. An analysis of the literature shows that, for suspensions, one generally uses equations with one phenomenological parameter: the critical concentration of inclusions of the dispersed phase φ max , at which the viscosity becomes infi nite. The adequacy of a phenomenological model is directly determined by quantitative assessment of the model′s parameters, which are identifi ed from experimental results. Formally, a one-parametric model can be verifi ed by one experimental point. However, the viscosities of diluted and highly fi lled suspensions differ by an order of magnitude or more. Therefore, one uses several experimental points to approximate the viscosity curve more accurately. Selection of the values and number of points, as the selection of the approximating equation, is subjective and has no substantiation.The aim of the present work is to work out recommendations as far as the selection and improvement of accuracy of phenomenological models are concerned.Procedure of Verifi cation of Phenomenological Models. The rheological properties of a suspension are characterized by the relative viscosity defi ned as the ratio of the viscosity of a suspension to the viscosity of a liquid dispersion phase. The literature gives different dependences of the relative viscosity of suspensions η r on the volume concentration of a dispersed phase φ. We will consider one-parametric equations describing this difference with one empirical constant φ max (Table 1).Experimental dependences of the relative viscosity of different suspensions on the volume fraction of a dispersed phase are presented in Fig. 1. It is seen that the corresponding curves differ considerably. Therefore, for each composition of the suspension, we should determine its own empirical constant φ max . First we consider suspensions with a low (curve 1) and a high (curve 6) viscosity. We will approximate experimental data by equations of models 3, 6, and 9 (Table 1) which are the most accurate. The empirical con...