Modeling the effects of polydispersity on the viscosity of noncolloidal hard sphere suspensions

Abstract

The present study develops an extension of the approach pioneered by Farris [Trans. Soc. Rheol. 12, 281-301 (1968)] to model the viscosity in polydisperse suspensions. Each smaller particle size class is assumed to contribute to the suspension viscosity through a weighting function in two ways: first, indirectly, by altering the background viscosity, and second, directly, by increasing the contribution of the larger particles to the suspension viscosity. The weighting functions are developed in a consistent fashion as a power law with the exponent, h, a function of the relative volume fraction ratio and the base, g, a function of the solid particle size ratio. The model is fit to available theoretical and experimental results for the viscosity of several binary suspensions and shows good to excellent agreement depending on the functions g and h chosen. Once parameterized using binary suspension viscosity data, the predictive capability to model the viscosity of arbitrary continuous size distributions is realized by representing such distributions with equivalent ternary approximations selected to match the first six moments of the actual size distribution. Model predictions of the viscosity of polydisperse suspensions are presented and compared against experimental data. V

Modeling the viscosity of polydisperse suspensions: Improvements in prediction of limiting behavior

“…Recently, there has been renewed interest in modeling higher order effects of polydispersity on suspension viscosity (Qi and Tanner, 2012;Dörr et al, 2013;Farr, 2014;Faroughi and Huber, 2014;Shewan and Stokes, 2015;and Mwasame et al, 2016). In a previous publication (Mwasame et al, 2016), we described a modification and extension of the approach of Farris (1968) to develop a model for the viscosity of binary and polydisperse non-colloidal suspensions.…”

“…In a previous publication (Mwasame et al, 2016), we described a modification and extension of the approach of Farris (1968) to develop a model for the viscosity of binary and polydisperse non-colloidal suspensions. A key element of this approach is the ability to quantitatively predict the viscosity of polydisperse suspensions based on insights obtained solely from monodisperse and binary suspensions viscosity data.…”

“…As before (Mwasame et al, 2016), the starting point of the improved constitutive equation is provided by the hydrodynamic function through which the relative viscosity, η r , can be defined by…”

“…Note that f m (0) = 0 by definition. Improving on Mwasame et al (2016), we postulate the binary hydrodynamic function, f bi , to be defined as…”

“…(4). Mwasame et al (2016) have described several rules for formulating the size and volume fraction dependence of the weighting function. In particular, the following rules: and…”