471882 Modeling the Viscosity of Polydisperse Suspensions

Monday, November 14, 2016
Market Street (Parc 55 San Francisco)
Paul M. Mwasame, Norman J. Wagner and Antony N. Beris, Chemical and Biomolecular Engineering, University of Delaware, Newark, DE

Polydisperse particulate suspensions are commonplace in many industrial processes and modeling their rheological behavior is important towards understanding their flow properties. The present study develops a more consistent extension of the approach pioneered by Farris (1968) to model the viscosity in polydisperse suspensions. A key element outcome of this work is the development of formulae that by construction preserve all know limiting rheological behaviors of suspensions and is therefore compatible with previous arguments on binary suspension behavior. This work outlines the development of the model in the limit of binary suspensions and presents a generalization to polydisperse suspensions. An important property of the model is that once parameterized for non-colloidal hard sphere binary suspension behavior, assumed to represent ideal binary suspensions, it may be used to predict more complex suspension behavior. The systematic extension of the model to ternary suspensions is also presented. Following Wagner and Woutersen (1994), we demonstrate that polydisperse suspensions may be modeled by representing them as equivalent ternary suspension. This is accomplished by matching the first 6 moments of the polydisperse distribution to those of a ternary suspension. Convergence studies are also presented to demonstrate the robustness of the approach. The model is applied toward predicting the viscosity of non-colloidal polydisperse suspensions and demonstrates satisfactory agreement with experimental data on the viscosity of suspensions with continuous size distributions. In addition, we also demonstrate the assumptions behind the resultant model through carefully selected and designed experiments involving polydiserse suspensions. Moving beyond ideal binary suspension behavior, we also present an extension to the viscosity model for complex suspensions in which the two or more particle sizes obey different monodisperse viscosity correlations. This demonstrates the model’s robustness and applicability to an even wider variety of suspension such as a binary suspensions of spheres and cubes or colloidal and non-colloidal particles. Comparison against experimental data will also be presented.


  1. Farris, R. J., "Prediction of the viscosity of multimodal suspensions from unimodal viscosity data,” Transactions of the Society of Rheology 12, 281-301 (1968).
  2. Wagner, N. J., and A. T. J. M. Woutersen, ‘‘The viscosity of binary and polydisperse suspensions of hard spheres in the dilute limit,’’ Journal of Fluid Mechanics 278, 267-287 (1994).
  3. Mwasame, P. M., N. J. Wagner, and A. N. Beris. "Modeling the effects of polydispersity on the viscosity of noncolloidal hard sphere suspensions," Journal of Rheology 60, 225-240 (2016).

Extended Abstract: File Not Uploaded
See more of this Session: Poster Session: Fluid Mechanics (Area 1J)
See more of this Group/Topical: Engineering Sciences and Fundamentals