An experimental study of multimodal glass suspension rheology to test and validate a polydisperse suspension viscosity model

Abstract

Experimental measurements of non-colloidal multimodal suspension viscosities are performed over a wide range of mixing ratios and used to test the robustness and predictive capability of a recent viscosity model (Mwasame et al. in Phys Fluids 28:061701, 2016b), subsequently referred to as the MWB model. Three unimodally distributed particle suspensions with narrow size distributions are blended to make the bimodal and trimodal suspensions used in the rheological experiments. We demonstrate how predictions for mixture viscosities can be made using the MWB model only requiring the volume-weighted average particle sizes and viscosity correlations of the individual unimodal suspensions comprising the blend. The resultant model predictions are found to be in good agreement with measured bimodal and trimodal viscosity data to within expected experimental uncertainty. The datasets provided here can be used to validate future modeling efforts, and the MWB model can be used to optimize the viscosity of multimodal suspension mixtures for specific performance criteria.

Appendices

Appendix 1

This appendix summarizes the data on the experimentally determined particle size distributions. The data in Table 4 correspond to the sizes determined from the microscopy images processed using ImageJ software. The volume-weighted average sizes reported in Table 2 are computed from this data.

Table 4 Summary of particle sizes in a sample of 50 particles determined from processing microscopy images using ImageJ software

Appendix 2

This appendix summarizes the calculations used to determine the volume fractions, density, and error bars in Fig. 3. The values of the volume fraction reported in this paper are nominal volume fractions. This section describes the process by which error was propagated to obtain the unimodal viscosity correlations in Fig. 2. For accuracy, all the suspensions were prepared on a gravimetric basis to ensure maximum accuracy. The determination of the error in the volume fractions starts with determining the density of the particles and PEG-200 medium. For this, volumetric flasks with a given uncertainty as well as a Fisher Scientific analytical balance were used. By determining the densities of the particles and medium by carrying out multiple replica experiments, the density and the associated error in its value are determined—see Table 5. Knowing the uncertainty in the micro-balance measurements as well as the density measurements on both the PEG-200 and the particles allowed for error to be further propagated to the level of the volume fractions at the stock solutions and the subsequent dilutions of the stock solution. The individual errors propagated for the volume fraction result in the horizontal error bars—see last two columns of Table 6.

Table 5 Summary of density and error for the three unimodally distributed particle sizes

Table 6 Summary of volume fractions for the three unimodally distributed particle sizes