Stress decomposition analysis in hard and soft sphere suspensions: double peaks in the elastic stress of hard sphere suspensions and its characteristic and structural origin

Abstract

Brownian dynamics simulations under large amplitude oscillatory shear flow at an intermediate volume fraction in both hard and soft sphere systems have been carried out. Elastic and viscous stresses for the two systems are calculated by using the stress decomposition method. Careful investigation of “double peaks,” which are experimentally observed only in the elastic stress of hard sphere systems, has been conducted. When comparing hard and soft sphere systems in simulation, double peaks are observed only in hard sphere systems, within a specific strain amplitude range. The structures of hard sphere systems at different strain amplitudes, where double peaks appear and not, are compared. Excess entropy concept is adopted to evaluate the extent of particle alignment during the cycle. According to the structural analyses, double peaks are created when the structural difference between maximum-ordered and minimum-ordered states is large during 1 cycle.

Appendices

Appendix 1. Comparison of double peaks between simulation and experiment

Comparison of depth and width of double peaks between simulation and experiment is given in Fig. 13. As mentioned in previous section, double peaks are observed only in hard sphere systems. Simulation was performed by using the potential-free method which describes hard sphere (Fig. 4). Γ/Γ _freezing was set to 0.61 for simulation. Experimental data ware adopted from Fig. 9b and c of Nam et al. (2011) who used hard sphere systems. Volume fraction was 0.514 in experiments. In Nam’s paper, elastic and viscous stress were plotted at two γ ₀ (0.7 and 4) which clearly shows existence of double peaks.

Fig. 13

Comparison of a) depth and b) width between simulation and experiment. Simulation data is obtained by using potential-free method (hard sphere), and experimental data is adopted from Nam et al. (2011)

For depth, the experimental data are larger than those of simulation. However for width, the experimental data are very close to the prediction of simulation. Larger value of depth in experiment seems to be originated from a steep decrement in total stress near the flow reversal (Fig. 9a of Nam et al.). But this steep decrement is not observed in the simulation, in which hydrodynamic interactions is not considered properly. BD simulation provides only a qualitative description of the system.

Depth increases and width decreases in experiments as γ ₀ changes from 0.7 to 4. However, direct comparison of depth and width as a function of γ ₀ could not be conducted due to the lack of experimental data. They increase followed by a decrease in simulation as γ ₀ increases, but these characteristics could not be completely matched with experiment.

Appendix 2. Effect of volume fraction on double peaks and excess entropy

The depth and width at different Γ/Γ _freezing are given in Fig. 14 and the difference in the maximum and minimum of excess entropy is plotted in Fig. 15. All data were obtained by using the potential-free method. De = 80, and Γ/Γ _freezing = 0.61, 0.71 and 0.81.

Fig. 14

Double peaks a) depth and b) width at De = 80 as a function of γ ₀ for the potential-free method at Γ/Γ _freezing = 0.61, 0.71 and 0.81

Fig. 15

The difference in the maximum and minimum of excess entropy as a function of γ ₀ at Γ/Γ _freezing = 0.61, 0.71 and 0.81

As Γ/Γ _freezing increases, both depth and width decrease, and the γ ₀ range where double peaks appear decreases. The difference in excess entropy decreases too and it affects the γ ₀ range of double peaks as well as its depth. The effect of Γ/Γ _freezing also supports that double peaks are observed in systems when the structural difference between the maximum- and minimum-ordered states is large.