BIRD experiment properties

The quantities in Eqs. (21.6) and (21.7) are tj (Q) and tj"(Q) where tj and rf are the quantities defined in 7 for the small amplitude oscillatory experiment. Hence when the limit is taken as T->0, xXJ(—QY) - rj and xyJ(— QY)->t)". The same limiting result was obtained for this flow by Bird and Harris (4) using an integral continuum model. Thus, this gives additional support to the argument that the Maxwell orthogonal rheometer flow provides the possibility of measuring the dynamic properties of fluids. 

These quantities have been well studied in polymeric fluids (Bird et al. 1987), where Ni > 0 and IN1/N2I 1, and the anisotropic elongation of polymer chains provides the basis for these properties. The situation is rather different because the microscopic basis for the stresses is different. What has most commonly been observed in noncolloidal suspensions is that Ni <0 and N2 < 0, with IN2/N11 3-4 in experiments (Zarraga et al. 2000 Dai et al. 2013) while simulations tend to find IN2/N1I closer to unity for noncolloidal or strongly sheared Brownian suspensions (Foss and Brady 2000 Sierou and Brady 2002) see Figure 11.1. Yeo and Maxey... 

These limitations can be alleviated in the second coarse-grained approach, where the particles are stiU explicitly tracked, but collisions with neighboring particles are determined stochastically through collision prob-abihty theory. This can be combined with a parcel approach where, to save computational costs, only a small subset of all real particles are simulated. For the calculations of the collision probabihties, the nonsimulated particles are then assumed to be in the neighborhood of the simulated particles and have the same statistical properties as the local ensemble of simulated particles. Such an approach is advantageous when deaHng with extremely high numbers of particles. Two important methods that fall into this class are multiphase particle in cell (see Andrews and O Rourke, 1996 Xie et al, 2013) and DSMC (see Bird, 1976 O Rourke, 1981). Primarily because of our own experience with the method, here we will focus on DSMC. 

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