Numerical study of stress tensors in Poiseuille flow of suspensions
A Chatterjee and DR Heine, PHYSICAL REVIEW E, 82, 021401 (2010).
In this paper, the flow of dense suspensions of monodisperse spheres in wall-bounded channels is studied using a mesoscopic numerical model based on the dissipative particle dynamics (DPD) technique. Experimental observations for instance, L. Isa et al., Phys. Rev. Lett. 98, 198305 (2007) have confirmed that understanding the relevant physics of this problem requires probing at the mesoscopic level to account for the particle scale behavior. The DPD-based approach presented here enables us to explore various aspects of suspension flow at the particle scale. The yielding behavior of the suspensions is studied using macroscopic stress components calculated from the particle level. The relationship between various normal and shear stress components at the yielding plane is presented and discussed. It is seen that in dense suspensions, yielding is characterized by a strong dependence on all the stress components: tau(xx), tau(xy), and tau(yy). It is also seen that different stress components have different length-scale dependencies. While the normal stress in the flow direction, tau(xx), depends on macroscopic parameters such as the driving force, tau(yy), the normal stress transverse to the flow, depends on particle level parameters and is independent of the driving force. Wall topologies with characteristic dimensions on the order of the suspension particle size have a strong effect on the flow characteristics and the stress components.
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