Rheological modeling of carbon nanotube suspensions with rod–rod interactions

To explain the shear‐thinning behavior of untreated carbon nanotube (CNT) suspensions in a Newtonian matrix, a new set of rheological equations is developed. The CNTs are modeled as rigid rods dispersed in a Newtonian matrix and the evolution of the system is controlled by hydrodynamic and rod–rod interactions. The particle–particle interactions is modeled by a nonlinear lubrication force, function of the relative velocity at the contact point, and weighted by the contact probability. The stress tensor is calculated from the known fourth‐order orientation tensor and a new fourth‐order interaction tensor. The Fokker‐Planck equation is numerically solved for steady simple shear flows using a finite volume method. The model predictions show a good agreement with the steady shear data of CNTs dispersed in a Newtonian epoxy matrix as well as for suspensions of glass fibers in polybutene, 1 demonstrating its ability to describe the behavior of micro‐ and nanoscale particle suspensions. © 2013 American Institute of Chemical Engineers AIChE J , 60: 1476–1487, 2014