Modeling interactions in carbon nanotube suspensions: Transient shear flow

Abstract

Transient shear flow data of untreated multiwalled carbon nanotubes (MWCNTs) dispersed in a Newtonian epoxy matrix are analyzed. A sequence of shearing and rest steps was applied to characterize the transient responses of the suspensions. Stress overshoots appeared at very small deformation during forward and reverse flow experiments and their intensity increased with rest time between two consecutive flows, during which the suspension structure was reconstructed. The transient behavior of the MWCNT suspensions is explained with the help of a recently proposed model [G. Natale et al., AIChE J. 60(4), 1476–1487 (2014)]. The MWCNTs are described as rigid rods dispersed in a Newtonian matrix, and the evolution of the system is controlled by hydrodynamics, rod-rod interactions, and Brownian motion. The force due to the interactions is modeled as a nonlinear lubrication force and the total stress tensor is evaluated introducing a fourth-order interaction tensor. The Fokker–Planck equation is numerically solved for transient simple shear flow using a finite volume method, avoiding the need of closure approximations. The model predictions show that interactions slow down the orientation evolution of the rods. For the first time, the effect of shear rate is directly accounted by the model, which predicts that a critical shear rate is necessary to break down the structure and let the rods orient in the flow direction. In addition, we confronted the model predictions with the rheological data of a glass fiber-filled polybutene [M. Sepehr et al., 48(5), 1023–1048 (2004)], demonstrating its ability to describe the behavior of micro and nano-scale particle suspensions.