Effects of temperature change on the rheological property of modified multiwall carbon nanotubes

Solvent-free nanofluids hold promise for many technologically significant applications. The liquid-like behavior, a typical rheological property of solvent-free nanofluids, has aroused considerable interests. However, there has been still lack of efficient methods to predict and control the liquid-like behavior of solvent-free nanofluids. In this paper, we propose a semi-discrete dynamic system with stochastic excitation describing the temperature change effects on the rheological property of multiwall carbon nanotubes (MWCNTs) modified by grafting sulfonic acid terminated organosilanes as corona and tertiary amine as canopy, which is a typical covalent-type solvent-free nanofluid system. The vibration of the grafting branches is simulated by employing a structure-preserving approach, and the shear force of grafting branches at the fixed end is computed subsequently. By taking the shear forces as an excitation acting on the MWCNTs, the axial motion of the MWCNTs is solved with the 7-point Gauss-Kronrod quadrature rule. The critical temperature associated with the appearance of the liquid-like behavior as well as the upper bound of the moving speed of the modified MWCNTs is determined, which can be used to predict and control the liquid-like behavior of the modified MWCNTs in engineering applications.