Self-Similar Elastic Response of Carbon Nanotube Forests to Aerodynamic Stresses

The ability to determine static and (hydro)dynamic properties of carbon nanotubes (CNTs) is crucial for many applications such as shear sensors' and mechanical actuators' technologies. While their static properties (e.g., solubility and wettability) are fairly well understood, their mechanical responses (e.g., deflection under shear) to ambient fluid flow are to a large extent unknown. First, we analyze the elastic response of single-walled CNT forests, attached to the bottom wall of a channel, to the aerodynamic loading exerted by turbulent flows. Our analysis yields analytical expressions for velocity distributions, the drag coefficient, and bending profiles of individual CNTs. The model predictions agree with laboratory experiments for a large range of channel velocities. Then, self-similar solutions for the average filtration velocity, the hydrodynamic shear in the forest, its deflection profile and maximum bending are analytically obtained as an intermediate asymptotic of the closed-form expressions. Such formulae are finally employed to show dynamical similarities across different data samples and to estimate flexural rigidity of CNTs by linear fit of maximum deflection measurements.