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In conversation with Notion, Kamal delves into what we can expect from his debut EP, letting his music write itself, the ebb and flow of his songwriting process, staying connected with fans, and much more.
Using molecular dynamics simulations we investigate the shear-induced rotational dynamics of a Brownian nanographene (hexabenzocoronene) freely suspended in a liquid. We demonstrate that, owing to a finite hydrodynamic slip at the molecular surface, these flat molecules tend to align with a constant orientation angle instead of performing the classical periodic orbits predicted by Jeffery's theory. Results are extracted for different Péclet numbers and compared to the predictions by a theory developed for a rigid axisymmetric particle with orientation confined to the flow-gradient plane. The theory is based on the resolution of a one-dimensional Fokker-Planck equation for the angle φ made by one of the particle's diameters with the flow direction. Remarkably, our results show that the essential features of the three-dimensional orientational statistics of the nanographene are captured by the one-dimensional model, given that the hydrodynamic velocity is closed in terms of the slip length λ. Finally, we explore the situation in which multiple nanographenes are suspended in the liquid, and show that slip results in a reduction in specific viscosity.
The large-scale processing of nanomaterials such as graphene and MoS2 relies on understanding the flow behaviour of nanometrically-thin platelets suspended in liquids. Here we show, by combining non-equilibrium molecular dynamics and continuum simulations, that rigid nanoplatelets can attain a stable orientation for sufficiently strong flows. Such a stable orientation is in contradiction with the rotational motion predicted by classical colloidal hydrodynamics. This surprising effect is due to hydrodynamic slip at the liquid-solid interface and occurs when the slip length is larger than the platelet thickness; a slip length of a few nanometers may be sufficient to observe alignment. The predictions we developed by examining pure and surface-modified graphene is applicable to different solvent/2D material combinations. The emergence of a fixed orientation in a direction nearly parallel to the flow implies a slip-dependent change in several macroscopic transport properties, with potential impact on applications ranging from functional inks to nanocomposites.
a Perspective view of a graphene bilayer in a shear flow of strength \(\dot\gamma \), as extracted from MD simulations80. The blue and white dots are water molecules, and the black layers at the top and bottom are the shearing walls. b Zoom on the graphene bilayer, inclined by an angle α with respect to the flow. Comparison with continuum simulations is made by calculating the stress on the continuous surface represented by the dashed outline.
Schematic of the dominant contributions to the torque applied on the platelet under shear flow for small slip length (a) and large slip length (b). The coloured arrows indicate the direction of rotation.
Rigid platelike particles displaying interfacial slip can attain a constant orientation in a shear flow when the slip length is sufficiently large. But actual thin particles such as single-layer graphene are flexible and prone to bending deformations when exposed to shear stress. To study the effect of bending deformation on the dynamics of flexible platelike particles with large interfacial slip in a shear flow, we develop a two-dimensional (2D) fluid-structure interaction model. Our model is based on coupling the Euler-Bernoulli beam equation with a boundary integral method to solve the hydrodynamic stress at the particle surface. Emphasis is placed on resolving accurately the stress distribution at the edges of the particle. We find that (i) a stable alignment occurs even for relatively flexible particles and that (ii) edges effects on the shape of the plate are important for values of the length-to-thickness aspect ratio as large as 100. Our results are particularly relevant in view of recent research on the hydrodynamics of suspended flexible sheets made of 2D nanomaterials.
(a) Sketch of the central line x0 (red dashed line) of a flexible 2D platelet in a shear flow field γ̇y. The rotational angle ϕ is measured in the anticlockwise direction from êx, and θ(s) in the clockwise direction from ês0. (b) Undeformed surface of the 2D platelet. The parameter ξ is the radius of curvature of the corners.