In liquid-based material processing, hydrodynamic forces are known to produce severe bending deformations of two-dimensional (2D) materials such as graphene. The non-linear rotational and deformation dynamics of these atomically thin sheets is extremely sensitive to hydrodynamic particle-particle interactions. To investigate this problem, we developed a computational model of the flow dynamics of elastic sheets suspended in a linear shear flow, solving the full fluid-solid coupling problem in the two-dimensional, slender-body, Stokes flow regime. Both single and pairs of sheets in close proximity are analyzed. Despite the model being two-dimensional, the critical non-dimensional shear rate yielding single-particle buckling is comparable in order of magnitude to that reported for fully three-dimensional, disk-like sheets. For pairs of interacting sheets, hydrodynamic interactions lead either to parallel sliding or bending, depending on the value of an elasto-viscous number based on particle length. For sufficiently low bending rigidity or large shear rates, large deformations of initially stacked sheets lead to sheet reattachment after separation, unlike for the rigid case. A peeling-like dynamics where lubrication provides a viscous bonding force is observed for sheet pairs when one of the two sheets is more rigid than the other. Practical implications for graphene processing and exfoliation are discussed.

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Liquid-phase exfoliation, the use of a sheared liquid to delaminate graphite into few-layer graphene, is a promising technique for the large-scale production of graphene. However, the microscale and nanoscale fluid-structure processes controlling the exfoliation are not fully understood. Here, we perform non-equilibrium molecular dynamics simulations of a defect-free graphite nanoplatelet suspended in a shear flow and measure the critical shear rate γ̇ c needed for the exfoliation to occur. We compare γ̇ c for different solvents, including water and N-methyl-pyrrolidone, and nanoplatelets of different lengths. Using a theoretical model based on a balance between the work done by viscous shearing forces and the change in interfacial energies upon layer sliding, we are able to predict the critical shear rates γ̇ c measured in simulations. We find that an accurate prediction of the exfoliation of short graphite nanoplatelets is possible only if both hydrodynamic slip and the fluid forces on the graphene edges are considered and if an accurate value of the solid–liquid surface energy is used. The commonly used “geometric-mean” approximation for the solid–liquid energy leads to grossly incorrect predictions.@en

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.

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Through boundary integral simulations and asymptotic analysis, we investigate the effect of a finite Navier slip length on the rheological proprieties of a dilute two-dimensional suspension of plate-like particles in the creeping flow limit. Specifically, we study the effects of Navier slip, particle thickness and Péclet number on the effective shear viscosity and average normal stress difference of an isolated two-dimensional plate-like particle in an unbounded shear flow field. We find that Navier slip induces a significant reduction in the effective viscosity and increases the average normal stress difference. The effect of slip becomes more enhanced as the thickness of the particle decreases and as the Péclet number increases. Remarkably, the analysis suggests that it is theoretically possible for a dilute suspension of slip plate-like particles at high Péclet numbers to have a shear viscosity smaller than that of the suspending fluid.@en

The classical theory by Jeffery predicts that, in the absence of Brownian fluctuations, a thin rigid platelet rotates continuously in a shear flow, performing periodic orbits. However, a stable orientation is possible if the surface of the platelet displays a hydrodynamic slip length comparable to or larger than the thickness of the platelet. In this article, by solving the Fokker-Plank equation for the orientation distribution function and corroborating the analysis with boundary integral simulations, we quantify a threshold Péclet number, above which such alignment occurs. We found that for smaller than, but larger than a second threshold, a regime emerges where Brownian fluctuations are strong enough to break the platelet's alignment and induce rotations, but with a period of rotation that depends on the value of. For below this second threshold, slip has a negligible effect on the orientational dynamics. We use these thresholds to classify the dynamics of graphene-like nanoplatelets for realistic values of and apply our results to the quantification of the orientational contribution to the effective viscosity of a dilute suspension of nanoplatelets with slip. We find a non-monotonic variation of this term, with a minimum occurring when the slip length is comparable to the thickness of the particle. @en

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.

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Combining molecular dynamics (MD) and continuum simulations, we study the dynamics of propagation of a peeling front in a system composed of multilayered graphene nanosheets completely immersed in water. Peeling is induced by lifting one of the nanosheet edges with an assigned pulling velocity normal to the flat substrate. Using MD, we compute the pulling force as a function of the pulling velocity, and quantify the viscous resistance to the advancement of the peeling front. We compare the MD results to a 1D continuum model of a sheet loaded with modelled hydrodynamic loads. Our results show that the viscous dependence of the force on the velocity is negligible below a threshold velocity. Above this threshold, the hydrodynamics is mainly controlled by the viscous resistance associated to the flow near the crack opening, while lubrication forces are negligible owing to the large hydrodynamic slip at the liquid-solid boundary. Two dissipative mechanisms are identified: a drag resistance to the upward motion of the edge, and a resistance to the gap opening associated to the curvature of the flow streamlines near the entrance. Surprisingly, the shape of the sheet was found to be approximately independent of the pulling velocity even for the largest velocities considered.

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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.@en